State of Science in 16th Century 645 Tediousness of Calculations 645 Napier’s Invention of Logarithms 645 Their Nature 645 Property of Numbers discovered by Stifelius 645 Extended to Magnitudes 646 By Napier 646 Tables of Napier and Briggs 646 Kepler’s New Geometry 647 Its Difference from the Ancient 647 Adopted by Galileo 648 Extended by Cavalieri 648 Applied to the Ratios of Solids 648 Problem of the Cycloid 648 Progress of Algebra 649 Briggs--Girard 649 Harriott 649 Descartes 650 His Application of Algebra to Curves 650 Suspected Plagiarism from Harriot 650 Fermat 651 Algebraic Geometry not successful at first 652 Astronomy--Kepler 652 Conjectures as to Comets 652 Galileo’s Discovery of Jupiter’s Satellites 653 Other Discoveries by him 653 Spots of the Sun discovered 653 Copernican System held by Galileo 654 His Dialogues, and Persecution 654 Descartes alarmed by this 655 Progress of Copernican System 655 Descartes denies General Gravitation 655 Cartesian Theory of the World 655 Transits of Mercury and Venus 656 Laws of Mechanics 656 Statics of Galileo 657 His Dynamics 657 Mechanics of Descartes 658 Law of Motion laid down by Descartes 658 Also those of Compound Forces 659 Other Discoveries in Mechanics 659