John Napier (1550-1617), a Scottish nobleman, invented logarithms. The story of this great mathematician's work is one of the most interesting in the history of science. Napier's first table of logarithms was published in 1614. Henry Briggs (1556-1631), professor at Oxford, made suggestions for the improvement of the tables, and persuaded Napier to make the base 10, as is now done in tables of common logarithms. Briggs published tables in 1624 containing the logarithms to 14 places of decimals for the numbers between 1 and 20,000 and from 90,000 to 100,000. Adrian Vlacq (1600-1667), a Dutchman, computed the logarithms of the numbers running from 20,000 to 90,000, and thus completed the whole series of logarithms between 1 and 100,000. Edmund Gunter (1581-1626), of London, calculated the logarithmic sines and tangents of angles for every minute to seven places. He invented the terms cosine and cotangent and used them in a work published in 1620. Another Englishman, William Oughtred (1574-1660), wrote textbooks on mathematics, and invented numerous mathematical symbols which are now in general use, as well as rectilinear and circular slide rules. Bonaventura Cavalieri (1598-1647) made many improvements in mathematical formulæ and expounded a new method of indivisibles which solved some of the difficult astronomical problems raised by Kepler, and enabled Torricelli, Viviani, de Roberval, and others to solve abstruse problems relating to all types of curved figures. Pierre de Fermat (1601-1665), one of the greatest of French mathematicians, developed rules for calculating maxima and minima. His functions in this type of equation closely approached those of the differential calculus. The calculus was developed from Fermat's work by Lagrange, Laplace, Fourier, and other Frenchmen. Pascal and Fermat developed the theory of probability. Pascal worked out many useful methods for dealing with curves. The intense mathematical activity in England and France resulting from the stimulation given by the invention of Napier, prepared the way for the discovery of the infinitesimal calculus by Newton and Leibnitz. Newton was born in England the same year that Galileo died in Italy. His greatest work is presented in his celebrated "Principia," or "Mathematical Principles of Natural Philosophy," in which the law of gravitation, the laws of motion, and the mathematical principles of mechanics are developed. The "Principia" was published in 1687, and it has ever since been regarded as the corner stone of mathematical and physical science. CHAPTER VIII SCIENCE IN THE SEVENTEENTH CENTURY The wonderful advances made in the mathematical, physical, and astronomical sciences, and the invention of many new scientific instruments, together with the publication of improved textbooks and scientific tables, like those mentioned in the preceding chapter, stimulated interest in other fields of science at the beginning of the seventeenth century.