HENRY SOTHERAN & CO., 140, STRAND, W.C., AND 43, PICCADILLY, W. 645 



12912 [PACIOLI (Luca, hie Lucas de Burgo Sancti Sepulcri, Ord. Mm.) SITMA de ARITHMETICA 

 GEOMETRIA PROPORTIONI & PROPORTIONALITA, prima edizione ; sig. a l surrounded by fine 

 woodcut border, also numerous woodcuts and geometrical figures on margin after LEONARDO DA 

 VlNCl, besides large woodcut initials (the first containing the AUTHOR'S PORTRAIT), 2 vols. folio in 

 1, gotfjic letter; newly and finely bound in hf. brown polished Levant morocco gilt, rough q. e. 

 (29 II. margined or very neatly mended on margin, and a few II. slightly soiled ; otherwise a very 

 fine and exceptionally tall copy, measuring 12 x 8J inches] ; very rare, 11. 11s 



[col. :] Vinegia . . . Paganino de Paganini da Brescia. 

 M.CCCC.LXLIIIJ [1494]. adi. 10. de noucbre. 



12913 ANOTHER COPY, unbound (wanting the first 9 and last 20 II., partly water-stained, and a 



few II. wormed), cheap, 2. 2s 



' Certainly the FIRST PRINTED WORK ON ALGEBRA AND PROBABLY THE FIRST ON BOOK-KEEPING.' Prof, de Morgan. 

 Hain-Copinger, 4105. Proctor 5168. 



There is another issue of this edition (a fact not noticed by bibliographers, e.g., Brunet or Graesse), in which the 

 woodcut border is absent, and the fine woodcut initials are replaced by smaller ones. 



12914 [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, gofbtc letter; boards (last 25 II. holed, rendering text of last 10 II. defective; also title 

 margined and guarded) ; VERY RARE, cheap, 3. 3s 



[col. :] per Paganino, in Tusculano sulla riva dil laco Benacense, 1523 



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 DI 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 great 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. E. Ball. 



1 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 r neno, co for cosa . . . ' Prof. Lajori. 



' II y a dans oe grand recueil une methode fort ingenieuse pour la resolution de plusieurs equations indeterminees du 

 second ou du quatrieme degre. . . . On y voit la resolution des equations derivees du second degre, et celle de certaines 

 equations exponentielles. Dans quelques problemes relatifs a la regie des partis, le calcul des probabilites se montre 

 pour la premiere fois. . . . Enfin on y trouve 1'application de 1'algebre a la geometric et une multitude de faits, relatifs ;\ 

 di verses branches des connaissances humaines et fort utiles aux personnes qui veulent etudier 1'histoire des sciences. 

 C'est, par example, dans un traite de commerce insere dans cette Somme, que Ton trouve pour la premiere fois la tenue 

 des livres en partie double,' etc. etc. etc. G. Libri. 



12915 PAGE (David, F.G.S., Prof. Geol., Durham Coll. of Science) ADVANCED TEXT-BOOK of 

 GEOLOGY [with GLOSSARY (pp. 35)], 4th Edition, enlarged, with numerous woodcuts, cr. 8vo. cl., 3s 

 (p. 7s Qd) 1867 



12916 FIFTH EDITION, enlarged, with numerous woodcuts, cr. 8vo. (pp. 488), cl., 3s Qd (p. 7* Qd) 



Edin., 1872 



12917 PAGE (James Morris, Univ. Va.) On the PRIMITIVE GROUPS of TRANSFORMATIONS in SPACE 

 of FOUR DIMENSIONS: Inaugural Dissertation at Leipzig, roy. 4to. (pp. 54), sewn, 3s Baltimore, 1888 



12918 PAGE (Thomas, M.I.C.E.) REPORT on the SYSTEM of WEAVING by COMPRESSED AIR in the 

 PATENT PNEUMATIC LOOM [of CHARLES WEIGHTMAN HARRISON], 4to. (pp. 19), sewn, with 

 author's inscr., 4s Qd Cambridge, 1864 



12919 PAGE (Sir Thomas Hyde, R.E. ; F.R.S.) ESTIMATE of the EXPENSE for carrying into Execu- 

 tion the PLAN of EMBANKMENT for the IMPROVEMENT of the DRAINAGE of the SOUTH and 

 MIDDLE LEVELS, and other Lands having their Drainage through the RIVER OUSE, and for the 

 Improvement of its Navigation, etc. etc., with folding map, 8vo. (pp. 29), sewn, with marginal 

 MS. notes (? by JOHN RENNIE, F.R.S. ), 7s Qd 1794 



' He was chief engineer for forming the New Cut from Eau Brink to King's Lynn, a problem of navigation and drainage 

 that has puzzled engineers since the time of Charles I.' D. N. B. 



12920 PAJOT des CHARMES (0., Inspecteur des Manufactures] L'ART du BLANCHIMENT des 

 TqiLES, FILS et COTONS de tout Genre, rendu plus facile et plus general, au Moyen des NOUVELLES 

 DECOUVERTES, avec la Methode de DECOLORER et de ramener a un Etat de Blancheur parfait 

 toutes les TOILES PEINTES ou IMPRIMEES ; suivi des Precedes les plus surs pour blanchir les 

 Soies et les Laines, et des De"couvertes faites par 1'Auteur dans 1'ART de BLANCHIR les PAPIERS, 

 premiere edition; with 9 folding copperplates, Svo. hf. red morocco, by BELZ-NIEDREE (rare), 

 15s " 1798 



12921 [NOUVELLE EDITION, corrigee] ; with folding copperplates, Svo. sewn, 10s An F///[1800] 



Interesting as an early work describing the chlorine bleaching process, discovered by Berthollet in 1785. 



12922 PALMER (Henry R., M.I.C.E.) DESCRIPTION of a RAILWAY on a NEW PRINCIPLE; with 

 Observations on those hitherto constructed, and TABLE shewing the comparative Amount of 

 RESISTANCE on several now in Use, also an Illustration of a newly observed Fact relating to the 

 Friction of Axles, and Description of an IMPROVED DYNAMOMETER, for ascertaining the Resist- 

 ance of Floating Vessels and Carriages moving on Roads and Railways ; 2nd Edition, revised, 

 with 2 folding plates, Svo. (pp. 68), sewn (SCARCE), 15s 1824 



This was perhaps the first suggestion lor a monorail line, as afterwards reduced to practice on the Lartigue system, as 

 on the Listowel and Ballybunion Railway. It was to follow the contour of the country, slightly raised on posts or trestles, 

 the trucks being drawn by a horse walking beside it. One plate gives a general view of the line, and the other con- 

 fftructional details. The resistance tables are compiled from the Cheltenham, Llanelly, and other tramroads of the time. 



The work is not mentioned by Allibone. nor can anything be traced concerning its author. 



43 



