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About 10,000 bce, wolves were probably domesticated. [added 02/01/03]

By 9000 bce, sheep were probably domesticated in the Middle East. 

About 7000 bce, there was probably an hallucinagenic mushroom, or 'soma,' cult in the Tassili-n-Ajjer Plateau in the Sahara (McKenna 1992:98-137).

By 7000 bce, wheat was domesticated in Mesopotamia. The intoxicating effect of leaven on cereal dough and of warm places on sweet fruits and honey was noticed before men could write.

By 6500 bce, goats were domesticated. "These herd animals only gradually revealed their full utility--sheep developing their woolly fleece over time during the Neolithic, and goats and cows awaiting the spread of lactose tolerance among adult humans and the invention of more digestible dairy products like yogurt and cheese" (O'Connell 2002:19). [added 02/01/03]

Between 6250 and 5400 bce at Çatal Hüyük, Turkey, maces, weapons used exclusively against human beings, were being assembled. Also, found were baked clay sling balls, likely a shepherd's weapon of choice (O'Connell 2002:25). [added 02/01/03]

About 5500 bce, there was a "sudden proliferation of walled communities" (O'Connell 2002:27). [added 02/01/03]
   

About 4800 bce, there is evidence of astronomical calendar stones on the Nabta plateau, near the Sudanese border in Egypt.  A parade of six megaliths mark the position where Sirius, the bright 'Morning Star,' would have risen at the spring solstice.  Nearby are other aligned megaliths and a stone circle, perhaps from somewhat later.
   

About 4000 bce, horses were being ridden on the Eurasian steppe by the people of the Sredni Stog culture (Anthony et al. 1991:94-95). 

About 4000 bce, light wooden plows were used in Mesopotamia. 

Between 4000 and 3500 bce, copper smelting in minute quantities was introduced in Mesopotamia. [added 02/01/03]
 

Between 4000 and 3500 bce, copper smelting in minute quantities was introduced in Mesopotamia.
   

By 3500 bce, irrigation was developed in Mesopotamia. 
   

Between 3300 bce and 2850 bce, numerals appeared in Sumerian, Proto-Elamite, and Egyptian hieroglyphics, and, somewhat later, the earliest known forms of pictographic writing. 
   

By 3200 bce, wheeled vehicles were used in Uruk. 

From about 3200 bce, there exist Egyptian sailboat drawings, showing a mast with a single broad square sail hung from it. [added 02/01/03]
   

By 3000 bce, cotton was being grown in India.

About 3000 bce, draft oxen were pulling plows and potters were using wheels in Mesopotamia.
   

About 2700 bce, cuneiform signs and numerals appeared on Sumerian tablets, with a slanted double wedge between number symbols to indicate the absence of a number, or zero, in a specific place.  .
   

About 2500 bce, the Stele of Vultures shows the Sumerian infantry in a phalanx: "all wearing helmets, advancing shoulder to shoulder behind a barrier of locked rectangular shields reinforced with bronze disks, and presenting a hedgehog of spears protruding from several rows back" (O'Connell 2002:32). [added 02/01/03]

About the middle of the third millenium, bronze enabled the dagger form to be stretched into swords. [added 02/01/03]

About 2400 bce, the short, composite bow was developed by mounted archers. Unstrung it curved forward and could pierce armor at 100 yards. [added 02/01/03]
   

About 2300 bce, Proto-Indian writing appeared in the Indus Valley.
   

Before 2000 bce, the Egyptians considered the souring of wine comparable to the souring of milk.
   

In the first half of the second millenium bce, Assyro-Babylonian cuneiform decimal notation gradually supplanted the Sumerian sexagesimal system for representing numbers below 60.  For representing higher numbers the sexagesimal place-value principle with base 60 was invented (Ifrah 1981:371-372).
   

In the seventeenth century bce, an Egyptian papyrus listed many diagnoses of head and neck injuries and their treatment and is the "first known document in which the brain's role in controlling limbs or organs at a considerable distance is established" (Changeux 1983:4; Breasted 1930). [added 02/01/03]
 

In the seventeenth century bce, the first use was made of phonetic signs, derived from Eqyptian hieroglyphics, in the Serabit el Khadim inscriptions, in the Sinai peninsula.
   

In the second millenium bce, in the Rig-Veda it was maintained the Earth was a globe and in the Yajur-Veda that the Earth circled the Sun.
   

By 1500 bce, Babylonian mathematicians understood "the determination of the diagonal on the square from its side," that is to say, the 'Pythagorean theorem' (Neugebauer 1957:36).
   

In the fourteenth century bce, the first known alphabetic writing, in thirty cuneiform signs, appeared on Ugaritic tablets.
   

In the late twelfth century bce, modern alphabetic writing was prefigured in the Phoenician alphabet.
   

Between 1200 and 1000 bce, iron smelting was introduced on an industrial scale in Armenia.

About 1000 bce, mule breeders noticed that "a mare crossed with a donkey yields a mule, whereas a stallion crossed with a donkey produces a hinny, which has shorter ears, a thicker mane and tail, and stronger legs than the mule.  This made [modern] researchers aware that there could be parent-specific effects in off-spring" (Pennisi 2001:1065). 
   

About 850 bce, impaling rams jutted from the prows of Greek galleys. These galleys were propelled by ten oarsmen on each side. By the middle of the seventh century, Phoenician galleys, or triremes, employed crews of 200 and three levels of oarsmen (O'Connell 2002:99-104). [added 02/01/03]
   

About 800 bce, vowels were by the Greeks to consonants of Phoenician origin.About 800 bce, vowels were by the Greeks to consonants of Phoenician origin.
   

From 747 bce, a continuous record of solar and lunar eclipses was kept in Mesopotamia.
   

In the early seventh century bce, gold coins were introduced in Lydia, western Anatolia, as a standard of exchange.
   

About 600 bce, Thales of Miletus, arguing from the fact that wherever there is life, there is moisture, speculated that the basic stuff of nature is water, according to Aristotle.
   

About 560 bce, Anaximander, a monist of Miletus like Thales, said that the primal substance, the substratum of the opposites, the originative stuff, is the apeiron, which seems to have meant, at that time, the spatially indefinite or unbounded (Kirk et al. 1983:110).
   

About 530 bce, Pythagoras discovered the dependence of musical intervals on the arithmetical ratios of the lengths of string at the same tension, 2:1 giving an octave, 3:2 the fifth, and 4:3 the fourth.  He is also credited with a general formula for finding two square numbers the sum of which is also a square, namely (if m is any odd number), m2+{1/2(m2-1)}2={1/2(m2+1)}2. "The Pythagoreans and Plato [as well as the Renaissance Neo-Platonists] noted that the conclusions they reached deductively agreed to a remarkable extent with the results of observation and inductive inference.  Unable to account otherwise for this agreement, they were led to regard mathematics as the study of ultimate, eternal reality, immanent in nature and the universe, rather than as a branch of logic or a tool of science and technology" (Boyer 1949:1). Consequently, when the Pythagoreans developed the theory of geometric magnitudes, by which they were able to compare two surfaces' ratio, they were led, for lack of a system which could handle irrational numbers, to the 'incommensurability problem': Applying the side of a square to the diagonal, no common rational measure is discoverable.
   

About 510 bce, Almaeon of Crotona, a member of the Pythagorean medical circle, located the seat of perception in the brain, or enkephalos, and maintained that there were passages connecting the senses to the brain, a position he was said to have arrived at by dissections of the optic nerve.
   

About 500 bce, Heraclitus of Ephesus maintained that permanence was an illusion and the only possible real state was the process of becoming. He also said that to the logos, all things are one, all opposites are joined.  Logos, a word which Anaximander also used, seems to be a principle manifesting itself in the process or cohering of things, and to occupy a place in Greek ideology similar to dharma for Hindus or 'Wisdom' for Jews (Park 1990:10).

About 500 bce, Xenophanes examined fossils and speculated on the evolution of the earth. 
   

About 480 bce, Parmenides of Elea founded the Eleatic School where he taught that 'all is one,' not an aggregation of units as Pythagoras had said, and that to arrive at a true statement, logical argument is necessary. Truth "is identical with the thought that recognizes it" (Lloyd 1963:327).  Change or movement and non-being, he held, are impossibilities since everything is 'full' and 'nothing' is a contradiction which, as such, cannot exist. "Parmenides is said to have been the first to assert that the Earth is spherical in shape...; there was, however, an alternative tradition stating that it was Pythagoras" (Heath 1913:64).
   

[[Corollary to Parmenides' rejection of the existence of 'nothing' is the Greek number system which, like the later Roman system, refused to use the Babylonian positional number system with its marker for 'nothing.'  Making no clear distinction between nature and geometry, "mathematics, instead of being a science of possible relations, was to [the Greeks] the study of situations thought to subsist in nature" (Boyer 1949:25).  Moreover, "almost everything in [Greek] philosophy became subordinated to the problem of change....  All temporal changes observed by the senses were mere permutations and combinations of 'eternal principles,' [and] the historical sequence of events (which formed part of the 'flux') lost all fundamental significance" (Toulmin and Goodfield 1965:40).]]
   

About 470 bce, Zeno of Elea propounded forty paradoxes probably to point out inconsistencies in Pythagorean positions.  One of the most famous is this: The fleeing and slower runner can never be overtaken by the faster, pursuer because the faster must first reach the point where the slower is at a that time, but by then the slower will be some distance ahead.  Other paradoxes made the same or apposite points, but, in fact, mathematical analysis shows that infinite aggregates and the nature of the continuum are not self-contradictory but only counter to intuition.
   

About 450 bce, Empedocles of Agrigento explained changes in quality or quantity of a thing as movement by the basic particles of which the thing consisted, Fire, Earth, Air, and Water.  These elements mix and separate "under the guidance of two opposing principles, Love, which draws them together, and Strife, which drives them apart" (Park 1990:25).

About 450 bce, Anaxagoras of Athens taught that the moon shines with the light of the sun and so was able to explain the eclipses.
   

