264 HENRY SOTHERAN & CO., 140, STRAND, W.C, AND 37, PICCADILLY, W. 



5183 WALLIS (Johannes, d.d., s.e.s., Prof. Savilianus) Opera Mathematica ; with fine portrait 

 after Sonmans of the author wt. 83, besides numerous diagrams, 3 vols, folio, old calf gilt (very 

 rare), £4. 105 'Oxonioe, e Theatro Sheldomano, 1695-3-9 



Comprising also the author's editions of ancient authors, viz. : Claudius Ptolemtt-us ; Porphyry ; i\ranuel Bryennius • 

 Archiniedes's Arenarius, and Dimensio Circuli ; Aristarchus ; and Pappus ; as well as his voluminous correspondence with 

 various mathematicians. 



Vol. II contains the first published account of Sir Isaac Newton's invention of the fluxional calculus. 



' In mathematical history Wallis ranks as the greatest of Newton's English precursors. He was as laborious as he was 

 original ; and, by the judicious use of his powers of generalisation, he prepared all the subsequent discoveries of that age. 

 The principles of analogy and continuity were introduced by him into mathematical science. His interpretation of 

 negative exponents and unrestricted employment of fractional exponents greatly widened the range of higher algebra. 

 Finally, he invented the symbol for infinity, CD.'—Miss A. M. Gierke. 



5184 Opera Mathematica ; with folding plate, and numerous diagrams, 2 vols. sm. 4to. 



sound copy in old vellum, £1. 12s Qd ibidem, L. Lichfield, 1657-6 



5185 Another Copy, with Commercium Epistolicum, de Quaestionibus quibusdam Mathe- 



maticis, edidit Johannes Wallis ; with diagrams, Oxonii, 1658 — 3 vols. sm. 4to. in 2, contemp- 

 orary calf {back of binding of v. I slightly damaged, otherwise A VERY SOUND COPY), £2. 5* 



The first collected edition of the author's works then published, comprising: Oratio Inavgurulis ; Mathesis Univer- 

 salis, embodying the substance of his professorial lectures ; Adversus Meibomii de Proportlonibus Dialogum, TracicUvs 

 Elencticus ; de Anqulo Contactus; de Sectionibus Conicis, the first clear exposition of Descartes's invention of analytical 

 geometry ; Arithmetica Infinitorum, his most important work, ' the most stimulating mathematical work so far published 

 in England, and containing the germs of the differential calculus ' ; Eclipscos Solaris Observatio. Each of these treatises has 

 a separate titlepage and pagination. 



The above edition was unknown to Lowndes, Allibone, Watt, and Poggendorff, and is very rare ; while most of the 

 treatises it contains appear here for the first time. 



5186 Grammatica Lingua Anglicans, cui praefigitur, de Loquela sive Sonorum Form- 



ATIONE, Tractatus Grammatico-Physicus, et (nunc primuni) subjungitur, Praxis Grammatica, 

 Ed. IV., prioribus avictior, 12mo. old calf (fine copy), \0s Qd ib., apud eundem, 1674 



5187 De Loquela, sive Sonorum P'ormatione, Ed. VI. : Jo. Conradi Amman Surdus 



LOQUENS, sive Dissertatio de Loquela, qua non solum Vox liumana, et loquendi artitieium ex 

 originibus suis eruuntur, sed et traduntur media quibus Surdi et Muti loquelam adipiscantur — 

 2 vols. 16mo. in 1, boards, with bookplate of Charles 3rd Earl Stanhope, F.E.S., 12s 6d 



Lugd. Batav., 1727 



Wallis's ' De Loquela' was originally published with his 'Grammatica Linguie Anglicanae', and describes in detail the 



various modes of production of articulate sounds. It led Amman, the writer of the second tract, to his invention of a 



method for imparting the art of speech to deaf-mutes. The above edition of Amman's work has a letter from Wallis 



prefixed. 



