[201] This appears in _J. Scaligeri cyclometrica elementa duo_, Lugduni Batav., 1594.

[202] Adriaen van Roomen (1561-1615) gave the value of [pi] to sixteen decimal places in his _Ideae mathematicae pars prima_ (1593), and wrote his _In Archimedis circuli dimensionem expositio & a.n.a.lysis_ in 1597.

[203] Kastner. See note 30 on page 43.

[204] Bentley (1662-1742) might have done it, for as the head of Trinity College, Cambridge, and a follower of Newton, he knew some mathematics.

Erasmus (1466-1536) lived a little too early to attempt it, although his brilliant satire might have been used to good advantage against those who did try.

[205] "In grammar, to give the winds to the ships and to give the ships to the winds mean the same thing. But in geometry it is one thing to a.s.sume the circle BCD not greater than thirty-six segments BCDF, and another (to a.s.sume) the thirty-six segments BCDF not greater than the circle. The one a.s.sumption is true, the other false."

[206] The Greek scholar (1559-1614) who edited a Greek and Latin edition of Aristotle in 1590.

[207] Jacques Auguste de Thou (1553-1617), the historian and statesman.

[208] "To value Scaliger higher even when wrong, than the mult.i.tude when right."

[209] "I would rather err with Scaliger than be right with Clavius."

[210] "The perimeter of the dodecagon to be inscribed in a circle is greater than the perimeter of the circle. And the more sides a polygon to be inscribed in a circle successively has, so much the greater will the perimeter of the polygon be than the perimeter of the circle."

[211] De Morgan took, perhaps, the more delight in speaking thus of Sir William Hamilton (1788-1856) because of a spirited controversy that they had in 1847 over the theory of logic. Possibly, too, Sir William's low opinion of mathematics had its influence.

[212] Edwards (1699-1757) wrote _The canons of criticism_ (1747) in which he gave a scathing burlesque on Warburton's Shakespeare. It went through six editions.

[213] Antoine Teissier (born in 1632) published his _Eloges des hommes savants, tires de l'histoire de M. de Thou_ in 1683.

[214] "He boasted without reason of having found the quadrature of the circle. The glory of this admirable discovery was reserved for Joseph Scaliger, as Scevole de St. Marthe has written."

[215] _Natural and political observations mentioned in the following Index, and made upon the Bills of Mortality.... With reference to the government, religion, trade, growth, ayre, and diseases of the said city._ London, 1662, 4to. The book went through several editions.

[216] _Ne sutor ultra crepidam_, "Let the cobbler stick to his last," as we now say.

[217] The author (1632-1695) of the _Historia et Antiquitates Universitatis Oxoniensis_ (1674). See note 163, page 98.

[218] The mathematical guild owes Samuel Pepys (1633-1703) for something besides his famous diary (1659-1669). Not only was he president of the Royal Society (1684), but he was interested in establishing Sir William Boreman's mathematical school at Greenwich.

[219] John Graunt (1620-1674) was a draper by trade, and was a member of the Common Council of London until he lost office by turning Romanist.

Although a shopkeeper, he was elected to the Royal Society on the special recommendation of Charles II. Petty edited the fifth edition of his work, adding much to its size and value, and this may be the basis of Burnet's account of the authorship.

[220] Petty (1623-1687) was a mathematician and economist, and a friend of Pell and Sir Charles Cavendish. His survey of Ireland, made for Cromwell, was one of the first to be made on a large scale in a scientific manner. He was one of the founders of the Royal Society.

[221] The story probably arose from Graunt's recent conversion to the Roman Catholic faith.

[222] He was born in 1627 and died in 1704. He published a series of ephemerides, beginning in 1659. He was imprisoned in 1679, at the time of the "Popish Plot," and again for treason in 1690. His important astrological works are the _Animal Cornatum, or the Horn'd Beast_ (1654) and _The Nativity of the late King Charls_ (1659).