About 440 bce, Leucippus of Miletus said that the world consisted in the void and atoms, which are imperceptible individual particles that differ only in size, shape, and position.  That these particles were imperceptible meant they met Parmenides' objection to the Pythagorean's geometric points and, since they alone were unchanging, change could be explained as mere sense impressions.  "It is scarcely an exaggeration to say that even in 1900 the only new idea to Leucippus's  theory was that each chemical element was identified with a separate atomic species" (Park 1990:41).

About 440 bce, Protagoras of Abdera held that man is the measure of all things by which he meant that we only know what we perceive, not the thing perceived (Dictionary of Philosophy 1984:273). 

About 440 bce, Oenopides of Chios probably created the first three of what became Euclid's 'postulates' or assumptions.  What is postulated guarantees the existence of straight lines, circles, and points of intersection.  That they needed to be postulated is because they require 'movement,' the possibility of which was challenged by the Eleatics (Szabó 1978:276-279).
   

About 430 bce, Hippocrates of Chios squared the lune, a major step toward squaring the circle, probably using the theorem that circles are to one another as the squares of their diameters.
   

Prior to about 425 bce, Herodotus wrote the first scientific history; that is, he began by asking questions, rather than just telling what he thinks he knows.  Moreover, these questions were "about things done by men at a determinate time in the past, [and the history itself ] exists in order to tell man what man is by telling him what man has done" (Collingwood 1946:18).
   

About 420 bce, Democritus of Abdera developed Leucippus's atomic theory: Atoms vibrate when hitched together in solid bodies and exist in a space which is infinite in extent and in which each star is a sun and has its own world.  He also produced two major concepts in the history of ideas concerning the brain--that thought was situated there and, anticipating the nervous system, that psychic atoms constituted the material basis of its communication with the rest of the body and the world outside.  Socrates, and hence the Platonic school, followed Democritus in locating thought in the brain.
   

About 400 bce, Hippocrates of Cos, also locating thought, pleasure, and pain in the brain, maintained that diseases have natural causes, and observed that head injuries led to impairments on the opposite side of the body. The 'Hippocratic method' of treatment of the sick was to keep the patient in bed and let nature take its course.

About 400 bce, an arrow-shooting catapult was developed at Syracuse. Its main significance is that it "embodied the deliberate exploration of physical and mechanical principles to improve armaments" (O'Connell 2002:86) [added 02/01/03]
   

After about 380 bce, Plato said, in the Timaeus, that "as being is to becoming, so is truth to belief" (Plato 1929:29c).  In other words, we can only believe, not know, on the basis of experience.  Like, Parmenides, he held being and truth, indeed the world, to be timeless and unchanging, an ideal of which man can only hold the idea.  This permitted him a certain amount of flexibility: He was willing to accept objections to his view of the universe, for example, if the new hypothesis would provide a rational explanation or 'save the appearance' presented by the planets.  In the Timaeus, he also held that the 'world soul' was constructed according to mathematical principles, and, therefore, these principles are already fixed in the individual.  (Forms or ideas that have existence independent of any particular mind came to be called archtypes.)  He scattered reflections on mathematical issues throughout his dialogues; e.g., in the Meno, he illustrates the difference between a class and its members by reference to the difference between defining 'figure' and enumerating specific figures.  References to ratios and proportions are everywhere. The five regular polygons he ascribed to the four elements plus the "decoration" of the universe (Plato 1929:55c), probably the animals of the zodiac.
   

By the fourth century bce, Babylonian astronomers had learned enough about the moon's motion that they could predict the occurence of lunar eclipses.
   

About 370 bce, Eudoxus of Cnidus invented a model of twenty-seven concentric spheres by which he was able to calculate the sun's annual motions through the zodiac, the moon's motion including its wobble, and the planets' retrograde motion.  He used what came much later to be called the 'exhaustion method' for area determination.  This method involved inscribing polygons within circles, reducing the difference ad absurdum, and was wholly geometric since there was at that time no knowledge of an arithmatical continuum, at least among the Greeks.
   

By about 335 bce, Aristotle had said that universals are abstractions from particulars and that we "have knowledge of a scientific fact when we can prove that it could not be otherwise."  But "since observation never shows whether this is the case," he established "reason rather observation at the center of scientific effort" (Park 1990:32).  A deductive argument is "a 'demonstration' when the premises from which the reasoning starts are true and primary....  Things are 'true' and 'primary' which are believed on the strength not of anything else but themselves" (Aristotle 1928:100a-100b).  Aristotle defined the syllogism as a formal argument in which the conclusion necessarily follows from the premises, and said that the four most common statements of this sort are 'all Subject is Predicate,' 'no S is P,' 'some S is P,' and 'some S is not P.' He also discerned four sorts of 'cause.'  The 'formal cause' is the design of a thing.  The 'material cause' is that of which it is made.  The 'efficient cause' is the maker.  And the 'final cause' is the purpose of the thing.  Aristotle also insisted on the operational character of mathematics and rejected any metaphysical character of number.

At the same time, Aristotle often states both his observations and his reasons with rather too much conviction: "The shape of the heaven is of necessity spherical; for that is the shape most appropriate to its substance and also by nature primary" (Aristotle 1930:286b).  "A heavenly essence could not, according to [his] physics, manifest any but its own 'natural' movement, and its only natural movement [so his reason informed him] was a uniform rotation around the center of the universe" (Duhem 1908:15). His name for the heavenly essence, the quintessence, is aiqhr, of which the Latin cognate is 'aether' (Although Aristotle is perhaps the earliest theorist of aiqhr, he was not the first to use the word, e.g., Heraclitus used it to mean heavenly fire.) In fact, "in dealing with [any] concrete, physical problem, it is...always necessary to take into account the world order, to consider the realm of being to which a given body belongs by its nature....  It is only in 'its' place that a being comes to its accomplishment and becomes truly itself" (Koyré 1968:6,24n1). He also put forth the view that each species has an essence and that divergence from this type was not possible beyond a certain limit.  These remained the dominant views until the acceptance of those of Johannes Kepler, in the first case, and Charles Robert Darwin and Alfred Russell Wallace, in the second.  If the properties of a thing are its 'form,' then, according to Aristotle, perception is the process whereby the form, and not just the representation of it, enters the soul.  This account of perception "was taken as the exact, literal truthby almost every educated person down to the sixteenth century" (Park 1990:44).  Also. Aristotle "considered the changes undergone by inanimate things to be analogous to those seen in the biological world.  Thus grape juice is the infantile form of wine, fermentation is the process of maturation; the further change to vinegar is the death of the wine" (Fruton 1972:24).  Since all matter is formed from the mixture of the four elements, he taught the elements are not permanent and could be transmuted one into another, inspiring all who practice alchemy.  After weighing the evidence, Aristotle decided that the organ of thought and sensation  was the heart.  But he was also the first to perceive the antithesis between epigenesis, "fresh development," and preformation, the "simple unfolding of pre-existing structures."  The subsequent history of this controversy is "almost synonomous with the history of embryology" (Needham 1934:40). [revised 02/01/03]
   

About 330 bce, Heraclides of Pontus said that the earth turns daily on its axis "while the heavenly things were at rest..., considered the cosmos to be infinite..., [and] with the Pythagoreans, considered each planet to be a world with an earth-like body and with an atmosphere" (Dreyer 1906:123-125).  He also suggested that Mercury and Venus have the sun at the center of their spheres.
   

In 323 bce, Theophrastus, suceeded Aristotle as head of the Peripatetic school of philosophy of which he was the co-founder.  In Historia Plantarum and De Causis Plantarum, he classified and described the "external parts of plants from root to fruit..., set forth the 'homology' of the perianth members [or floral envelope] of flowers..., to some extent distinguished between monocotyledons and dicotyledons, [and] described the fertilization of the date palm" (Crombie 1952:367).
   

About 310 bce, Autolycus of Pitane defined uniform motion as being when "a point is said to be moved with equal movement when it traverses equal and similar quantities in equal times" (Clagett 1959:164).
   

About 300 bce, Eukleides, better known as Euclid, published his Elements, a reorganized compilation of geometrical proofs including new proofs and a much earlier essay on the foundations of arithmetic. Elements concludes with the construction of Plato's five regular solids. Euclidean space has no natural edge, and is thus infinite. In his Optica, he noted that light travels in straight lines and described the law of reflection.
About 300 bce, Epicurus attempted to deal with the contradiction between atoms falling through the void in parallel paths at the same speed and the appearance of novel combinations, or matter, by supposing very slight, chance deviations, or 'clinamen,' in an atom's path.  He saw this as analogous to the question of human freedom in a determined nature; i.e., there is no room for ethical considerations Indeed, "Epicureans saw the development of the world as a random, one-way process" (Toulmin and Goodfield 1965:50).
   

About 280 bce, Herophilus of Alexandria studied anatomy and compared humans and animals, distinguished between sensory and motor nerves,and between the cerebellum and the brain, noted that the cortex was folded into convolutions, and named the 'duodenum.' [revised 02/01/03]
   

About 260 bce, Aristarchus of Samos, in On the Sizes and Distances of the Sun and Moon, used trigonometry to estimate the size of the Moon and its distance by the Earth's shadow during a lunar eclipse. Archimedes and others said that he maintained that the Moon revolved around the Earth and the Earth around the Sun which remained stationary like the stars.

About 260 bce, Archimedes of Syracuse contributed numerous advances to science including the principle that a body immersed in fluid is buoyed up by a force equal to the weight of the displaced fluid and the calculation of the value of p. "His method was to select definite and limited problems.  He then formulated hypotheses which he either regarded, in the Euclidean manner, as self-evident axioms or could verify by simple experiments.  The consequences of these he then deduced and experimentally verified" (Crombie 1952:278).
   

About 250 bce, Erasistratus of Alexandria dissected the brain and distinguished between the cerebrum and the cerebellum.

About 250 bce, 'zero' appeared in the Babylonian place-value system.
   

About 240 bce, Eratosthenes of Cyrene calculated the diameter of the earth by measuring noontime shadows at sites 800 km. apart.  Assuming the earth is a sphere, the measured angle between the sites is seven degrees and the circumference is about 50 times 800 km., or about 40,000 km.
   

Before the end of the third century bce, astrolabes were in use for taking the angular distance between any two objects, usually the elevation in the sky of planets.
   

