2i2 HENRY SOTHERAN & CO., 140, STRAND, W.C., AND 37, PICCADILLY, W, 



4741 TANNER (Henry S.) DESCRIPTION of the CANALS and RAIL ROADS of the UNITED STATES, 

 comprehending Notices of all the Works of Internal Improvement throughout the several States, 

 with fine folding maps, roy. 8vo. cl., 10-s Gd New York, 1840 



An interesting account of U. S. railways in their infancy. Appended is a Glossary of Railway Terms (pp. 30). 

 Although railways were a purely English invention, it must have been satisfactory to Mr. B. Sawin to be assured in the 

 preface that 'the general extension of railways in the United States is one effect of that enlightened constitution of 

 Government which impresses an indelible mark of distinction between the enterprizing American and the plodding 

 inhabitant of the other hemisphere '. 



4742 TANNERY (Paul) La GEOMETRIE GRECQUE, comment son Histoire nous est parvenue et ce 

 qu'on nous en savons. I re Partie [seule parue] : Histoire ge"nerale de la Geometric elementaire, roy. 

 bvo. scivn, 3s 1887 



4743 TARTAGLIA [sive TARTALEA] (Niccolo) : OPERE del FAMOSISSIMO NICOLO TARTAGLIA, 

 cioe QUESITI, TRAVAGLIATA INVENTIONS, NOVA SCIENTIA, RAGIONAMENTI sopra ARCHIMEDE ; 

 with portrait on 3 titles, and numerous other fine woodcuts, and folding plan, 4 vols. sm. 4to. in 1, 

 old limp vellum (RARE), 1. 10s Venetia, 1606 



Apparently the last edition of the above four works published, and the only one with a collective title. 



EUCLIDE MEGARENSE v. No. 1237, ante. 



4744 - - GENERAL TRATTATO di NUMERI, et MISURE; with portraits (duplicated), and numerous 

 diagrams, 6 vols. folio in 2, old vellum (back of binding of v. I damaged, title of v. Ill margined 

 and stamped, a few II. wormed, and a number slightly water-stained, but on the whole a sound and 

 large copy] ; very rare, 2. 15s ibidem, per Curtio Troiano, 1556-60 



Forming to some extent a continuation of the Arithmetica (q. v. infra). ' In this he showed how the coefficients of x 

 in the expansion of (l + x] n could be calculated, by the use of an arithmetical triangle, from those in the expansion of 

 (1 + #) l for the cases when n is equal to 2, 3, 4, 5, or 6. The treatise on arithmetic and numbers is one of the chief 

 authorities for our knowledge of the early Italian algorism. It is verbose, but gives a clear account of the different arith- 

 metical methods then in use, and has numerous historical notes which, as far as we can judge, are trustworthy, and are 

 ultimately the authorities for many of the statements in the last chapter [of Mr. Ball's 'History of Mathematics']. It 

 contains an immense number of questions on every kind of problem which would be likely to occur in mercantile arith- 

 metic, and there are several attempts to frame algebraical formula 1 , suitable for particular problems. These problems 

 give incidentally a good deal of information as to the ordinary life and commercial customs of the time,' etc. etc. etc. 

 W. W. R. Ball. 



4745 TUTTE 1'OPERE d' ARITHMETICA, nelle quali in XVII Libri con varie Prove, & Ragioni, 



mostrasi ogni Prattica Naturale, & Artificiale, i Modi, & le Regole da gli Antichi, & Moderni 

 usate nell' ARTE MERCANTILE; & ove interviene Calcolo, Pesi, Denaii, Tariffe, Calmeri, Baratti, 

 Cambi di Banchieri, ecc. ; with device on titles, 2 vols. sm. 4to. in 1, old Italian vellum (first title 

 stained) ; VERY RARE, 1. 5s ib., 1592-3 



A reprint of the first volume of the Tratlato di Numeri (q. v. supra). 