[223] Isaac D'Israeli (1766-1848), in his _Curiosities of Literature_ (1791), speaking of Lilly, says: "I shall observe of this egregious astronomer, that there is in this work, so much artless narrative, and at the same time so much palpable imposture, that it is difficult to know when he is speaking what he really believes to be the truth." He goes on to say that Lilly relates that "those adepts whose characters he has drawn were the lowest miscreants of the town. Most of them had taken the air in the pillory, and others had conjured themselves up to the gallows. This seems a true statement of facts."

[224] It is difficult to estimate William Lilly (1602-1681) fairly. His _Merlini Anglici ephemeris_, issued annually from 1642 to 1681, brought him a great deal of money. Sir George Wharton (1617-1681) also published an almanac annually from 1641 to 1666. He tried to expose John Booker (1603-1677) by a work ent.i.tled _Mercurio-Coelicio-Mastix; or, an Anti-caveat to all such, as have (heretofore) had the misfortune to be Cheated and Deluded by that Grand and Traiterous Impostor of this Rebellious Age, John Booker_, 1644. Booker was "licenser of mathematical [astrological] publications," and as such he had quarrels with Lilly, Wharton, and others.

[225] See note 171 on page 100.

[226] This is the _Ars Signorum, vulgo character universalis et lingua philosophica_, that appeared at London in 1661, 8vo. George Dalgarno antic.i.p.ated modern methods in the teaching of the deaf and dumb.

[227] See note 200 on page 110.

[228] If the hyperbola is referred to the asymptotes as axes, the area between two ordinates (x = a, x = b) is the difference of the logarithms of a and b to the base e. E.g., in the case of the hyperbola xy = 1, the area between x = a and x = 1 is log a.

[229] "On ne peut lui refuser la justice de remarquer que personne avant lui ne s'est porte dans cette recherche avec autant de genie, & meme, si nous en exceptons son objet princ.i.p.al, avec autant de succes." _Quadrature du Cercle_, p. 66.

[230] The t.i.tle proceeds: _Seu duae mediae proportionales inter extremas datas per circulum et per infinitas hyperbolas, vel ellipses et per quamlibet exhibitae_.... Rene Francois, Baron de Sluse (1622-1685) was canon and chancellor of Liege, and a member of the Royal Society. He also published a work on tangents (1672). The word _mesolabium_ is from the Greek [Greek: mesolabion] or [Greek: mesolabon], an instrument invented by Eratosthenes for finding two mean proportionals.

[231] The full t.i.tle has some interest: _Vera circuli et hyperbolae quadratura cui accedit geometriae pars universalis inserviens quant.i.tatum curvarum trans.m.u.tationi et mensurae. Auth.o.r.e Jacobo Gregorio Abredonensi Scoto ... Patavii_, 1667. That is, James Gregory (1638-1675) of Aberdeen (he was really born near but not in the city), a good Scot, was publishing his work down in Padua. The reason was that he had been studying in Italy, and that this was a product of his youth. He had already (1663) published his _Optica promota_, and it is not remarkable that his brilliancy brought him a wide circle of friends on the continent and the offer of a pension from Louis XIV. He became professor of mathematics at St Andrews and later at Edinburgh, and invented the first successful reflecting telescope. The distinctive feature of his _Vera quadratura_ is his use of an infinite converging series, a plan that Archimedes used with the parabola.

[232] Jean de Beaulieu wrote several works on mathematics, including _La lumiere de l'arithmetique_ (n.d.), _La lumiere des mathematiques_ (1673), _Nouvelle invention d'arithmetique_ (1677), and some mathematical tables.

[233] A just estimate. There were several works published by Gerard Desargues (1593-1661), of which the greatest was the _Brouillon Proiect_ (Paris, 1639). There is an excellent edition of the _Oeuvres de Desargues_ by M. Poudra, Paris, 1864.

[234] "A certain M. de Beaugrand, a mathematician, very badly treated by Descartes, and, as it appears, rightly so."