In the early second century bce, Diocles, in On Burning Mirrors, proved the focal property of a parabola and showed how the Sun's rays can be made to reflect a point by rotating a parabolic mirror (Toomer 1978).

About 210 bce, Apollonius of Perga, in Conics, introduced the terms 'parabola' and 'hyperbola,' curves formed when a plane intersects a conic section, and 'ellipse,' a closed curve formed when a plane intersects a cone. 
   

About 170 bce, parchment, superior to papyrus because it can be printed on both sides and folded, was invented in Pergamon.
   
   

About 134 bce, Hipparchus of Rhodes measured the year with great accuracy and built the first comprehensive star chart with 850 stars and a luminosity, or brightness, scale.  He is credited with the discovery of the precision of the equinoxes, and seems to have been very impressed that either of two geometrically constructed hypotheses could 'save the appearance' of the path that a planet follows: One shows the planets moving in eccentric circles and the other moving in epicycles carried by concentric circles (Duhem 1908:8).
   

In the first half of the first century bce, Titus Lucretius Carus, writing in Latin, set forth the teachings of the Epicurean school in De rerum natura. There he held that "the soul is itself material and so closely associated with the body that whatever affects one affects the other.  Consciousness ends with death.  There is no immortality of the soul.  The universe came into being through the working of natural laws in the combining of atoms" (Columbia Desk Encyclopedia 1975:1626). This view is supported by the force of the wind which is the result of the impact of innumerable atoms.
   

In 45 bce, Sosigenes of Alexandria designed a calendar of 365.25 days which was introduced by Julius Caesar.
   

Late in the first century bce, Strabo published his Geographia, based on his observations and those of his Greek predecessors.

Late in the first century bce, Marcus Vitruvius Pollio, in De architectura, wrote of the properties of building materials in terms of atoms.  This book remained the standard architectural treatise into the Renaissance.
   

About the 25th year of the common era, Pomponius Mela, in De situ orbis, published a map of the known world and formalized the notion of climatic latitudes.
   

In the first century, Pedanius Dioscorides published recommendations as to the medicinal use of specific plant extracts.
   

About 100, Hero of Alexandria explained that the four elements consist of atoms.  He also observed that heated air expanded.  In Catoptrica, he demonstrated geometrically that the "path taken by a ray of light reflected from a plane mirror is shorter than any other reflected path that might be drawn between the source and the point of observation" (History of Optics 2001:1).

About 100[?], Plutarch, in On the Face That Can Be Seen in the Lunar Disk, compared the Moon to the Earth, upheld the idea of the plurality of worlds, and tried to overturn Aristotle's theory of  'natural places' (Duhem 1985:479).
   

Between 127 and 141, Claudius Ptolemaeus, better known as Ptolemy, put together a thirteen volume compendeum of opinion and data concerning the stars, including the Mesopotamian eclipse record.  In this book, the Almagest, Ptolemy rejected the Peripatetic physics of the heavens, using circles rather than spheres.  He did so in order to simplify his calculations, judging the circles to be only models devised for the purpose of calculation and recognizing that the actual movements were unknowable.  The Almagest also contains errors which were not corrected until the sixteenth and seventeenth centuries: e.g., saying that the earth is the center of the universe, the planets have circular, if eccentric, orbits, and the earth does not move--because the centrifugal force would cause anything even temporarily disconnected to lag behind.  On the other hand, the tables of the planet's positions were of such accuracy that Nicholas Copernicus computed most of his numbers from them.
   

About 170, Claudius Galen used pulse taking as a diagnostic, performed numerous animal dissections, and wrote treatises on anatomy aid.  The Galenic doctrine assumed that health depends on a balance of affinities or antagonisms associated with various bodily fluids or 'humors:' blood and fire (hot and dry), yellow bile and air (hot and wet), black bile and earth (cold and dry), and phlegm and water (cold and wet).  "The object of good medical practice...was to restore the balance of the humors by such treatment as bleeding or  purgation with plant extracts" (Fruton 1972:27).  Galen eskewed 'action at a distance' through the agency of gods or spirits, in his formulas he employed many odd ingredients, such as crocodile bllod and mouse dung.  But, if he can, he relates the efficacy to some mechanism: for example, for a root worn around the neck, inhalation of the particles of the root.  He distinguished three ventricles and proposed that nerves are ducts conveying fluid pneuma secreted by the brain and spinal cord to the periphery of the body, which was the basis of the idea, widespread until the eighteenth century, that nervous tissue had a glandular function He broke pneuma, which means spirit or soul in Greek, down into various faculties, motor, sensory including the five senses, and rational. He divided the rational pneuma into several functions, imagination, reason, and memory. He also wrote of 'seeds of disease,' presumably what are now called germs. [revised 02/01/03]
   

About 250, Diophantus pioneered in solving certain indeterminate algebraic equations, i.e., an equation in which the variables can take on integer values and has an infinite but denumerable set of solutions: e.g., x+2y=3.
   

In perhaps the middle of the third century, Calcidius translated the first 53 chapters of Plato's Timaeus into Latin.  He translated 'analysis' and 'synthesis' as resolutio and compositio, and maintained in his commentary that combining these was the proper method of philosophical research.
   

In the late third century, Porphyry wrote an introduction to Aristotle's logic, the Eisagoge, which was much read in the course of the Middle Ages.  It emphasized the distinction between facts held to be universally true because they existed 'prior to experience,' the Platonic opinion, or 'posterior to experience,' the Aristotelian opinion.  This difference grew into the distinction between 'realists,' who hold that universals are the ultimate reality, and 'nominalists,' who hold that universals are derived from real experience.  In our time, this distinction lives in the controversy concerning the 'humanity' of a fetus (Park 1990:100).
   

About 385, Aurelius Augustinus, later known as Augustine, a Christian saint, writing in Latin, found the Platonist notion of eternal ideas a certain basis for knowledge which he promulgated in his books Confessiones and Civitas Dei.
   

[["The fourth and fifth centuries saw the intellectual triumph of [Roman] Christianity in Europe....  In 389 Christian monks sacked the great Greek library in Alexandria....  Since Greek was the language of a literature whose most famous works expressed a pagan culture [and] by 425 Saint Jerome's [official Latin or] Vulgate Bible was being copied and distributed..., Western scholars no longer needed Hebrew or Greek" (Park 1990:78-79).]]
   

About 450 or later, Proclus, the final head of Plato's Academy, said that astronomers "do not arrive at conclusions by starting from hypotheses, as is done in the the other sciences; rather, taking conclusions [the appearance of the heavens] as their point of departure, they strive to construct hypotheses from which effects conformable to the original conclusions follow with necessity" (Proclus, quoted by Duhem 1908:20).  The astronomer is only interested in saving the appearance of the phenomena, and whether this conforms to reality is left to the other sciences to decide.
   

In 458, the Lokavibhaga, a Jain work in Sanscrit on cosmology, demonstrated a clear understanding of place-values and the concept of zero.
   

In 517, John Philoponus determined that falling objects do so with the same acceleration, or 'impetus,' specifically opposing Aristotle's notion that the air through which a projectile moved was its motive force.
   

After about 520, Ancius Manlius Severinus Boethius wrote De consolatione philosophiae in Latin, probably the most widely read book in Europe in the Middle Ages, and translated Aristotle's logical books.  "Until the rediscovery of Aristotle in the twelfth century his translations were the basic texts for all students of logic" (Park 1990:79).  He also wrote a commentary on Porphyry's logic.  Aside from Boethius and Augustine, students in the monasteries read Pliny's first century Historia Naturalis, Cassiodorus's sixth century encyclopedia, Isadore of Seville's sixth century Etymolagiarum, and Discorides' De Materia Medica.
   

About 530, Simplicius of Cilicia, in a commentary in Greek on Aristotle's writings on 'gravity', interpreted him to mean that the intensity of the tendency of bodies toward their natural place varied with their distance from that place.
   

In the first half of the seventh century, Brahmagupta regarded zero, the place holder in the base-10 number system as "an infinitissimal quantity which ultimately reduces to nought."  For Hindus, "arithmetic and mensuration, rather than geometry and considerations of congruence, were fundamental" (Boyer 1949:62).  By this time, Hindus also conceived of negative numbers and did not disregard the the irrational roots of quadratics, as had the Greeks.
   

In 662, Severus Sebokt referred to calculations with Indian numerals by fellow Syrians.
   

In 673, the Muslim fleet, laying seige to Constantinople, probably used 'Greek fire,' an inflammable mixture of quicklime, naptha, pitch, and sulphur.
   

About 700, the venerable Bede tried to determine an atom of time, arriving at something like "about 1/6 of our second, and therefore on the order of the briefest sounds that we can distinguish in speech" (Park 1990:98).  He also made original observations concerning the tides at ports. His writings are virtually a summary of learning of his time.  His best known scientific treatises are those on chronology.
   

In the early eighth century, stirrups were introduced in Frankish lands, enabling the development of the armored knight. They were common in China as early as 477, and Muslim cavalry wore them in Persia in 694. [added 02/01/03]

By 770, iron horseshoes were common. [added 02/01/03]
   

In 793, the first paper, a Chinese invention, was made in Baghdad.
   

About 800, Jabir ibn Hayyan, later known as Geber, was educated reading translations from Greek and based his chemical system "on two substances: sulphur, which...is hot and dry, and mercury, which is cold and wet.  Since each contains all four elements, any other material can be formed by the proper combination of these two, and since we cannot know substance but only form, our search must aim at the most desired product, gold" (Park 1990:115).  This is the most perfect, most virtuous product since, as Aristotle said, all things, even base metals, struggle upward.
   

About 820, Muhammed ibn Musa al-Kwarizmi wrote essays on Hindu arithmetic and al jabr, translated as 'the transposition,' and pronounced 'algebra.'  The word 'algorism,' which we have refashioned 'algorithm,' is thought to be derived from his name and denotes the decimal system of notation, which is thought to have passed from India to the West in the translation of his algebra into Latin.
   

About 850, Moors in Spain prepared pure copper by reacting its salts with iron, a forerunner of electroplating.

