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



6343 BORDIER-MARCET (J. A., successeur & Ami Argand, inventeur de lampes) NOTIONS sur 



1'AREOMETRK CENTIGRADE, 1'ALAMBIC AMBULANT, et le PLASTRON NAUTIQUE ; with plate 



(stained), 8vo. (pp. 48), sewn, 5s 



THE FIRST BOOK OF ARITHMETIC : 



6344 BORGO [o BORGI] (Piero, da Venesia) LIBRO de ABACHO. [F. 2a :] Qui comenza la 

 nobel opera de | arithmethica ne la qual se tracta tutte cosse amercantia pertinente 

 | facta z compilata p Piero borgi | da veniesia ; printed in tjotjjic letter, with numerous 

 woodcut initials, sm. 4to. newly and finely bound in polished brown Levant morocco extra, 

 rough g. e., by W. PRATT (title very neatly mended, a few other II. slightly margined or 

 repaired, also parts of a few letters on ff. 9 and 10 defective through wormhole, otherwise 

 a FINE AND VERY LARGE COPY), 40. [coZ. :] Nela incllta cita de venetia 



a corni. 2. augusto. 1484. fu impostofine ala presente opera 



FIRST EDITION OF THE FIRST PRINTED TREATISE ON ARITHMETIC, AND OF EXCESSIVE RARITY. No copy has happened 



for sale at auction within the last 22 years, and probably not for many years before. The Libri copy, sold in 1861, is the 

 last sale-record that can be traced. 



It consists of one unnumbered leaf with verses, beginning ' Chi de arte matematiche ha piacere, Che tengon di certeca 

 el primo grado . . . ', 116 numbered 11., and one unnumbered 1. of Table, or signatures a o in eights and p in six. On the 

 reverse of the last 1. are verses in Italian, from which it can be gathered that the edition was printed by Erhard Ratdolt of 

 Augsburg. The above copy is, save for the few defects mentioned, in a most desirable condition, and uniform in binding 

 with the following copy of the second edition. 



(3345 SECONDA EDIZIONE. [F. 2a:] Qui come/a la nobel opera de | arithmeticha ne 



laqualse tracta | tutte cosse amercantia pertinen- | te facta z compilata per Piero | borgi 

 da Vieniesia ; printed in gotfjtc letter, with numerous woodcut initials, sm. 4to. newly 

 and finely bound in polished brown Levant morocco extra, rough g. e., by W. PRATT, 

 uniform with the above (an exceptionally fine and large copy), 2L 



\_col. .-] Stampito in Veniema per zoudne de HalV 1498 



5346 ANOTHER COPY, boards (slight hole in first 2 and last 4 II. , also some II. 



water-stained, or slightly soiled, otherwise a SOUND AND VERY LARGE COPY), 14. 14s 



This second edition is also of great rarity, although to a less degree than the first. It consists of i0 unnumbered 11., 

 or signatures a m in eights, the first 1. having on obverse the verses contained in the first edition. The table and verses 

 at end contained in the first edition are however absent in this as well as in all other editions. 



6347 QUARTA EDIZIONE. [F. la :] LIBRO De ABACHO. [F. 2a :] Qui comeza la nobel opera de 



arith | meticha ne laqual se tratta tutte cos- | se a mercantia pertinente fatta z com | pifata per 

 Piero Borgi da Venesia ,; printed in Roman character, with Sessa' s cat and mouse on title, and 

 numerous woodcut initials, sm. 4to. vellum cover from a XlVth Century MS. (small hole in title, 

 otherwise a FINE AND LARGE COPY), 8. 85 



[col:] Impressa in Venetia per Zuane Baptista Sessa. 1501. a di. 10. Decembrio. 

 With MS. index in an old hand. 



6348 ANOTHER COPY, boards (title guarded, but a SOUND AND CLEAN COPY), 6. 6* 



6349 ANOTHER COPY, sewn (f. 8 in fs., and a number of blank corners gnawed; also water- 

 stained, but a very tall copy], 3. 105 



This edition, the first printed by Sessa, was unknown to Graesse, who mentions however all the other editions. It 

 consists of 96 numbered 11., or signatures A M in eights. 



6350 QUINTA EDIZIONE. [F. la:] LIBRO De ABACHO. [F. 2a :] Qui comeza la nobel opera de 



arith | meticha ne laqual se tracta tute cose a | merchatia pertinente facta z copilata | per Miser 

 Piero borgi da Venesia ; printed in Roman characters, with woodcut initials, sm. 4to. contemporary 

 oaken boards (Jialfof one missing], with leathern back andclasp, and flyleaves from a XIV th Century 

 MS. on vellum (some II. wormed, and a few blank corners slightly worn, otherwise A VERY SOUND 



AND EXCEPTIONALLY LARGE COPY), 5. 5* 



[col. :] Stampata in Venetia per Jacomo pentio \ anno diii. 1509. adi. 5. de novembre. 

 This edition, containing 6 pp. of additions, consists of 100 numbered 11. (the last 4 being misnumbered 91 -4), or signatures 

 A M in eights, and N in four. 



6351 BE8TA EDIZIONE. [F. la:] LIBRO De ADACHO. [F. 2a:] Qui comeza la nobel opera de 



arith | meticha ne laqual se tracta tutte co | se a merchantia pertinente facta | i compilata per Miser 

 Piero bor | gi da Venetia ; Dinted in Roman characters, with small woodcut initials, sm. 4to. old 



Vellum (A VERY SOUND AND LARGE COPY), 3. 3s 



[col. .] Stampata Venetia per Jacomo pentio da Lecho ad insta \ tia de Marchio 

 Sessa ufc Piero di Rauani compagni \ anno dili. 1517. adi. 25. de zugno. 



The collation of the above edition corresponds exactly with that of the foregoing. The above copy contains a MS. index 

 in an old hand. 



'Tutte le edizioni di questa operetta, ma in particolare le prime, sono ricercatissime dai bibliografi. 1 Riccardi. 



1 Toutes les editions de cet Abacho sont dilticiles a trouver, et depuis quelques annees on les recherche beaucoup.' Brunei. 



' The author begins by saying that there are plenty of sufficiently good masters, and not less abundance of most excellent 

 authors. His arrangement of the five acts of arithmetic is strange ; they are numeration, multiplication, partition, 

 summation, and subtraction. He uses the word million, and his numeration goes to millions of millions of millions. He 

 then proceeds to multiplication, and forms a table of the nine multiples of 1, 2 ... 10, with those or 12, 10, 20, 24, 32, 

 and 30. He then points out how to prove processes by casting out sevens and nines; in doing which he shews how to 

 divide by 7, and uses the sum of the digits to find the remainder 9. Then follow multiplications done each in one line, even 

 when the multiplier has threo or four figures. . . . Division is said at the head of a chapter, to be done in three ways ; but 

 only two are given : that per cholnna, where the whole is done in one line, and that per latelo. Subtraction is then 

 explained ; and after some applications, the rules for fractions (which are expressed in the same way as now' are introduced. 

 The rule of three {rlegdv del tre) is given, and a large number of money applications.' Prof, de Morgan. 



The first two editions are by most bibliographers mistakenly quoted as a different work. 



The work was reprinted in 1528, 1540, 1550, l"i>l, and 1507. 