4746 La NOVA SCIENTIA, con una Gionta al Terzo Libro ; with woodcut title, and woodcuts, 



[col.:] Venetia, Nic. de Bascarini, 1550: QUESITI, et INVENTIONI DiVERSi ; prima edizione; 

 with fine portrait, and other woodcuts, and diagrams, ib., Vent. Euffinelli, 15462 vols. sm. 4to. 

 in 1, very sound copies in Italian vellum, 1. 5s 1546-50 



4747 NEW EDITIONS OF BOTH WORKS, with woodcut title, and numerous woodcuts and 



diagrams, 2 vols. sm. 4to. in 1, old limp vellum (binding damaged, the 2nd work wanting title and 

 preliminary II. , and some U. slightly wormed), 15s [col. :] Vinegia, 1558-62 



In the Nova Scientia the author investigates the fall of bodies under gravity, and first makes known the theorem that 

 the range of projectiles is largest if the angle of projection is 45 ; while in the Qucsiti (which contains a dedication to 

 Henry VIII.) the author claims the invention of the theorem for solving cubic equations (known as ' Cardan's Formula '), 

 which was treacherously published by Cardan in 1545 as his own in his Ars Magna. See No. 684, ante. It further 

 contains investigations on gunnery, the composit ion of Gunpowder, the invention of which the author ascribed to Archimedes, 

 and chapters on fortification ; and gives interesting autobiographical information. 



4748 QUESITI, et INVENTIONI DIVERSE, prima edizione, with portrait, woodcuts, and 



diagrams (title stained and mended), [col.:] Venetia, 1546: La NOVA SCIENTIA, con una Gionta al 

 Terzo Libro; with woodcut title, woodcuts and diagrams, ib., 1551: REGOLA GENERALE da 

 SULEVARE con RAGIONE e MISURA no solamete ogni affondata Nave ; ma una Torre Solida di 

 Mettallo, trovata da Nicola Tartaglia, delle discipline Mathematice amatore intitolata la 

 TRAVAGLIATA INVENTIONS, prima edizione; with portrait (different from that in ' Quesiti'), 

 and woodcuts (ib., 1551): RAGIONAMENTI sopra la sua TRAVAGLIATA INVENTIONS, nelli quali se 

 dechiara volgarmente quel libro di Archimede Siracusano intitolato de Insidentibus Aqiifle, con 

 altre Speculative Pratiche da lui ritrovate sopra le Materie, prima edizione, ib., 15514 vols. 

 sm. 4to. in 1, old Italian vellum, 2. 5s 1546-1551 



4749 _ GLI STESSI ('Regola' e ' Ragionamenti ' delle prime edizioni), with 3 portraits (one 

 duplicated), and numerous fine woodcuts and diagrams ; 4 vols. sm. 4to. in 1, old vellum gilt 

 (FINE COPIES), 2. 2s ibidem, 1550-4 



4750 REGOLA GENERALE da SULEVARE con RAGIONE e MISURA no solamete ogni affondata 



Nave ; ma una Torre Solida di Metallo .... intitolata la TRAVAGLIATA INVENTIONS : RAGIONA- 

 MENTI sopra la sna TRAVAGLIATA INVENTIONS, 2 vols. sm. 4to. in 1, both first editions, with 

 2 portraits (duplicated), and other fine woodcuts ; old limp vellum (large and fine copies], 15s 



ibidem [1551J-51 

 The first work contains an account of some ingenious contrivances for lifting and salving submerged vessels. 



4751 - - RISPOSTE (V) a Messer LUDOVICO FERRARO et HIERONIMO CARDANO [over Dispute 

 Mathematice], 5 pamphlets : QUINTO CARTELLO di LODOVICO FERRARO contra Messer Nicolo 

 Tartaglia; with diagrams in. 1 vol. sm. 4to. Italian white vellum extra, 3. 15s 



ib., lotf-8Milano, 1547 



EXCESSIVELY RARE, and unknown to Graesse and Poggendorff, and important in connexion with the origin and history 

 of Cardan's Formula. ' Ouvrage fort rare dont on ne connait qu'un eeul exemplaire, celui que M. Silvestro Gherardi a ced6 

 & M. Libri, apres 1'avoir reproduit a Cologne, en 1846.' Brunei. 