[235] This is a very old approximation for [pi]. One of the latest pretended geometric proofs resulting in this value appeared in New York in 1910, ent.i.tled _Quadrimetry_ (privately printed).

[236] "Copernicus, a German, made himself no less ill.u.s.trious by his learned writings; and we might say of him that he stood alone and unique in the strength of his problems, if his excessive presumption had not led him to set forth in this science a proposition so absurd that it is contrary to faith and reason, namely that the circ.u.mference of a circle is fixed and immovable while the center is movable: on which geometrical principle he has declared in his astrological treatise that the sun is fixed and the earth is in motion."

[237] So in the original.

[238] Franciscus Maurolycus (1494-1575) was really the best mathematician produced by Sicily for a long period. He made Latin translations of Theodosius, Menelaus, Euclid, Apollonius, and Archimedes, and wrote on cosmography and other mathematical subjects.

[239] "Nicolaus Copernicus is also tolerated who a.s.serted that the sun is fixed and that the earth whirls about it; and he rather deserves a whip or a lash than a reproof."

[240] "Algebra is the curious science of scholars, and particularly for a general of an army, or a captain, in order quickly to draw up an army in battle array and to number the musketeers and pikemen who compose it, without the figures of arithmetic. This science has five special figures of this kind: P means _plus_ in commerce and _pikemen_ in the army; M means _minus_, and _musketeer_ in the art of war;... R signifies _root_ in the measurement of a cube, and _rank_ in _the army_; Q means _square_ (French _quare_, as then spelled) in both cases; C means _cube_ in mensuration, and _cavalry_ in arranging batallions and squadrons. As for the operations of this science, they are as follows: to add a _plus_ and a _plus_, the sum will be _plus_; to add _minus_ with _plus_, take the less from the greater and the remainder will be the sum required or the number to be found. I say this only in pa.s.sing, for the benefit of those who are wholly ignorant of it."

[241] He refers to the _Joannis de Beaugrand ... Geostatice, seu de vario pondere gravium secundum varia a terrae (centro) intervalla dissertatio mathematica_, Paris, 1636. Pascal relates that de Beaugrand sent all of Roberval's theorems on the cycloid and Fermat's on maxima and minima to Galileo in 1638, pretending that they were his own.

[242] More (1614-1687) was a theologian, a fellow of Christ College, Cambridge, and a Christian Platonist.

[243] Matthew Hale (1609-1676) the famous jurist, wrote a number of tracts on scientific, moral, and religious subjects. These were collected and published in 1805.

[244] They might have been attributed to many a worse man than Dr. Hales (1677-1761), who was a member of the Royal Society and of the Paris Academy, and whose scheme for the ventilation of prisons reduced the mortality at the Savoy prison from one hundred to only four a year. The book to which reference is made is _Vegetable Staticks or an Account of some statical experiments on the sap in Vegetables_, 1727.

[245] _Pleas of the Crown; or a Methodical Summary of the Princ.i.p.al Matters relating to the subject_, 1678.

[246] _Thomae Streete Astronomia Carolina, a new theory of the celestial motions_, 1661. It also appeared at Nuremberg in 1705, and at London in 1710 and 1716 (Halley's editions). He wrote other works on astronomy.

[247] This was the Sir Thomas Street (1626-1696) who pa.s.sed sentence of death on a Roman Catholic priest for saying ma.s.s. The priest was reprieved by the king, but in the light of the present day one would think the justice more in need of pardon. He took part in the trial of the Rye House Conspirators in 1683.

[248] Edmund Halley (1656-1742), who succeeded Wallis (1703) as Savilian professor of mathematics at Oxford, and Flamsteed (1720) as head of the Greenwich observatory. It is of interest to note that he was instrumental in getting Newton's _Principia_ printed.

[249] Shepherd (born in 1760) was one of the most famous lawyers of his day. He was knighted in 1814 and became Attorney General in 1817.