340 



NOTES AND QUERIES. 



[2"<i S. IX. May 5. *C0. 



mentariorum librum IIII.' • A Francisco Barocio Pa- 

 tritio Veneto' . . . ' editi ' . . . ' Excudebat Gratiosus 

 Perchacinus.' Folio. 



The words " vide et Gem. in 6 lib. Geometri- 

 carum enarrationum " in the margin of p. 262. may 

 be a reference by Barorius to Geminus. 

 The first edition of Leslie's work is — 

 Edinburgh, eighteeu-seventeen. Leslie, John. ' Phi- 

 losophy of Arithmetic; exhibiting a progressive view of 

 the theory and practice of calculation, with an enlarged 

 table of "the products of numbers under one hundred.' 

 Octavo. 



The title-page of the 1st ed. of Montucla's 

 Histoire differs from that of the 2nd only in the 

 presence of a motto from Bacon, and in the occur- 

 rence of ' M.' in place of Montucla's initials. 



It is sometimes difficult, not only to obtain a 

 correct description of a book, but to ascertain the 

 name of its author. Thus Murhard (vol. i. p. 

 139.) ascribes the work " De Characteribus Nu- 

 merorum Vulgaribus " to Joh. Fr. Weidler, 

 while the Penny Cyclopcedia (vol. xxvii. p. 192.) 

 informs us that this work is by J. F. and George 

 Immanuel Weidler, and Mr. De Morgan (whom it 

 seems almost as hopeless to detect in an inaccuracy 

 of detail as in an error of principle), in his Refer- 

 ences simply names " Weidler." 



Wallis, Weidler, Heilbronner, Leslie, Peacock, 

 Delambre and De Morgan may be placed among 

 the historians of arithmetic. 



Mr. De Morgan places the works of Decbales 

 and Wolf among the bibliographies, and in the 

 same list with those of Lipenius, Beughem, Ey- 

 rin<r, Murhard, Reuss, and Muller, and with the 

 " Einleitung zur Mathematischen Bucherkent- 

 niss." 



Lipsice, seventeen-ninety-seven. Mvrhard Frid. 

 Gvil. Avg., ' Bibliotheca Mathematical ' Volvmcn 

 Primvrn continens Scripta generaliade mathesi, de arith- 

 metica et geometria.' Octavo. 



Lipsice, seventeen -ninety-eight . . . . ' Volvmen 

 secundum continens scripta geometrica et analytica.' 

 Octavo. 



Lipsia, eighteen -three . . . ' Tomvs III. continens 

 scripta de scientiis mechanicis et opticis. Pars Prima.' 

 Octavo. 



Lipsia, eighteen-four. . . . ' Tomvs IV. continens 

 Scripta de scientiis mechanicis et opticis. Pars Secunda.' 

 Octavo. 



Each volume of Murhard's ' Bibliotheca Mathe- 

 matical or ' Litteratur der mathematischen Wis- 

 senschaften ' has a Latin as well as a German 

 title-page. So has the following : — 



Tubingm, eighteen-thirty. Rogg, J. ' Bibliotheca 

 Mathematica sive criticus librorum mathematicorum, 

 qui inde ab rei typographic* exordio ad anni It- $0 mi 

 usque finem excusi sunt, index ad varios usus commode 

 dispositus ab . . . .' ' Sectio I. Libros aritbmeticos et 

 geometricos complectens.' Octavo. The ' Prsefatio Kdi- 

 toris' opens with the statement ' Prima hujusce operis 

 sectio eos, qui ad scientiam arithmeticam et geometricam, 

 alias generatim matheseos puree nomine venientem spec- 

 tant, libros complectitur. Sectio altera in iis operibus, 

 qua? ad malhesin adplicatam pertinent, tota versabitur.' 



The following has an English title-page : — 



Leipsic and London, eighteen-fifty-four. Sohnckk, 

 L.A., Professor of Mathematics at Halle. ' Bibliotheca 

 Mathematica. Catalogue of Books in Every Branch of 

 Mathematics, Arithmetic, higher Analysis, constructive 

 and Analytical Geometry, Mechanics, Astronomy, and 

 Geodesy, which have been published in Germany and 

 other Countries from the Year 1830 to the Middle of 

 1854. Edited by [Sohncke], With a complete Index 

 of Contents.' Octavo. 



In connexion with the names of Wallis, Cossali, 

 and Hutton, who have treated specially of the 

 history of algebra, must be mentioned those of 

 Waring, Montucla, Strachey, Taylor, Colebrooke, 

 Rosen and Libri. 



Cantabrigia, seventeen -sixty two. Waring, Edward. 

 ' Miscellanea Analytica, de tcquationibus algebraicis et 

 curvarum proprietatibus.' Quarto. In the opening of 

 the ' Prefatio ' Waring, speaking of the ' Ars Analytica,' 

 says that ' De hujusce Scientiae Progressu, et qu» diversis 

 temporibus acceperit, incrementis, abs re baud alienum 

 erit pauca prrefari.' 



Less than three pages, however, would com- 

 prise all Waring's historical matter. 



Cantabrigian, seventeen-seventy. Waring, Edward. 

 ' Meditationes Algebraical.' Quarto. ' De incrementis 

 iis, qua; gradatim res ceperit algebraica, narratiouem hie 

 contexui brevem, ut sua inventoribus deferatur gloria; 

 atque ut iis simul, qui progressus artium investigant 

 curiosius, aliqua sit ex parte satisfactum. Ex historiis 

 clar. virorum Wallisii et Monteclu quasdam mutuatus 

 sum, quorum alter Harriotto nostrati nimis favet, alter 

 quidem gallicis scriptoribus, sed huuianum est sic errare,' 

 is the opening of the ' Prasfatio.' 



This second contribution of Waring to history, 

 comprised in four or five pages, is rather more 

 ample than the first. 



A short history of algebra was given in Hall's 

 Cyclopcedia, and a more elaborate one in Rees's. 



A paper ' On the early History of Algebra,' 

 by Edward Strachey is printed at pp. 158 — 185. 

 of vol. xii. (Calcutta, 1816), of the ' Asiatick 

 Researches.' 



London, eighteen-thirteen. Strachey, Edward, of 

 the East India Company's Bengal Civil Service. ■ Bija 

 Ganita: or the Algebra of the Hindus.' Quarto. 



Bombay, eighteen-sixteen. Taylor, John, M.D. of 

 the Hon'ble East India Company's Bombay Medical 

 Establishment. ' Lilawati : or a treatise on Arithmetic 

 and Geometry, by BHASCARA ACHARYA, trans- 

 lated from the original Sanscrit by . . .' Quarto. 



London, eighteeu-seventeen. Colebrooke, Henry 

 Thomas. ' Algebra, with Arithmetic and Mensuration, 

 from the Sanscrit of BRAHMEGUPTA and BHAS- 

 CARA.' Quarto. 



The following contains some little history and 

 the germ of recent mathematical discoveries : 



London, eighteen-fourteen. Spence, William. ' Out- 

 lines of a Theory of Algebraical Equations, deduced from 

 the principles of Harriott, and extended to the Fluxional 

 or Differential Calculus.' Octavo. 



This little tract was not intended for general 

 circulation, and it is stated, in Davis and Dick- 

 son's advertisement, or " Literary Intelligence " 



