HENRY SOTHERAN & CO., 140, STRAND, W.C., AND 43, PICCADILLY, W. 757 



15081 STEVINUS (Simon, de Bruges) ARITHMETIQUE, reveue corrigee et augmentee de plusieurs 

 Traictez et Annotations par ALBERT GiRARD ; with fine engraved title and diagrams, thick 8vo. 

 contemporary white vellum (somewhat browned, but a FINE COPY); very rare, 2. 15* 



Leide, de VImprimerie des Elzeviers, 1625 



This edition contains the author's Arithmetique theorique, first published in 1585, his ' Arithmetique pratique', and 

 'Les Six Premiers Livtes d'Algebre de Diophante d'Alexaudrie, dont les quatre premiers sont traduicts et expliquez par 

 Simon Stevin, et les deux derniers par Albert Girard.' 



In it appeared first ' La Pratique d'Arithmetique' (pp. 695-822), La Disme, enseignant facilement expedier par nombres 

 entiers sans rornpuz, tous cornptes se rencontrans aux affaires des Hommes ' (pp. 823-49), and ' Traicte" des Incommensur- 

 ables Grandeurs, avec Appendice de 1'explication du IQe livre d'Euclide (pp. 850-85). 



1 La Disme ' contains, according to Prof, de Morgan, ' the first announcement of the use of decimal fractions.' 

 ' He introduced in his Arithmetic exponents to mark the power to which quantities were raised ... He further sug- 

 gested the use of fractional (but not negative) exponents, and a decimal system of weights and measures. His geometry 

 is ingenious . . . Some theorems on perspective are enumerated.' W. W. R. Ball. 



15082 De BEGHINSELEN der WEEGHCONST: De WEEGHDAET: De BEGHINSELEN des WATER- 



WICHTS ; all first editions, with vignette on titles, and numerous woodcuts and diagrams, 3 vols. 

 sm. 4to. in 1, old white vellum (first title slightly soiled, and a few slight water-stains, otherwise 

 FINE COPIES) ; excessively rare, 7- 15s ' ibidem, CHRISTOFFELL PLANTIJN, 1586 



15083 THE SAME, 3 vols. in 1, hf- citron calf, as good as new (neat library stamp on third title, 



otherwise remarkably fine and exceptionally tall copies), 9. 9s 



'It is however on his Statics and Hydrostatics, published (in Flemish) at Leyden in 15S6, that his fame rests. In 

 these works he enunciates the triangle of forces a theorem which some think was first propounded by Leonardo da Vinci. 

 Stevinus regards this as the fundamental proposition of the subject. Previous to the publication of his work the science 

 of statics had rested on the theory of the lever, but subsequently it became usual to commence by proving the possibility 

 of representing forces by straight lines, and thus reducing many theorems to geometrical propositions, and in particular to 

 obtaining in this way a proof of the parallelogram (which is equivalent to the triangle) of forces . . . Stevinus also found 

 the force which must be exerted along the line of greatest slope to support a given weight on an inclined plane a problem 

 the solution of which had been long in dispute. He further distinguishes between stable and unstable equilibrium. In 

 hydrostatics he discusses the question of the pressure which a fluid can exercise, and explains the so-called hydrostatic 

 paradox.' W. W. R. Ball. 



A full account of this classic of statics will be found in Prof. E. Mach's ' Science of Mechanics.' The above original 

 editions are excessively rare, the work being generally quoted by historians of mathematics from the Latin translation 

 in the rep r int in Hypomnemata Mathematica. 



15084 STIFEL (Michael) ARITHMETIC^ INTEGRA, cum Praefatione PHILIPPI MELANCHTHONIS, 

 editio princeps; with numerous diagrams, thick sm. 4to. old calf (back of binding damaged, 

 title mounted, and a few wormholes in blank margin, nevertheless a SOUND COPY) ; very rare, 

 5. 5* Norimbergce, apud Johan. Petreium, 1544 



' The first two books deal with surds and iucommensurables, and are Euclidean in form. The third is on algebra, and 

 is noticeable for having called general attention to the German practice of using the signs + and - to denote addition and 

 subtraction. ... It used to be said that Stifel was the real inventor of logarithms, but it is now certain that this opinion 

 was due to a misapprehension of a passage in which he compares geometrical and arithmetical progressions. Stifel is said 

 to have indicated a formula for writing down the coefficients of the various terms in the expansion of (1 + x)n if those in 

 the expansion of (1 + x)n-\ were known.' -W. W. R. Ball. 