About 850, Abu Yusek Yacob ibn Ishak al-Kindi commented on Aristotle and wrote numerous treatises on optics, perspective, and medicine.
   

About 900, Abu Bakr al-Razi, better known as Rhazes, distinguihed smallpox from measles in the course of writing several medical books in Arabic. Holding against any sort of orthodoxy, particularly Aristotle's physics, he maintained "the conception of an 'absolute' time, regarded by him as a never-ending flow" (Pines 1975:125).
   

About 976, a manuscript from non-Moslem Spain showed the first examples of the nine Hindu-Arabic numerals in Europe.
   

About 1000, Ibn Sina, or Avicenna, hypothesized two causes of mountains: "Either they are the effects of upheavals of the crust of the earth, such as might occur during a violent earthquake, or they are the effect of water, which, cutting itself a new route, has denuded the valleys, the strata being of different kinds, some soft, some hard....  It would require a long period of time for all such changes to be accomplished, during which the mountains themselves might be somewhat diminished in size" (Toulmin and Goodfield 1965:64). In Kitah al-Shifa, he denied the Aristotelian notion that an object thrown through the air is pushed by that air and held that "every motion occurs through a power in the moving object by which it is impelled" (Avicenna, quoted in Pines 1975:141). He also published Al-Quanun, or Canon of Medicine, where he held that medicines were to be known either by experiment or by reasoning.

About 1000, Ibn al-Haitam, or al-Hazen, in Opticae Thesaurus, introduced the idea that light rays emanate in straight lines in all directions from every point on a luminous surface.  He also discussed spherical and parabolic mirrors and was aware of spherical aberration.  In Epitome of Astronomy, he took a position against Ptolemy, insisting that the hypothetical spheres corresponded "to the true movements of really existing hard or yielding bodies [and] so...were accountable to the laws of physics" (Duhem 1908:28).  This led to disageements that persisted through the twelfth century.
   

Early in the eleventh century, crossbows with sights and mechanical triggers were introduced into warfare.
   

About 1050, Solomon ben Judah Ibn Gabirol, or Avicebron, held that every material thing possesed a 'common corporeity' which was continuous through the universe.
   

[In 1054, Chinese astronomers at the Sung national observatory at K'ai-feng observed the explosion of a supernova in the Crab Nebulae, visible in daylight for twenty-three days.  Since then debris has moved out about three light years.]
   

In 1079, Omar Khayyam, computed the length of the year as 365.24219858156 days, which approaches the accuracy of the late 16th century Gregorian Calendar.  The length of a year decreases in the sixth decimal within a typical human lifetime and is today 365.242190 days.  Khayyam also, in Treatise on Demonstrations of Problems in Algebra, produced a complete classification of cubic equations and their geometric solutions.
   

As early as 1091 or 1092, Walcher of Malvern, having observed an eclipse in Italy, determined the difference in longitude of England by discovering the time which it was observed there.
   

By the twelfth century, alchemists had developed the art of distillation to the stage at which distillates could be captured by cooling in a flask, and wine could be distilled to yield aqua vitae.
   

About 1100, Pierre Abelard began teaching Aristotelian dialectic and took a moderate position between the extreme Augustinians and the extreme nominalists; i.e., he held that universals are entities which exist only in thought but which are based in particulars.  In consequence, observation of material nature and the importance of the individual increased.

About 1100, the crossbow was developed in Europe and outlawed, in 1139, by the second Ecumenical Lateran Council, "as humankind's first formal attempt at arms control" (O'Connell 2002:64). The crossbow could be shot accurately with comparatively little training. [added 02/01/03]
   

About 1120, Awhad al-Zaman Abu'l-Barakat al-Baghdadi, Kitah al-Mu'tabar, denied Aristotle's notion that a constant force produces a uniform motion and maintained that the 'violent inclination' by which a stone is thrown declines and is replaced by an accelerating 'natural inclination' as it returns to earth: "The farther the power moves the stone away from its natural region, the more natural inclinations are produced" (Abu'l-Barakat, quoted in Pines 1975:142).
   

About 1126, Adelard of Bath translated Euclid's Elements and al-Kwarizmi's arithmetic and astronomical tables from Arabic into Latin.
   

About 1145, Robert of Chester translated al-Kwarizmi's Algebra.

After 1145, Abraham ben Meir Ibn Ezra explained the Arabic system of numeration and the use of the symbol 0.
   

After about 1150, Ibn Rushd, better known in Latin Europe as Averroës, and also sometimes as the Commentator, wrote commentaries on several of Aristotle's books where he explained that prime matter, matter at its most fundamental level, has no form of its own.  Its essence is its potential.  He also criticized the artificiality of Ptolemy's orbits: "Astronomers propose the existence of these orbits as if they were principles and then deduce conclusions from them" (Averroës, quoted by Duhem 1908:30).
   

By 1175, Gerard of Cremona had translated from Arabic into Latin most of Aristotle's work as well as Ptolemy's Almagest, Autolycus of Pitane's De spera mota, Avicenna's Canon, al-Kindi's treatise on optics, and some of Rhazes' medical books.
   

About 1185, Burgundio of Pisa translated from Greek into Latin various treatises by Galen and Aphorisms by Hippocrates of Cos.
   

About 1190, Moses ben Maimon, better known as Maimonides, wrote The Guide for the Perplexed in Arabic for Arabic-speaking Jews and included his ideas about astrological systems.  For sublunar physics, he accepted the word of Aristotle as wholly true: This is man's sphere.  But the heavens are the 'deity's,' and therefore man cannot know them, but can only try to describe them "rely[ing] on the arrangement postulating the lesser number of motions" (Maimonides 1963:274), reiterating Ptolemy and Proclus.
   

In 1202, Leonardo Pisano, better known by his nickname Fibonacci, in Liber abbaci, asked the question, "How many pairs of rabbits can be produced from [one] pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?"  The resulting sequence 1, 2, 3, 5, 8, 13, 21, 34... is formed by adding the prior sum.  He was a well-known and prolific mathematical writer and his publications were instrumental in the the introduction of Arabic numerals to Europe (Fibonacci, quoted in the archive of The MacTutor History of Mathematics 2000:"Fibonacci"2-3). He also interpreted a negative number as a debit and solved geometric problems using algebra.
   

In 1206, al-Jazari published a book in which he demonstrated some understanding of the use of a crank for producing reciprocal rotary motion.  "No secure evidence evidence for it is found in Europe earlier than c. 1405" (White 1962:111).  The crank had been understood at least as early as Archimedes, but presumably forgotten in the Dark Ages.
   

[Beginning in the thirteenth century, medical doctors, especially in Italy, wrote consilium, or case-histories, describing the symptoms and courses of numerous diseases.  In Italy, the study of surgery and, therefore, anatomy was encouraged in the universities, but, in France and England, the universities were closed to surgeons because the Catholic Church forbade clerks to shed blood.]
   

After about 1215, Robert Grosseteste "made the first thorough logical analysis of the inductive and experimental procedures of practical science" (Crombie 1953:35).  He called for investigation of effects leading to discovery of causes followed by demonstration of how causes produce effects, i.e., resolutio and compositio, Aristotle's double movement.  But since this only provided a possible cause, at the end of compositio, a process of experimental verification and logical falsification is required.  Grosseteste considered light to be the basis of all natural causes so he considered optics the basis of all explanation: He not only attempted mathematical explanations of the properties of mirrors and lenses, rainbows and refraction, but also to explain the rectilinear propagation of light as a sucession of waves.  "He was the first medieval writer to discuss these subjects systematically" (Crombie 1953:116).  He also translated from Greek into Latin part of Simplicius' commentary on Aristotle's De Caelo et Mundo.
   

In 1217, Michael Scot translated into Latin Averroës' commentaries on Aristotle as well as some texts of Aristotle's.  Probably later, he gave the University of Salerno recipe for anesthesia as equal parts opium, mandragora, and henbane.  He also wrote a treatise ascribing to each of the practical sciences a corresponding theoretical science of which it is the manifestation.
   

About 1230, Jordanes de Nemore demonstrated the law of equilibrium of the lever: "Whatever can lift a given weight to a given height can also lift a weight 24 k times heavier to a height k times smaller.  This is the principle which [René] Descartes will take as the foundation of all statics and, which due to Jean Bernoulli, will become the 'Principle of Virtual Displacements" (Duhem 1905:90).

About 1230, Vincent of Beauvais compiled about six thousand folio pages in an encyclopedia, Speculum majus, of knowledge gleaned from translations of Greek and Arabic books on philosophy, science, and mathematics.
   

[Throughout the Middle Ages there were various schools of thought about the Aristotelian system of the universe.  Among the Franciscans at Oxford, there were two schools.  Most accepted only some explanations of natural phenomena such as the movement of heavenly bodies.  Others, such as Roger Bacon, were less offended by pagan metaphysics and had great interest in Aristotelian medicine, physics, and mathematics.  At the University of Paris, there were also two schools.  Dominicans, such as Albertus Magnus and Thomas Aquinas, accepted most Aristotelian principles, except for determinism.  The other school of thought, represented by Siger de Brabant, accepted an entirely deterministic interpretation of the universe.  At Montpellier in the south of France and at the Italian universities, Salerno, Padua, and Bologna, theological matters counted for less and Aristotle and the Arabs were studied mainly for medical learning (Crombie 1952:41).]
   

About 1250, Albert of Bollstadt, called Albertus Magnus, in De Vegeabilibus et Plantis, a commentary on a pseudo-Aristotelian plant book, shows "a sense of morphology and ecology unsurpassed from Aristotle and Theophrastus to [Andrea] Cesalpino" (Crombie 1952:204).  Probably following this, Albertus wrote De Animalibus, a commentary on three treatises of Aristotle as well as commentaries on Avicenna's Canon and some of Galen's works.

About 1250, Gilbert the Englishman described the local loss of sensation of the skin, that is, the peripheral nerves of early stage leprosy.  This remains one of the best early diagnostic symptoms.  "So successful were the methods of [early] diagnosis and segregation that by the early sixteenth century Europe was almost entirely free from leprosy, and similar preventitive measures were taken against other infectious diseases" (Crombie 1952:204).
   

