172 HENRY SOTHERAX & CO., 140, STRAND, W.C., AND 37, PICCADILLY, W. 



3428 OZANNE (Nicolas Marie ; brother of the foregoing] MARINE MILITAIRE, ou Recueil des differens 

 VAISSEAUX qui servent a la Guerre, suivi des Manoeuvres qui out le plus de raport an Combat ainsi 

 qua 1'Ataque et la Defence des Ports ; 50 fine vignettes on copper, with text engraved beneath, roy. 

 Svo. FINE COPY in contemporary French mottled calf gilt (RARE), 1. 10s [c. 1760] 



3429 [PACIOLI (Luca, Orel. Min'.}} SUMA de ARITHMETICA GEOMETRIA PROPORTIONI & PROPOR- 

 TIONALITA ; sig. j surrounded by fine ivoodcut border, also numerous woodcuts and geometrical 

 figures on margin after LEONARDO DA VINCI, besides large woodcut initials, 2 vols. folio in 1, gutfitr 



letter ; oldhf. vellum (blank margin of title and of a few other II. mended, 2 pp. soiled, and blank corner 

 of 3 II. cutoff, otherwise a VERY SOUND AND LARGE COPY, measuring 11 x 8 inches); very 

 rare, 9. 15s [last leaf:] Vinegia . . . Paganino de Paganini da Brescia. M.CCCC.LXLIIIJ 



[1494] . adi. 10. de nougbre. 

 The above constitutes THE EARLIEST PRINTED BOOK ox ALOEBRA. Hain-Copinger 4105. Proctor 51US. 



3430 ANOTHER COPY, hf. parchment ; wanting f. 24 of vol. If, some II. wormed, last I. mended, 

 also partly water-stained, but a VERY LARGE COPY (12 x 8 inches], 6. Qs 



The above copy is in a very rare state (probably uniijui-) in having no woodcut border round sig. a, and in a large 

 number of the smaller woodcut initials, as well as the large one on sig. al being left out, while for a large initial on page 1 

 of vol. II is substituted one of a wholly different design. 



3431 - - SECONDA EDIZIONE : SUMMA de ARITHMETICA, GEOMETRIA, PROPORTIONI, et PROPOR- 

 TIONALITA, nouamente impressa ; with fine woodcut border on title and first leaf of text, and num- 

 erous fine woodcut initials (one giving the author's portrait), besides numerous diagrams on margin, 

 folio, otf)tC lettfT ; hf. vellum (title slightly mended, otherwise a fine copy] ; VERY RARE, 6. 



[col. :]per PAGANINO, in Tusculano sidla ri'va dd laco Benacense, 1523 



3432 ANOTHER COPY, hf. russia extra (an exceptionally fine and tall copy, measuring 

 llf x 8| inches), 7. 17s Qd 



The above second edition is as rare as the first, and perhaps preferable to it. on account of its typographical execution. 

 The author, perhaps better known as LUCA r>i BORGO [or BURGO], the name he took on entering religion, was the first to 

 introduce symbols in algebra. 



' In the arithmetic Pacioli gives rules for the four simple processes, and a method for extracting square roots. He 

 deals pretty fully with all questions connected with mercantile arithmetic, in which he works out numerous examples, and 

 in particular discusses at </reat length bills of exchange and the theory of book-keeping by double entry. This part was 

 then the first systematic exposition of algoristic arithmetic. . . . In the algebra he discusses in some detail simple and 

 quadratic equations, and problems on numbers which lead to such equations. He mentions the Arabic classification of 

 cubic equations, but adds that their solution appears to be as impossible as the quadrature of the circle. . . . Though 

 much of the matter described is taken from Leonardo's Liber Abaci, yet the notation in which it is expressed is superior to 

 that of Leonardo,' etc. etc. etc. W. W. R. Ball. 



' In the mathematical writings of the monk Luca Pacioli symbols began to appear. They consisted merely in abbrev- 

 iations of Italian words, such as p for pin, m for me no, co for cosa . . . ' Prof. Cajori. 