15085 STILLMANN (Thomas Bliss) ENGINEERING CHEMISTRY: a Manual of QUANTITATIVE 

 CHEMICAL ANALYSIS for the Use of Students, Chemists, and Engineers, 3rd Edition [enlarged] , 

 with 139 illustrations, 8vo. cl., 9s (p. 19* nett) Easton, Pa., 1905 



15086 STIRLING (James, F.R.S.) LINEJE TERTII ORDINIS NEUTONIAN^:, sive Illustratio Tractatus 

 D. NEUTONI de Enumeratione Linearum Tertii Ordinis, cui subjungitur, Solutio trium Probleni- 

 atum ; with numerous diagrams, and view of Sheldonian Theatre on title, 8vo. old calf (joints 

 cracked), with auto, of Michael Fryer (VERY RARE), i. 5s Oxonice, 1717 



' It supplied four additional varieties to' Newton's seventy-two forms of the cubic curve.' D. N. B. The work forms a 

 necessary supplement to Newton's Enumeratio Linearum III. Ordinis (v. Nos. 12572-3 ante). It contains a long list of 

 subscribers, including Sir Isaac Newton. A note by Michael Fryer (1806) on the flyleaf states : ' Extremely rare cost me 

 cbl Is. JM, F* 



15087 METHODUS DIFFERENTIALS : sive Tractatus de SUMMATIONE et INTERPOLATIONS 



SERIERUM INFINITARUM, editio princeps ; with diagrams, 4to. large and sound copy in con- 

 temporary calf gilt (name cut off title] ; very rare, 2. Londmi, 1730 



15088 - ANOTHER COPY, contemporary calf, with bookplate of, and MS. notes by, Philip 2nd 

 Earl Stanhope, F.R.S. (fine copy), 2. 2s 



15089 EDITIO SECUNDA ; with diagrams, 4to. hf. calf (joints cracked), with bookplates o/[SiR] 



GEORGE PRETYMAN [TOMLINE] , Bp. of Winchester, William Pitt's tutor and biographer, and 

 Prof. Lloyd Tanner, F.R.S. (RARE), 1. 10s ibidem, 1764 



15090 The DIFFERENTIAL METHOD : or a Treatise concerning Summation and Interpolation 



of Infinite Series, translated, with the Author's Approbation, by FRANCIS HOLLIDAY, with 

 diagrams, 1749 : The Two BOOKS of APOLLONIUS PERG^EUS, concerning TANGENCIES, as they 

 have been restored by Franciscus Vieta and Marinus Ghetaldus, with a Supplement by JOHN 

 LAWSON, pr., with 6 plates, Cambridge, '642 vols. 4to. in 1, hf. bound (first title mounted), with 

 autos. of Michael Fryer and Samuel Roberts, F.R.S., and MS- notes by the former (VERY RARE), 

 1. 15s 1749-64 



This work is of importance in the history of the differential calculus, as haying been the first to give the proof of 

 what is known as ' Maclaurin's theorem ' [v. Nos. 2761-3, ante] ; but, save for Montucla, who gives a full account in his 

 Histoire des mathematiques, v. Ill, pp. 223-7, and Cantor (Vorlesungen, iib. Gesch. d. Mathematik, Bd. Ill pp. 025-30), the 

 work is curiously enough almost unnoticed in modern histories of mathematics. 



' La premiere partie de cet ouvrage a pour objet la sommation des suites dans lesquelles chaque terme est forme du 

 precedent, multiplie par une fonction rationnelle de son rang. Un grand nombre des resultats sont fort interessants .... 

 Ses recherches presentent quelque utilite dans certaines questions speciales dependant du calcul des probabilites. ' M . Marie. 



15091 STKEETEB (Edwin William ; jeweller) GOLD : Legal Regulations for the Standard of Gold 

 and Silver Wares in different Countries of the World, translated and abridged from the Work of 

 A. v. STUDNITZ by MRS. BREWER, with Notes and Additions; 6th Edition, enlarged, with 2 

 coloured plates, and map, post 8vo. cl. (scarce), 8s 1878 



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