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(He is often credited with inventing the names for parabola,hyperbola and ellipse; but these shapes were previously describedby Menaechmus, and their names may also predate Apollonius.)Although astronomers eventually concluded it was not physically correct,Apollonius developed the "epicycle and deferent" model of planetary orbits,and proved important theorems in this area.

(After Fibonacci, Europe still did not embrace the decimal systemuntil the works of Vieta, Stevin, and Napier.)

Ptolemy may be the most famous astronomerbefore Copernicus, but he borrowed heavily from Hipparchus,who should thus be considered (along with Galileo and Edwin Hubble)to be one of the three greatest astronomers ever.

For his experimental methods and discoveries,his laws of motion, and for (eventually) helpingto spread Copernicus' heliocentrism, Galileo may have beenthe most influential scientist ever; heranks #12 on Hart's list of the Most Influential Persons in History.

He also made very important contributions to the earlydevelopment of biology; but perhaps Galileo's most important contributionwas to postulate laws of mechanics, in contrast to Aristotelian and religious notionsof separate laws for heaven and earth.

As a famous astronomer, Galileopointed out that Jupiter's Moons, which he discovered, providea natural clock and allow a universal time to be determinedby telescope anywhere on Earth.

Galileo Galilei was born on February 15, 1564, in Pisa, Italy, and was the first of seven children of Vincenzio Galilei, a trader and Giula Ammannati, an upper-class woman who married below her class....

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One reason I've ranked him at #1 is a comment byGottfried Leibniz himself:"Taking mathematics from the beginning of the world to the time whenNewton lived, what he has done is much the better part."

Leibniz was one of the most brilliant and prolificintellectuals ever; and his influence in mathematics (especiallyhis co-invention of the infinitesimal calculus) was immense.

He is famous for his Three Laws of Motion(inertia, force, reciprocal action) but, asNewton himself acknowledged, these Laws weren't fully novel:Hipparchus, Ibn al-Haytham, Descartes, Galileo and Huygens had alldeveloped much basic mechanics already; and Newton credits the First Lawto Aristotle.

He made advances in analysis (including theintroduction of )and in trigonometry (introducingthe hyperbolic functions and );proved a key theorem of spherical trigonometry,and solved the "trinomial equation."Lambert, whom Kant called "the greatest genius of Germany,"was an outstanding polymath: In addition to several areas of mathematics,he made contributions in philosophy, psychology,cosmology (conceiving of star clusters, galaxies and supergalaxies),map-making (inventing several distinct map projections),inventions (he built the first practical hygrometer and photometer),dynamics, and especially optics (several laws of optics carry his name).

Later, Planck, Einstein and Bohr, partly anticipated by Hamilton,developed the modern notion of wave-particle duality.)Huygens is famous for his inventions of clocks and lenses.

(Although he continued to refine this invention,it was never a commercial success.)He suffered poor health throughout his life,abandoned mathematics for religion at about age 23,wrote the philosophical treatise ("We arrive at truth, not by reason only, but also by the heart"),and died at an early age.

As mathematical physicist, he extended Galileo's results, wasfirst to explain winds correctly, and discovered several key principlesincluding Torricelli's Law (water drains through a small hole with rateproportional to the square root of water depth).

Galileo said of Cavalieri, "Few, if any, since Archimedes, have delvedas far and as deep into the science of geometry."

Pierre de Fermat was the most brilliant mathematicianof his era and, along with Descartes, one of the most influential.

(His calculus was partly anticipated by Galileo, Kepler and Luca Valerio,and developed independently, though left unpublished, by Fermat.)Among his theorems in this calculus was

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