About 1260, Albertus wrote a geology book, De Mineralibus et Rebus Metallicis, in which he "worked his authorities into a coherent theory and made a number of observations of his own, [including extending] Avicenna's account of fossils.  He was the first to produce arsenic in a free form.

About 1260 [?], Siger taught that the universe was predetermined and "that the individual soul had no immortality....  [He] adopted the Averroist notion of 'double truth'--that something could be true in rational philosophy but false in religious belief" (Columbia Encyclopedia 1975:2515).
   

In 1266, Hugh and Theodoric Borgogoni advocated putting surgical subjects to sleep with narcotic-soaked sponges.  They also recommended that wounds should be "cleaned with wine, the edges brought together with stitches, and left for nature to heal" (Crombie 1952:206).
   

During the second half of the thirteenth century, gunpowder became known in Europe, perhaps introduced from China through the Mongols. "Knowledge of the explosive properties of salpetre, sulphur, and charcoal seems to have been perfected [in China] about 1000 " (Crombie 1952:192). The evolution of the gun in China appears to have been, first, bamboo flame throwers, then metal tubed flame throwers, then arrow throwers, and, after 1280, ball throwers (O'Connell 2002:113). [revised 02/01/03]
   

In 1267 and 1268, Bacon published proposals for educational reform, arguing for the study of nature, using observation and exact measurement, and asserting that the only basis for certainty is experience, or verification. In a book on optics, he noted that the maximum altitude of the bow, reached when the sun is on the horizon, is 42 degrees   He considered the speed of light to be finite and that it is propagated through a medium in a manner analogous to that of sound.  He wrote a Greek grammar and also noted that the power of the new explosive powder "would be increased by enclosing it in an instrument of solid material" (Crombie 1952:192).

Between 1267 and 1273, Aquinas, in Summa Theologica, pointed out the "difference between a hypothesis which must necessarily be true and one which merely fitted the facts.  Physical (or metaphysical) hypotheses were of the first type, mathematical hypotheses of the second" (Crombie 1952:61).  This was a 'realist' position.
   

In 1269, Petrus Peregrinus of Maricourt, in Epistola de Magnete, reflected on his experience with 'lodestones.'

In 1269, William of Moerbeke translated from Greek into Latin Archimedes' On Plane Equilibriums and De lis quae Humido Vehuntur.  Earlier, after 1260, he had translated Hero of Alexandria's Catoptrica.
   

After 1274, Ramon Lull claimed that, in every branch of knowledge, "there are a small number of simple basic principles or categories that must be assumed without question.  By exhausting all possible combinations of the categories we are able to explore all the knowledge that can be understood by our finite minds.  To construct tables of possible combinations we call upon the aid of both diagrams and rotating circles" (Gardner 1982:9).
   

About 1285, somebody, perhaps Alessandro della Spina, invented spectacles for far-sightedness.
   

After about 1290, John Duns Scotus began teaching that "being must be regarded as the ultimate abstraction that can be applied to everything that exists" (Columbia Encyclopedia 1975:809), a nominalist position.

About 1290, Giles of Rome put forward an atomic theory, based on Avicebron's theory of matter, which rendered geometric arguments against the existence of natural 'minima' irrelevant: Magnitude was either a mathematical abstraction or realized in a material substance.  If the last, there must become a point in its division when it becomes something else.
   

Before the end of the thirteen century, greater efficiency in iron smelting was achieved by the introduction of mechanisms for producing blasts of air under pressure from a head of water.
   

At the end of the thirteenth century, the Royal Bethlehem Hospital, later simply Bedlam, was built in London specialized for mental patients.
   

Between 1304 and 1310, Theodoric of Freiberg showed that rainbows could be explained through experiments with hexagonal crystals and spherical crystal balls; i.e., "the rays were refracted on entering each raindrop, reflected at the inner surface, and refracted on passing out again" (Crombie 1953:237).
   

In 1304, Giotto di Bondone, reviving the antique Roman style, began painting the frescoes in the Scrovegni Chapel, Padua, in which he achieved a new naturalism in the human figure and a convincing representation of space.
   

In 1316, Mondino of Luzzi published Anatomia.  He had already introduced the practice of public dissections for teaching.
   

In 1323 or earlier, William Ockham, in Questiones super quattuor libros sententiarum, introduced the distinction between 'being in motion' and 'being moved,' that is, as it is now called, between dynamic motion and kinematic motion.  Motion, he maintained, does not exist separate from a moving body, rather it is "a term standing for a series of statements that the moving body is now here, now here, etc." (Clagett 1959:521).
   

In 1327, Francesco Petrarca, or Petrarch, began to write poems to Laura which ignored courtly conventions and, surpassing the medieval picture of woman as a spiritual symbol, created images of a real woman and real emotions.
   

In 1328 or earlier, Ockham, in Summa Logicae, wrote that universals exist only in men's minds and in language, disputing the Aristotelian principle that such things as the final cause were self-evident or necessary.  In other words, facts could only be correlated, not caused.  Preferring the notion of 'intuition,' he also denied the efficacy of reason in matters of faith and thus the self-evidence of Christian theological principles, such as the existence of God.  He also elevated Aristotle's and Grosseteste's pragmatic economic principle, or lex parsimonae, into the cornerstone of his methodology, known as 'Ockham's razor:' What can be done with fewer assumptions is done in vain with more.
   

In 1328, Thomas Bradwardine, in Tractatus de Proportionibus, made clear, in geometric terms, Ockham's distinction between being in motion and being moved, that is, between 'potentias,' or force, and "the magnitude of the thing moved and of the space traversed" (Bradwardine, quoted in Clagett 1959:208).  He also introduced the distinction "between 'qualitative' (instantaneous or intensive) velocity and 'qualitative' velocity (the total velocity of some period of time measured by the distance traversed during that period of time)" (ibid.:411).  Studies with William Heytesbury, in Regule solvendi sophismata, Richard Swineshead, in Liber calculationum, and John Dumbleton, in Summa de logicis et naturalibus, all at Merton College, Oxford, produced the Mertonian Rule wherein the measure of uniform acceleration is shown to be its medial velocity.  Dumbleton's proof used algebraic symbols.
   

In the second quarter of the fourteenth century, Richard Suiseth, also known as the Calculator, pointed out that a finite part cannot be in ratio to an infinite whole.
   

In 1333 or earlier, Ockham, in the Quodlibeta, wrote that "all causes properly so-called are immediate causes....  This is the special characteristic of a final cause, that it is able to cause when it does not exist....  This movement towards an end is not real but metaphorical" (Ockham, quoted in Crombie 1953:174).
   

In 1348, Gentile da Foligno used Galen's words 'seeds (semina) of disease' in a consilium on the bubonic plague.
   

About 1350, Jean Buridan extended Philoponus's idea by specifying the nature of 'impetus,' that is, the motive power which the agent gives to the moving body which would maintain it at a constant velocity were it not for air resistence and natural gravity.  In falling bodies, the impetus, which is analogous to Isaac Newton's 'momentum,' was gradually increased by the accelerating force of natural gravity.  In each case, Buridan is arguing against theories of Aristotle's largely on the basis of exprerience.

About 1350, Albert of Saxony was perhaps the first to distinguish between the center of gravity and the geometric center.  Drawing from this theory, he concluded that Earth's center of gravity does not coincide with its center of volume: The Sun's heat caused part of the Earth to expand, forming dry land and mountains. He also did logical exercises with infinite sets.
   

In 1360, Guy de Chauliac, in Chirurgia Magna, recommended extending fractured limbs with pulleys and weights and recommended replacing lost teeth with bone fastened to the sound teeth with gold wire.
   

Probably before 1361, Nicole Oresme, in his chief work, associated continuous change with a geometric diagram and revived the Greek use of a coordinate system to represent it. Although he to algebra the conception of a fractional power, in his graphs there is no systematic association of an algebraic relationship.  In De Configurationibus Intensionum, he a geometric proof to the Mertonian Rule, namely, in a given time the space traversed by a body with uniformly 'difform,' or accelerating, velocity is equal to the total time multiplied by the mean velocity.  He also disposed of an argument against the earth's rotation by pointing out that is "if a man in the heavens, moved and carried along by their daily motion, could see the earth distinctly..., it would appear to him that the earth is moving in daily rotation" (Oresme 1968:523).  It should be noted that Oresme, Buridan, and Albert of Saxony, who each observed the same rule of procedure, namely, that "all the facts of experience...are brought to bear on [their hypotheses]," were at the University of Paris (Duhem 1908:60).
   

In 1364, Giovanni di Dondi built a complex clock which kept track of calendar cycles and computed the date of Easter by using various lengths of chain.
   

In 1370, the clocks of Paris were synchronized.
   

In 1410, Benedetto Rinio published a herbal which contained 450 paintings of plants, botanical notes, citations of authorities used, and the names of the plants in various languages including Greek and Arabic.
   

About 1420, Filippo Brunelleschi drew panals in scientifically-accurate perspective.
   

About 1431, Nikolaus von Cusa established by internal evidence that the document known as the Donation of Constantine, for at least six hundred years the foundation of the Pope's political claims, could not have had the antiquity it purported.
   

About 1437, Johann Gutenberg became the first in Europe to print with movable type cast in molds.
   

In 1440, Cusa, in De docta ignorantia, said that the Truth can neither be increased nor diminished and that Intellect, or Reason, can never completely comprehend Truth.  But "the more deeply we are instructed in this ignorance, the closer we approach the truth" (Cusa 1440:53).  This is at the same time NeoPlatonist mysticism and post-Scholastic Humanism.  Instead of the opposition between physics and astronomy, he set up an opposition "between the absolute physics of real essences and genuine causes and the relative and developing physics of abstract essences and fictive causes" (Duhem 1908:58).  Revivng Platonic arithmology, Cusa "again associated the entities of mathematics with ontological reality and restored the cosmological status which Pythagoras had bestowed upon it" (Boyer 1949:90). In other words, he viewed mathematics as independent of the evidence of the senses.  This encouraged the conceptual possibility of the infinite and the infinitesimal, which had been inimical to the Aristotelianism of the Middle Ages.  Cusa held that "a finite intelligence can approach the truth only asymptomatically[; i.e., the infinite was] the unattainable goal of all knowledge" (ibid.:91).  He compared man's search for the truth to the squaring of the circle, which, indeed, he attempted by treating the circle as a polygon with an infinite number of sides.  This was later named the 'exhaustion method.'
   

