LEIBNITZ. S3 



metical Triangle, he adds, "Adjiciemus hie Theoremata quorum 

 TO on ex ipsa tabula manifestum est, to Slotl ex tabulae funda- 

 niento." The only theorem here that is of any importance is that 

 which we should now express thus : if n be prime the number of 

 combinations of n things taken r at a time is divisible by n. 



(4) A passage in which Leibnitz names his predecessors may 

 be quoted. After saying that he had partly furnished the matter 

 himself and partly obtained it from others, he adds, 



Quis ilia primus detexerit ignoramus. Scliwentenis Belie. 1. 1, Sect. 1, 

 prop. 32, apud Hieronymum Cardanum, Johannem Buteonem et 

 Nicolaum Tartaleam, extare dicit. In Cardani tameu Practica Arith- 

 metica quae prodiit Mediolani anno 1539, nihil reperimus. Inprimis 

 dilucide, quicquid dudum habetur, proposuit Christoph. Clavius in Com. 

 supra Joh. de Sacro Bosco Spliaer. edit. Bomte forma 4ta anno 1785. 

 p. 33. seqq. 



With respect to Schwenter it has been observ^ed, 



Schwenter probably alluded to Cardan s book, " De Proportionibus," 

 in which the figurate numbers are mentioned, and their use shown in 

 the extraction of roots, as employed by Stifel, a German algebraist, 

 who wrote in the early part of the sixteenth century. Lubbock and 

 Drinkwater, page 45. 



(5) Leibnitz uses the symbols -1 = in their present sense ; 



he uses -— ^ for multiplication and --^ for division. He uses the 

 word productiun in the sense of a sum : thus he calls 4 the pro- 

 ductum of 3 + 1. 



46. The dissertation shews that at the age of twenty years 

 the distinguishing characteristics of Leibnitz were strongly de- 

 veloped. The extent of his reading is indicated by the numerous 

 references to authors on various subjects. We see evidence too 

 that he had already indulged in those dreams of impossible achieve- 

 ments in which his vast powers were uselessly squandered. He 

 vainly hoped to produce substantial realities by combining the 

 precarious definitions of metaphysics with the elementary tniisms 

 of logic, and to these fruitless attempts he gave the aspiring titles 

 of universal science, general science, and philosophical calculus. 

 See Erdmann, pages 82 — 91, especially page 84. 



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