3433 PADOVANI (Giovanni de ; Latine JOANNES PADUANIUS, Veronensis) De COMPOSITIONS, et 

 Usu MULTIFORMIUM HoROLOGlORUM SOLARIUM ad omnes totius Orbis Regiones, ac Situs in 

 qualibet Superticie ; nunc denuo multis in Locis illustratum et auctum ; adiectte sunt pra-terea 

 peculiares Method! ad dignoscenda stellarum loca, et supputandas quascunque tabulas, tain per 

 minutissimum calculum, quam per instrumentum nunquam hactenus ab ullo excogitate ; wdh 

 vignette on title, and numerous other woodcuts, 4to. old vellum, 1. 10s 



Venetiis, apud Franc. Franciscium, 15S2 



Houzeau-Lancaster No. 11,375. A VERY RARE WORK. An earlier edition, containing less than half the above, was 

 published in 1570. 



3434 PAGANI (Francesco, da Bagnacavallo] ARITHMETICA PRATTICA UTILISSIMA, artificiosamente 

 ordinata ; nella quale si contiene il vero, e facile MODO di CONTEGGIARE, con inolti Quesiti im- 

 portanti, e necessarij a Ragionieri. a Mercanti, et ad ogni persona, in tutti i Paesi, cr. 4to. , large 

 copy in old limp vellum, 1. 10s Ferrara, Vitt. Baldini, 1591 



A very rare work, quite unknown to Prof, de Morgan, who did not even mention it in his 'List of 1580 Names of 

 Reported Authors of Works on Arithmetic,' nor to PoggendorfT, Graesse, Brunet, and others. 



3435 PAGE (James Morris, Univ. Virginia) ORDINARY DIFFERENTIAL EQUATIONS, with Intro- 

 duction to LIE'S THEORY of the GROUP of ONE PARAMETER, post 8vo. cl., 3.v Qd (p. 6s Qd) 1897 



3436 PAINVIN (Louis) THEORIE des SURFACES POLAIRES d'un PLAN [Extrait, pp. 198] ; with 

 diagrams, Svo. cl., 2s Qd [1866] 



3437 PALAZ (Adrien, Lausanne) TREATISE on INDUSTRIAL PHOTOMETRY, with special Application 

 to ELECTRIC LIGHTING, trans, by GEORGE W. PATTERSON JR., and MKRIL ROWLEY PATTERSON, 

 with 92 illustrations and diagrams, roy. Svo. cl., Qs Qd ip. ]'2s Qd) New York, 189i 



The only work published on this subject. 



3438 PALLISER (John William) COMPLETE COURSE of PROBLEMS in PRACTICAL PLANE 

 GEOMETRY, diagrams, obi. 4to. cl., 2s Qd [1871] 



3439 PALMER (Charles, Gent.) TREATISE on the Sublime Science of HELIOGRAPHY, satisfactorily 

 demonstrating our Great Orb of Light, the SUN, TO BE ABSOLUTELY NO OTHER THAN A P>ODY OF 

 ICE ! Overturning all the received Systems of the Universe hitherto extant; proving the cele- 

 brated and indefatigable SIR ISAAC JSEWTON, in his Theory of the Solar System, to' be as far 

 removed from the Truth, as any of the HEATHEN AUTHORS of Greece or Rome, Svo. (pp. 54), 

 sewn (rare), 10s 1798 



The author burnt some tobacco with a burning glass, for which he found he could substitute a lens made of ice ; which 

 led him to the discovery that ' the sun is a crystalline body receiving the radiance of God,' etc. etc. 



3440 PALMER (Major-Gen. Henry Spencer, U.K.) The ORDNANCE SURVEY of the KINGDON : its 

 Objects, Mode of Execution, History, and present Condition. Svo. cl., 2s Qd 1873 



3441 PALMIERI (Luigi, Univ. Naples) The ERUPTION of VESUVIUS in 1872, with Notes and Intro, 

 on the present State of Terrestrial Vulcariicity, the Cosrnical Nature and Relations of Vulcanoes 

 and Earthquakes, etc., by ROBERT MALLET, F.R.S. ; 8 plates, roy. Svo. cl. (scarce), 8s Qd 1873 



Important for the editor's preface (pp. 7S), in which lie lays the foundation 'of his theory of the fracturing and folding 

 origin of The earth's crust. 