In 1444, Cusa denied that the earth could be at the center of the universe since the universe is unbounded and made several astronomical claims including that the Earth moved around the sun, the stars were other suns, and had inhabited worlds.  He also performed the first modern, formal biological experiment from which he concluded that plants absorb nourishment from the air.
   

In 1463, Marsilio Ficino finished the first complete translation of Plato's dialogues into Latin. His NeoPlatonism emphasized the conception that opposites are reciprocal, e.g., the higher actively strives for the lower, and that matter is not the mere opposite of form, i.e., evil, but the beginning of active form. Earlier, about 1460, Ficino had interrupted this labor to translate a newly discovered manuscript, the Pimander, which was purported to contain the 4000 year old wisdom and magic of Hermes Trismegistus.  This meant that it was the Egyptian source of Plato's learning as well as being a prefigurement of Christian theology.
   

Between May of 1449 and August 1450, employing bombards, "siege guns put together like beer barrels out of forged iron staves reinforced by hoops [which] fired stone projectiles up to thirty inches in diameter and weighing in excess of 1500 pounds," the French liberated seventy English-held castles, ending the Hundred Years War. Key to bombards was the discovery, about 1420, that when gunpowder was mixed with water it dried in grains which burned faster and was more powerful. In 1453, Turks used a huge bombard to reduce and capture Constantinople, sending "reverberations across the West so profound that [that year] is often called the end of the Middle Ages" (O'Connell 2002:115-116). [added 02/01/03]
   

About 1482, Leonardo da Vinci began his notebooks in pursuit of evidence that the human body is microcosmic, which, by 1510-1511, included dissections of the human body. These notebooks, which circulated in manuscript copies, also contained his thoughts on the impossibility of perpetual motion, dynamics, statics, numerous machines, and other matters.  "His devotion to the Archimedean ideal of measurement is shown by the scientific instruments which he tried to improve or devise, such as the clock, a hydrometer similar to Cusa's to measure moisture in the atmosphere, a hodometer similar to Hero's to measure distance travelled, and an anemometer to measure the force of the wind" (Crombie 1952:280).
   

In 1483, Theodore of Gaza translated Theophrastus's Historia Plantarum into Latin.
   

In 1486, Bartholomeu Dias sailed around the Cape of Good Hope, initiating an era of sea faring discoveries.
   

In 1492, Cristóbal Colón vastly underestimated the Earth's radius and his ships failed to reach China. 
   

At the end of the fifteenth century, Nuremberg watchmakers introduced clocks driven by springs rather than weights, making possible the invention of portable watches.
   

Before 1500, "screw-based breech loading and exploding shot, two prime factors in the artillery convulsion of the nineteenth century, were known....  The shoulder stock, the wheel lock (the basis for the pistol), and rifling were all in use by 1525" (O'Connell 1989:121).
   

About 1512, Nikolaus Kopérnik, better known as Copernicus, circulated a manuscript, the Commentariolus, which hypothesized that the Earth was a planet and planets revolved in circles and epicircles around the Sun, that the Earth rotated daily, and regressions in planetary orbits were explained by the Earth's motions (Park 1990:143).  The problem, as he saw it, was to save the appearance of the phenomena with an hypothsis which was compatible with the principle of physics that hypotheses be founded in the truth of nature, and to demonstrate that to reject this hypothesis meant that the appearances were not saved.

[It is the notion that the universe is earth- and, hence, man-centered and, therefore capable of being personalized and animated which distinguishes primitive man from civilized man.]
   

In the early sixteenth century, Theophrastus Bombastus von Hohenheim, who called himself Philippus Aureolus Paracelsus, opposed the four humors of Galenic medicine with "a triad of chemical properties: combustibility (termed 'sulphur'), fluidity and changeability (termed 'mercury'), solidity and permanence (termed 'salt')....  The medical doctrine of Paracelsus was a new humoralism, but it emphasized the use of specific medicines for specific diseases" (Fruton 1972:29). He wrote prolifically in German and his On Diseases of Miners is the earliest book on occupational diseases.
   

In 1521, Berengario da Carpi, in a commentary on Mondino, observed that "the kidney is not a sieve [and] the bladder [has] no opening other than the urinary pores..., gave the first clear accounts of the vermiform appendix, the thymus gland and other structures..., and coined the term vas deferens" (Crombie 1952:371).
   

In 1527, Matteo Bresan, supervisor of the Venice Arsenal, oversaw the construction of a full-rigged sailing ship with lidded gunports, called a 'galleon.' [revised 02/01/03]
   

In 1530, Girolamo Fracastoro published a long poem, Syphilidis, sive, De mordo gallico libri tres, the disease taking its name from the poem.  He also identified typhus.
   

In 1535, Niccoló Fontana, who was called Tartaglia, demonstrated a solution for cubic equations, but did not reveal the details.  When finally published in 1545, the expression was seen to be "built up from the coefficients by repeated addition, subtraction, multiplication, division, and extraction of roots.  Such expressions became known as radical expressions" (Stewart 1989:xiv).  This formula was "probably the first great achievement in algebra since the Babylonians" (Davis and Hersh 1981:196). 
   

In 1537, Ambrose Paré revived the practice of ligature for gunshot wounds, replacing cautery with hot oil.  Later, he performed herniotomies and manipulated fetuses so they could be born feet first.
   

In 1541, Giambattista Canano published illustrations of each muscle and its relation with the bones.
   

In 1543, Andreas Vesalius published a large collection of meticulous anatomical drawings, emphasizing especially the systems of organs.

In 1543, Copernicus published De revolutionibus orbium coelestium.  Although he made some astronomical observations, this work is that of a mathematician using Ptolemy's data, who could read Greek and cite Aristarchus of Samos.  NeoPlatonic and NeoPythagorean influences loom large: "In the center of it all rests the Sun.  For who would place this lamp of a very beautiful temple in another or better place than wherefrom it can illuminate everything at the same time?  As a matter of fact, not unhappily do some call it the lantern; others, the mind and still others, the pilot of the world.  Trismegistus calls it a 'visible god'" (Copernicus 1543:527).  In so placing the Sun, Copernicus "overthrew the hierarchy of positions in the ancient and medieval Cosmos, in which the central was not the most honorable, but, on the contrary, the most unworthy.  It was, in effect, the lowest, and consequently appropriate to the Earth's imperfection.  Perfection was located above in the celestial vault, above which were 'the heavens,' whilst Hell was deservedly placed beneath the surface of the Earth" (Koyré 1961:114n24).

In 1543, Pierre de la Ramée published two books of logic which were anti-Scholastic and anti-Aristotelian and were very influential in Protestant countries in the following century.
   

In 1545, Charles Estienne published illustrations showing the venous, arterial, and nervous systems.

In 1545, Girolamo Cardano, in Ars Magna, published a complete discussion of Tartaglia's solution for cubic equations.  Ars Magna also contained Ludovico Ferrari's method of solving the quartic equation by reducing it to a cubic. 
   

In 1546, Fracastoro published the idea that diseases were caused by disease-specific seeds "that could multiply within the body and be transmitted directly from person to person or directly on contaminated objects, even over long distance; moreover, he proposed that variations in the intensity of epidemics could be attributed to changes in the virulence of germs" (Ewald 1994:184).

In 1546, Pedro Nunes, in De arte atque ratione navigandi, described how to sail a great circle course.
   

In 1551, Erasmus Reinhold published a revised and enlarged version of Copernicus's planetary tables, known as the Prussian Tables, which greatly extended knowledge of Copernicus's theories among astronomers.
   

In 1552 or later, Konrad Gesner, in Opera Botanica and Historia Plantarum, distinguished genus from species and order from class. 
   

In 1553, Pierre Belon, in De Aquatilibus, observed that Cetaceans breathe air with lungs and depicted new-born dolphins still in their fetal membrane and porpoises attached to umbilical cord and placenta.

In 1553, Miguel Servet y Reves, better known as Michael Servetus, said that the blood circulates from the heart to the lungs and returns to the heart.
   

In 1554, Cardano, in De Subtiltate, wrote of da Vinci that "he demonstrates that nothing has perpetual motion" (Cardano, quoted in Duhem 1905:44) and recounts his demonstration.  He also demonstrated that the momentum of a suspended body increases in proportion to the velocity of its descent.  Later, Cardano appended his Opus novum de proportionibus, on statics, to this work.
   

In 1555, Belon, in L'Histoire naturelle des oyseaux, illustrated birds and man in which homologous bones were given the same names. 

In 1555, Guillaume Rondelet, in L'histoire Naturelle des Poissons, pointed out "differences between the respiratory, alimentary, vascular, and genital systems of gill- and lung-breathing aquatic vertebrates, and depicted the vivaparous dolphin and ovoviviparous shark....  He considered the teleostatean swim-bladder, which he discovered, to be a kind of lung" (Crombie 1952:377).
   

In 1556, Georg Bauer, better known as Georgius Agricola, in De re metallica, classified minerals and observed physical geography. 
   

Between 1556 and 1560, Tartaglia, in General trattato di numeri et misure, showed how to fix position and survey land by compass-bearing and distance.
   

In 1562 or earlier, Gabriel Fallopio described the ovaries and uterus and the tubes connecting them.
   

By 1562, Cardano had written Liber de ludo alaea, the first systematic computation of probabilities, which was not published, however, until 1663.
   

In 1564, Julius Caesar Arantius asserted that "although the fetal and maternal vascular systems were brought into close contact with the placenta there was no free passage between them" (Crombie 1952:381).
   

In 1569, Michel Eyquem de Montaigne, in Apologie de Raimond Sebond, wrote that "unless some one thing is found of which we are completely certain, we can be certain of nothing" (Montaigne, quoted in Toulmin 1990:42).

In 1569, Gerard de Cremer, better known as Gerardus Mercator, published the projection map of the world which bears his name.
   

In 1572, Tycho Brahe observed a supernova in the constellation Cassiopeia, now known as Tycho's star.
   