5188 MechanicA: sive, de MoTU, Tractatus Geometricus, Pars I. in qua, de Motu 



Generalia ; de Gravium Descensu, et Motuum Declivitate ; de Libra. Pars II. in qua, de Centro 

 Gravitatis, ejusque Calculo ; with finely engraved portrait by W. Faithorne, and folding plates^ 



2 vols. 4tO. in 1, VERY fine and large copy in THE ORIGINAL CALF (VERY RARE), £1. \()S 



Londini, Gul. Godbid, 1670 



One of the classics of mechanics, containing the first exhaustive treatment of the theory of the collision of bodies con- 

 sidered as imperfectly elastic bodies— being the solution of a problem propounded by the Royal Society— while Sir 

 Christopher Wren and Huygens treated the subject simultaneously, but confined their theory to perfectly elastic bodies. 

 On these investigations, according to Prof. Macii, Sir Isaac Newton based his researches c ntained in the Principia, 



' Wallis gelit von dejii Grundsatze aus, dass das Moment, das Produkt aus der Masse (Pondu.s) und der Geschwindigkeit 

 (Celeritas), bei dem Stosse maassgebend sei. Durch dieses Moment wird die Kraft des Stos.ses bestimmt. Stossen zwei 

 (unelastische) Korper mit gloinhen Momenten aufeinander, so besteht nach dem Stoss Ruhe. Bei ungleichen Momenten 

 ergibt die Differenz der Momente das Moment nach dem Stosse.' — Prof. Mach. 



5189 Treatise of Algebra, both Historical and Practical, with some Additional Treatises, 



I. Of the Cono-Cuneus. II. Of Angular Sections, III. Of the Angle of Contact. IV. Of Com- 

 binations, Alternations, and Aliquot Parts, first edition, with folding plates, and numerous 

 diagrams, folio, old ca^/(RARE), £\.\s J. Playford, 1685 



5190 Another Copy, old stamped white vellum [fine copy), £1. 5* 



Both the above copies contain at end ' A Brief (but full) Account of the Doctrine of Trigonometry, both Plain and 

 Spherical ', by John Caswell (pp. 17), 16S5. 



'In 1685 Wallis published an Algebra, preceded by an historical account of the development of the subject, which 

 contains a great deal of valuable information. This algebra is noteworthy as containing the first systematic use of formula;. 

 A given magnitude is here represented by the numerical ratio which it bears to the unit of the same kind of magnitude ', 

 etc. etc. etc.— IF. W. R. Ball. 



6191 : Commercium Epistolicum, de Qutestionibus quibusdam Mathematicis nuper habitum, 



inter D. GULIELMUM Vicecomitem Brouncker ; D. Kenelmum Digby, Equitem Anglum ; D. 

 Fermatium, in suprema Tholosatum Curia Judicem Primarium ; D. Freniclum, Nobilem 

 Parisinum. Una cum D. JOH. Wallis Geomet : Profess : Oxonii. D. Franc : A Schooten, Math : 

 Prof: Lugd. Bat.; Aliisque, edidit Johannes Wallis, S.Th.D. ; with diagrams, sm. 4to. old 

 mottled calf , rebacked {fine and large copy) ; RARE, with Westminster School bookplate, 18^ Qd 



Oxonii, A. Lichfield, 1658 

 The letters by Fermat and Frenicle (on the theory of numbers), are of importance, and have, with the sole exception of 

 the author's complete works, never been reprinted. 



V. Aristarchus, ante. 



5192 WANDELAINCOURT (Abbe Antoine Hubert) Le Manuel des Jeunes Physiciens, ou 

 Nouvelle Physique El^mentaire, contenant les D^couvertes les plus curieuses et les plus utiles ; 

 with woodcuts. 16mo. hf. rvssia, 5s Verdun, 1778 



5193 WANKLYN (James Alfred), and W. J. COOPER: Air-Analysis : a Piaclical Treatise, 

 with Appendix on Illuminating Gas. 9 plates, besides woodcuts, cr. 8vo. cL, 2s fid (p. 5s) 1890 



5194 , and Ernest Theophron CHAPMAN: W ater- Analysis : a Practical Treatise, 



10th Ed., revised, woodcuts, cr. Svo. cL, 2s 6c? (p. 5a) 1S96 



5195 WANNAN (A. C, C.E., and E. W. I., m.i.m.e.) Marine Engineer's Guide to Board of 

 Trade Examinations, with front, and numerous illustrations, post Svo. cZ., 3* (p. 8* 6c?) 1898 



