[514] Giovanni Alphonso Borelli (1608-1679) was professor of mathematics at Messina (1646-1656) and at Pisa (1656-1657), after which he taught in Rome at the Convent of St. Panteleon. He wrote several works on geometry, astronomy, and physics.

[515] See Vol. I, page 172, note 2 {381}.

[516] Ignace Gaston Pardies (c. 1636-1673), a Jesuit, professor of ancient languages and later of mathematics and physics at the College of Pau, and afterwards professor of rhetoric at the College Louis-le-Grand at Paris. He wrote on geometry, astronomy and physics.

[517] Pierre Fermat was born in 1608 (or possibly in 1595) near Toulouse, and died in 1665. Although connected with the parliament of Toulouse, his significant work was in mathematics. He was one of the world's geniuses in the theory of numbers, and was one of the founders of the theory of probabilities and of a.n.a.lytic geometry. After his death his son published his edition of Diophantus (1670) and his _Varia opera mathematica_ (1679).

[518] This may be Christopher Townley (1603-1674) the antiquary, or his nephew, Richard, who improved the micrometer already invented by Gascoigne.

[519] Adrien Auzout a native of Rouen, who died at Rome in 1691. He invented a screw micrometer with movable threads (1666) and made many improvements in astronomical instruments.

[520] See Vol. I, page 66, note 9 {86}.

[521] See Vol. I, page 124, note 7 {248}.

[522] John Machin (d. 1751) was professor of astronomy at Gresham College (1713-1751) and secretary of the Royal Society. He translated Newton's _Principia_ into English. His computation of [pi] to 100 places is given in William Jones's _Synopsis palmariorum matheseos_ (1706).

[523] Pierre Remond de Montmort (1678-1719) was canon of Notre Dame until his marriage. He was a gentleman of leisure and devoted himself to the study of mathematics, especially of probabilities.

[524] Roger Cotes (1682-1716), first Plumian professor of astronomy and physics at Cambridge, and editor of the second edition of Newton's _Principia_. His posthumous _Harmonia Mensurarum_ (1722) contains "Cotes's Theorem" on the binomial equation. Newton said of him, "If Mr. Cotes had lived we had known something."

[525] See Vol. I, page 135, note 3 {281}.

[526] See Vol. I, page 377, note 4 {769}.

[527] Charles Rene Reyneau (1656-1728) was professor of mathematics at Angers. His _a.n.a.lyse demontree, ou Maniere de resoudre les problemes de mathematiques_ (1708) was a successful attempt to popularize the theories of men like Descartes, Newton, Leibnitz, and the Bernoullis.

[528] Brook Taylor (1685-1731), secretary of the Royal Society, and student of mathematics and physics. His _Methodus incrementorum directa et inversa_ (1715) was the first treatise on the calculus of finite differences. It contained the well-known theorem that bears his name.

[529] Pierre Louis Moreau de Maupertuis (1698-1759) was sent with Clairaut (1735) to measure an arc of a meridian in Lapland. He was head of the physics department in the Berlin Academy from 1745 until 1753. He wrote _Sur la figure de la terre_ (1738) and on geography and astronomy.

[530] Pierre Bouguer (1698-1758) was professor of hydrography at Paris, and was one of those sent by the Academy of Sciences to measure an arc of a meridian in Peru (1735). The object of this and the work of Maupertuis was to determine the shape of the earth and see if Newton's theory was supported.

[531] Charles Marie de la Condamine (1701-1774) was a member of the Paris Academy of Sciences and was sent with Bouguer to Peru, for the purpose mentioned in the preceding note. He wrote on the figure of the earth, but was not a scientist of high rank.

[532] See Vol. I, page 136, note 5 {283}.

[533] See Vol. II, page 296, note 483.

[534] Thomas Baker (c. 1625-1689) gave a geometric solution of the biquadratic in his _Geometrical Key, or Gate of Equations unlocked_ (1684).

[535] See Vol. I, page 160, note 5 {350}.

[536] See Vol. I, page 87, note 4 {133}.

[537] See Vol. I, page 132, note 2 {272}.

[538] See Vol. I, page 118, second note 1 {231}.

[539] The name of Newton is so well known that no note seems necessary. He was born at Woolsthorpe, Lincolnshire, in 1642, and died at Kensington in 1727.

[540] John Keill (1671-1721), professor of astronomy at Oxford from 1710, is said to have been the first to teach the Newtonian physics by direct experiment, the apparatus being invented by him for the purpose. He wrote on astronomy and physics. His _Epistola de legibus virium centripetarum_, in the Philosophical Transactions for 1708, accused Leibnitz of having obtained his ideas of the calculus from Newton, thus starting the priority controversy.

[541] Thomas Digges (d. in 1595) wrote _An Arithmeticall Militare Treatise, named Stratioticos_ (1579), and completed _A geometrical practise, named Pantometria_ (1571) that had been begun by his father, Leonard Digges.

[542] John Dee (1527-1608), the most famous astrologer of his day, and something of a mathematician, wrote a preface to Billingsley's translation of Euclid into English (1570).

[543] See Vol. I, page 76, note 3 {112}.

[544] Thomas Harriot (1560-1621) was tutor in mathematics to Sir Walter Raleigh, who sent him to survey Virginia (1585). He was one of the best English algebraists of his time, but his _Artis a.n.a.lyticae Praxis ad Aequationes Algebraicas resolvendas_ (1631) did not appear until ten years after his death.

[545] Thomas Lydiat (1572-1626), rector of Alkerton, devoted his life chiefly to the study of chronology, writing upon the subject and taking issue with Scaliger (1601).

[546] See Vol. I, page 69, note 3 {96}.

[547] Walter Warner edited Harriot's _Artis a.n.a.lyticae Praxis_ (1631).

Tarporley is not known in mathematics.

[548] See Vol. I, page 105, note 2 {186}.

[549] See Vol. I, page 115, note 3 {224}.

[550] See Vol. II, page 300, note 509.

[551] See Vol. I, page 107, note 1 {190}.

[552] Sir Samuel Morland (1625-1695) was a diplomat and inventor. For some years he was a.s.sistant to John Pell, then amba.s.sador to Switzerland. He wrote on arithmetical instruments invented by him (1673), on hydrostatics (1697) and on church history (1658).

[553] See Vol. I, page 153, note 4 {337}.

[554] See Vol. I, page 85, note 2 {129}.

[555] See Vol. I, page 43, note 8 {33}.

[556] See Vol. I, page 43, note 7 {32}.

[557] See Vol. I, page 382, note 13 {786}. The history of the subject may be followed in Braunmuhl's _Geschichte der Trigonometrie_.

[558] See Vol. I, page 377, note 3 {768}.

[559] See Vol. I, page 108, note 2 {192}.

[560] Michael Dary wrote _Dary's Miscellanies_ (1669), _Gauging epitomised_ (1669), and _The general Doctrine of Equation_ (1664).

[561] John Newton (1622-1678), canon of Hereford (1673), educational reformer, and writer on elementary mathematics and astronomy.

[562] See Vol. I, page 87, note 4 {133}.