In 1576, Thomas Digges made the claim that Copernicus's 'Celestial Sphere' does not exist, that the stars are at different distances from the Earth, and that Copernicus's heliocentrism was a "most ancient doctrine of the Pythagoreans" (Digges, quoted in Nicholl 1992:207) [revised 02/01/03]
   

By 1578, Brahe completed the first eight chapters of De mundi aetherii recentioribus phaenomenis, a book on the comet of 1577, in which he showed that the comet "was beyond the Sun [an impossibility in the Aristotelian view] and that its orbit must have passed through the solid celestial spheres, if these existed" (Crombie 1952:314).  In the ninth chapter, he offers a new system in which the Earth is immoble and the planets, except for the Earth, revolve around the Sun, thus rejecting both Ptolemy's and Copernicus's systems.  This was published in 1588.
   

In 1582, the reform of the calendar, by which the so-called 'Gregorian calendar' was created, was based on tables constructed by means of the theories of Copernicus.  This in no way implied an endorsement of his heliocentrism, but just that his tables were dealt with as contrivances which better 'saved the appearance' of the heavens.
   

In 1583, Cesalpino, in De Plantis, classified plants with seeds according to the number, position, and shape of the parts of their fruit.

In 1583, Galileo Galilei discovered by experiment that the oscillations of a swinging pendulum took the same amount of time regardless of their amplitude.

In 1583, Giordano Bruno first preached "the doctrine of the decentralized, infinite and infinitely populated universe [and] also gave a thorough statement of the grounds on which it was to gain acceptance from the general public" (Lovejoy 1936:116).  Shortly thereafter, he published De l'infinito universo e mondi in which he maintained that "the infinite cannot be the object of sense-perception; [it is rather found] in the sensible object as in a mirror; in reason, by a process of argument and discussion.  In the intellect....  In the mind" (Bruno, quoted in Koyré 1957:45-46). Bruno's infinite universe, governed by the identity of its fundamental laws, may be contrasted to the "closed unity of a qualitatively determined and hierarchically well-ordered whole in which different parts (heaven and earth) are subject to different laws" (Koyré 1968:2). But Bruno's interest in Copernicus's heliocentrism was also "that of a magician imbued in all the currents of Renaissance occultism" (Nicholl 1992:207). Indeed, Bruno seems to have been the prototype for Christopher Marlowe's Dr Faustus. [revised 02/01/03]
   

In 1585, Giovanni Battista Benedetti, in Diversarum speculationum, foreshadowed the inertial concept: "Every body moved naturally or violently receives in itself an impression and impetus of movement, so that separated from the motive power, it would be moved of itself in space in some time" (Benedetti, quoted in Clagett 1959:663). He studied Archimedes and applied mathematics to the study of nature.
   

In 1586, Simon Stevin began a book on statics and hydrostatics, De Beghinselen der Weeghconst, with the assumption that perpetual motion was impossible and that therefore any given mass of water was in equilibrium in all its parts.  On this basis, he concluded that the pressure of a liquid on the base of a container depended only on depth.  He also demonstrated that the center of gravity of a triangle lies on its median.  He demonstrated the same for parabolic segments.

About 1586, Galileo wrote a manuscript, De motu gravium, which showed that the ratio between the gravity of a moving body on an inclined plane and gravity acting on free fall is the sine of the angle which the plane forms with the horizontal.
   

In 1590, Zacharias and Hans Janssen combined double convex lenses in a tube, producing the first telescope.
   

In 1591 and 1592, Thomas Harriot, or sometimes Hariot, measured an angular distance of 2 degrees 56 minutes between the celestial north pole and the North Star. [added 02/01/03]
   

In 1591, François Viète, in In artem analyticam isagoge, demonstrated the value of symbols to represent unknowns and suggested the use of letters.  He also introduced the term 'coefficient.'
   

About 1592, Galileo found that the path of a projectile is a parabola by assuming that the uniform motion preserved in the absence of an external force is rectilinear. The acceptance of a straight rather than a circular path as natural became a crucial turning point in planetary mechanics. 
   

In 1593, Viète represented p as an infinite product in what is thought to be the earliest use of that symbol.
   

In 1600, William Gilbert, in De Magnete, held that the earth behaves like a giant magnet with its poles near the geographic poles.  He coined the word 'electrica' (from the Greek word for amber, elektron), and distinguished electricity from magnetism.
   

About 1601, Harriot discovered that the extensa, or refractive index, is the same for all angles of incidence. This enabled him to compute refractions for one-degree intervals. [added 02/01/03]

In 1603, Harriot computed the area of a spherical triangle: "Take the sum of all three angles and subtract 180 degrees. Set the remainder as numerator of a fraction with denominator 360 degrees. This fraction tells us how great a portion of the hemisphere is occupied by the triangle" (Harriot, quoted in Lohne 1978:125). [added 02/01/03]
   

In 1604, Kepler, in Ad Vitellionem Paralipomena, said that the intensity of light varies inversely with the square of the distance from the source.  He also said that vision is the consequence of the formation of an image on the retina by the eye's lens and described the causes of near- and far-sightedness.

In 1604, Kepler and many other astronomers witnessed the outburst of a supernova in the constellation Serpens.  At its peak, it was as bright as Venus and then faded away over the next year.  It was the last supernova seen in the Milky Way galaxy.
   

In 1605, Francis Bacon, with the Advancement of Learning, began the publication of his philosophical works, in which he urged collaboration between the inductive and experimental methods of proof, as opposed to scholasticism's a priori method. "It is chiefly to his skill and value as a propagandist that Bacon owed his popularity among seventeenth- and eighteenth-century scientists" (Koyré 1965:5n3).
   

In 1608, Stevin deduced the law of the lever not merely from reasons, as Archimedes had, but from physical assumptions, or "instinctive knowledge" (Mach 1883:26-29).

About 1608, Jan Lippershey, and others independently, invented the telescope by combining lenses empirically.
   

In 1609, Kepler, in De Motibus Stella Martis, published the results of Brahe's calculations of Mars' orbit, which were inconsistent with then current assumption that it was a circle.  He claimed to base his "whole astronomy upon Copernicus's hypotheses..., the observations of Tycho Brahe, and lastly upon the Englishman William Gilbert's philosophy of magnetism" (Kepler 1614:850).  This publication included the first two of what became known as Kepler's laws.  Their gist is that the sun is off-center in the planetary ellipses, that the speed of planetary motion increases as their distance from the sun decreases, and, hence, the areas of the angles subtended by the sun and a given interval of time are the same. Cosmic space is no longer governed by the mechanism of spheres; it is spoken of in the abstract.  The Sun's magnetic force, which he took to consist of elastic chains, does the work of gravity and provided the model for the inverse varience of speed and distance. On the other hand, his term "inertia means for him the resistance that bodies oppose...solely to movement;...he needs a cause or a force to explain motion, and does not need one to explain rest" (Koyré 1968:11). For example, in his quest for a numerically ordered solar system, Kepler postulated an unobserved planet in the gap between Mars and Jupiter.
In 1609, Galileo built a telescope with which he discovered the mountains on the moon, that the Milky Way consisted of innumerable stars, the four largest satellites of Jupiter, the phases of Venus, and sunspots.  He announced these discoveries in Sidereus nuncius, and seems at this time to have become convinced of the correctness of Copernicus's theory. Also seeking to solve the navigational problem caused by the variability of the time value of a degree of longitude, he built tables showing the appearance and disappearance of Jupiter's moons.  By 1650, his method was generally accepted on land.
   

About 1610 or 1611, William Shakespeare created the earliest remembered opposition of 'nature' and 'nurture' when he had Prospero describe Caliban, in the Tempest, as "a born devil, on whose nature, nurture can never stick" (Shakespeare 1944:51).
   

In 1611, Kepler, in Dioptrice, explained the principles involved in the convergent/divergent lenses of microscopes and telescopes and suggested that telescopes could be built using only convergent lenses.  Astronomical lenses became this type. 
   

In 1612, Galileo, in Discorso intorno alle cose cho stanno in su l'acqua, observes that the roles of a lever, a windlass, a capstan, a pulley, and a block and tackle each consist "in transporting a great resistance very slowly and without dividing it by means of a small force moving rapidly" (Duhem 1905:179).
   

In 1614, Kepler, in the Epitome Astronomiae Copernicanae, said that an astronomer "ought to be able to provide reasons for the hypotheses [they] claim as the true causes of appearances, [and they] ought, therefore, at the outset, to seek the foundationsof [their] astronomy in a higher science, I mean, in physics or metaphysics" (Kepler, quoted in Duhem 1908:103). For example, in his quest for a numerically ordered solar system, Kepler postulated an unobserved planet in the gap between Mars and Jupiter.

In 1614, John Napier, in Mirifici logarithmorum canonis descriptio, created the first logarithmic tables and the first use of the word 'logarithm.'  It was not published until 1619.  Napier also introduced the decimal point in writing numbers.

In 1614, Isaac Casaubon demonstrated that the Hermetic writings in the Pimander were not the magical practices of a very ancient Egyptian priest but dated from post-Christian times.  This "is a watershed separating the Renaissance from the modern world.  It shattered at one blow the build-up of Renaissance NeoPlatonism" (Yates 1964:398).
   

In 1615, Kepler, in Steriometria doliorum, showed, following Cusa's exhaustion method, that the volume of a sphere is one-third the product of its radius times the surface area of an infinite number of cones, and that of all right circular cylinders inscribed in a sphere, that one is the greatest which has the diameter and altitude in the ratio of the square root of 2 to 1.  Kepler was concerned with statics and 'indivisibles' and expressed himself in numerical increments.
   

In 1619, Kepler, in Harmonica mundi, published his third law:  The square of the length of a planet's year varies with the cube of the mean radius of its orbit.  His three laws "are the only three exact and general mathematical laws of planetary motion, applying not only to this but to all similar planetary systems.  And he contributed a further revolutionary idea: that the planets move in their orbits...because the Sun exerts a force that causes them to move as they do" (Park 1990:157).  However, none of Kepler's laws was deduced from a consistent theoretical framedwork, which work was left for Newton
   

In 1620, Gaspar Bauhin, in Prodomus Theatri Botanici, gave precise, diagnostic descriptions to about 6000 plants.

About 1620[?], Joachim Jung made precise definitions of the parts of plants.

In 1620, F. Bacon, in The New Organon, pointed out, as an "instance of resemblance," that maps of Africa and South America show "similar isthmuses and similar promontories, and that does not happen without a reason" (Bacon 1620:147).

About 1620[?], Gasparo Aselli discovered the lacteal vessels, lymphatic vessels which conduct fatty substances into the blood stream at the jugular vein.
   

In 1621, Willibrord Snell, in Cyclometricus, discovered the law of refraction which says that the ratio of the sines of the angles of incidence and refraction is a constant and the index of refraction varies from one transparent substance to another. This law implies that the velocity of light in a medium is inversely proportional to its refractive index. Cyclometricus was published after Snell's death by René Descartes.  

In 1621, Galileo discerned that the acceleration of a falling body is proportional to the time and independent of weight and density.
   

In 1623, Edmund Gunter devised a logarithmic scale of equal parts and trigonomic functions which, with the aid of a compass, served as a slide rule.

In 1623, Wilhelm Schickard built a six digit calculator, driven directly by gears, which could add, subtract, and indicate overflow by ringing a bell.
   

In 1624, Pierre Gassendi , in Exercitationes paradoxicae adversus Aristoteleos, revived the "Democritean (or Epicurean) ontology,...modified [it] by doing away with the clinamen..., but...retained the essential feature, namely, atoms and vacuum" (Koyré 1968:119).  He revived Hippocrates' ideas about the brain and maintained that animals have memories, reason, and other psychological characteristics of man.
   

About 1625, Gregory of Saint Vincent said that "parallelepipeds [a solid contained by six parallelograms] can be so multiplied that they exhaust the body within which they are inscribed" (Gregory, quoted in Boyer 1949:136), which is the earliest recorded use of the word 'exhaust' in this context.  "Instead of thinking of static indivisibles, he reasoned in terms of a varying subdivision [that is, an infinite geometric progression], thus approximating the method of limits" (Boyer 1949:137).
   

In 1627, William Harvey was able to confirm his observation that the blood circulates throughout the body, which he inferred from the structure of the venal valves. The following year, in Exercitatio Anatomica, he published these conclusions as well as a description of the heart as a mechanical pump. 
   

Between 1628 and 1634, Giles Persone de Roberval invented a theory of indivisibles; however, "after dividing a figure into small sections, he allowed these continually to decrease in magnitude, the work being carried out largely arithmetically and the result being obtained by summing an infinite series"(Boyer 1949:142).  The arithmetic furthered the logical basis of the 'infinitessimal calculus,' but this new analysis would be the result of "suggestions drawn from geometry" (ibid.:104).
   

About 1629, Pierre de Fermat discovered that the equation f(x,y)=0 represents a curve in the xy-plane.  This is the fundamental principle of analytic geometry, and was first published by Descartes in 1637. He also formulated a method for determining the maximim and minimum values which give single solutions for problems which in general have two solutions.  This procedure is "almost precisely that now given in the differential calculus" (Boyer 1949:156).
   

In 1630, Jean Rey said that the slight increase in weight of lead and tin during their calcination "could only have come from the air, which he said mixed with the calx and became attached to its most minute particles" (Crombie 1952:359).
   

In 1631, Gassendi obderved the transit of Venus across the Sun, establishing that its orbit lies closer to the Sun than does the Earth's orbit.
   

In 1632, Galileo published a work in Italian for the non-specialist, the Dialogo, comparing the Ptolemaic system unfavorably to the Copernican.  For this, he was tried by the Inquisition in 1633 and forced to abjure belief that the Sun was central and that the Earth moved.  In addition, Due massimi sistemi contains Galileo's construction of the concept of 'inertia,' perpetual motion being the limiting case: In an ideal world without friction, given the acceleration and retardation of a body by gradually sloping planes tending toward horizontal, momentum persists indefinitely.  "Force could therefore be defined as that which produced, not velocity, but a change of velocity from a state of rest or of uniform velocity" (Crombie 1952:301).  When a body is acted on by two forces, each is independent of the other.  "Galileo's conception of science as a mathematical description of relations enabled him to...free [methodology] from the tendency to excessive empiricism" (Crombie 1953:305).  Thus 'gravity' was only the name for an observed regularity, with antecedent cause to be discovered by experiment, and not an 'essential cause;' i.e., "mathematical substance was substituted for Aristotelian qualitative substance as the identity persisting through change" (ibid.:310).
   

Probably in 1633, Descartes wrote Le Monde wherein "subtle matter, his celestial matter, what his contemporaries called 'the Cartesian aether,' comprises the second element [i.e., 'air'] permeated, as always by the first [i.e., 'fire']" (Cantor and Hodge 1981:12). The third and final element is 'earth.'  It was published posthumously in 1664.
   

In 1635, Bonaventura Francesco Cavalieri published a purely geometric theory of indivisibles.
   

In 1636, Galileo finished his final book, Discorsi e dimostrazioni matematiche interno a due nuove scienze, which contained most of his physics and some strenghtened arguments. The two sciences are statics and dynamics.  The Discorsi, together with the Dialogo, both works of popular science, "helped create a new age of scientific thought with their emphasis on observation, common sense, clear language, and persuasion by reasonable arguments" (Park 1990:206).
   

In 1637, Descartes, in Discours de la Méthod pour bien conduire sa raison, et chercher la vérité dans les sciences, held that science begins with observation which is followed by analysis, leading to the intuition of the self-evident nature of a proposition, and synthesis, or the reconstitution of the original observation.  Included with this work were three exemplary treatises: La Dioptrique, where 'matière subtile' includes whatever particles transmit light, La Gèometrie, where he demonstrated the so-called Cartesian coordinates and Cartesian curves, and, in algebra, where he contributed the convention of exponent notation, a study of negative roots, and the convention whereby known quantities are represented by letters near the beginning of the alphabet and unknowns by letters at the end; and Météores, where he showed that the primary rainbow was produced by sun rays coming to the eye at an angle of about 41 degrees.
   

About 1640, Jeremiah Horrocks showed that the moon travels in an elliptical orbit and thought of it as "continually falling toward Earth" (Park 1990:179).

In 1640, Fermat wrote his so-called 'lesser theorem;' namely, if p is prime, then a p- a is divisible by p.
   

In 1641, Descartes published his principle philosophical work, Meditationes de prima philosophia, with the goal of refuting the scepticism of the Renaissance humanists.  The kernal of this philosophy is universal doubt: What one can know is based in logic and rationalization, or res cogitans, whereas the physical world, or res extensa,the geometer's three dimensions, is mechanistic and entirely divorced from the mind. "The real truth about nature is learned from reason and not from the trial and error procedures of experimental science" (Park 1990:217).  The maintenance of this distinction is Cartesian dualism.  Thinking, and the awareness of thinking, are the substrates of being: "Je pense donc je suis."  This, so Descartes thought, was the necessary connection between what thinks and what is extended, and 'spirit' was the medium of their interaction.  He also thought he had confounded Montaigne's one 'certain' thing. 'Soul' is not alive, so it must be immortal.  This 'mechanical philosophy' caused the phantom of the imminent end of the world to begin to fade from peoples' consciousness: The mathematical principles underlying nature would continue to operate despite human sin. [revised 02/01/03]
   

In 1642, Gassendi, in De motu impresso a motore translato, extended Galileo's definition of inertia to include motion in any direction, not simply horizontal motion.
   

In 1643 or earlier, Fermat determined the center of gravity of a paraboloid segment "by means equivalent to those of differential calculus, instead of by means of a summation resembling those of integral calculus" (Boyer 1949:159).
   

In 1644, Descartes published Principia philosophiae which philosophically is essentially a Latin version of Meditationes, hence "Cogito, ergo sum."  Scientifically, the physics is much more extensive including notably the notion that "the most general cosmic processes produce magnetism," with the Earth's magnetic vortices appearing in a pattern similar to iron nails around a lodestone (Heilbron 1979:32).
   

In 1644, Evangelista Torricelli devised the mercury barometer and created an artificial vacuum. He was also a mathematician who restricted himself to geometric considerations and showed great facility in his handling of indivisibles.

In 1644, Blaise Pascal built a five digit adding machine, driven by rising and falling weights.  The 'Pascaline' became well-known in its time and established the computing machine concept.
   

In 1645, Marc Aurelio Severino, in Zootomia Democritaea, "discovered the heart of the higher crustacea..., recognized the respiratory function of fish gills, [and] recognized the unity of vertebrates, including man" (Crombie 1952:383).
   

In 1647, Cavalieri derived the relationship between the focal length of a thin lens and the radii of a surface's curvature.
   

In 1648, Jean Baptiste van Helmont, in Ortus Medicinae, published posthumously, concluded that plants derive their sustenance from water, demonstrated that acid digestion was neutralized by bile thus proving that physiological changes have chemical causes, coined the name 'gas' from the Greek chaos, distinguished gases as a class with liquids and solids, and showed that metals dissolved in the three main mineral acids could be recovered.

In 1648, Pascal said that barometric pressure results from atmospheric pressure and that pressure applied to a confined fluid is transmitted equally to all areas and at right angles to the surface of the confiner.
   

In 1649 or earlier, Daniel Sennert conceived a corpuscular theory of matter, and considered "fermentation to be a process in which whole bodies are separated into their smallest indivisible parts, followed by the reunion of these atoms to form new bodies" (Fruton 1972:30).

In 1649, Descartes, in Traité des passions de l'âme, held that emotions were basically physiological.

In 1649, Gassendi, in an appendix to Animadversiones in decium librum Diogenis Laertii, reported an experiment which demonstrated that the variation in the height of a column of mercury in a Torricellian tube is a function of the altitude at which it is placed.  Later, discussing this experiment in Syntagma Philosophicum, he explained that the weight of the column of air "compresses it, and it is this pressure that causes the mercury to rise in the tube" (Koyré 1968:129).
   

In 1650, Francis Glisson published an account of infantile ricketts.

 
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