450 Prof. De Morgan on the Additiofis made to the 



which the new editors say, " Hinc innotuit Methodum Tan- 

 gentium Gregorii et Slusii ex niethodo Barrovii consequi." 

 Here consequi, as to Gregory, means by his statement, that 

 his /cjwwledge of his own method came from his knowledge of 

 Barrow's ; and tliere is every appearance of the word being 

 intended to apply in the same manner to Shisius. 



V. (29, 103). The note is new. It is immaterial, and merely 

 amounts to reminding the reader that several is at least txvo. 



VI. (30, 105). The following note is new. "* Sc. in trac- 

 tatu quem Ncwtonus scripsit Anno 1671. Missum autem fuit 

 Apographum hujus Epistolae ad Tscurnhausiwn mense Maio 

 1675, et ad Leibnitium mense Junio 1676." The assertion 

 about Leibnitz will presently occur more definitely. How 

 the fact was known with reference to Tschirnhausen is not 

 stated. 



VII. (37, 113). The first sentence of the note, consisting of 

 the three words " Imo observata fuit," is new. Slight as the 

 matter is, the general tendency of the additions to bring out the 

 unfairness of the original, and to convert hints into assertions, 

 is curiously exemplified. The reader will see that the meaning 

 of the addition is as follows : — Leibnitz says it is wonderful that 

 Pascal did not notice, that when the binomial coefficients are set 

 down in rows, the columns are the triangular, pyramidal, &c. 

 (or what were also caWeiXjigurate) numbers. The note of the 

 old editors says in effect, " He did not exactly notice this, but 

 still you are not much in advance of Pascal, lor the latter did 

 note a very remarkable property of these columns, which is 

 known to belong to the figurate numbers." But the words 

 added by the new editors turn the note into " He did notice 

 it, and you are 7iot at cdl in advance of Pascal, for, &c." 

 Leibnitz was quite right, and the more so from Pascal's know- 

 ledge of the property. Both the original and the augmented 

 notes are unmerited comments on the modest remark by which 

 Leibnitz accompanies his natural expression of wonder, " Sed 

 est profecto casus quidam in inveniendo, qui non semper 

 maximis ingeniis maxima, sed so3pe etiam mediocribus non- 

 nuUa offert." 



VIII. ('■)7, 114 and 1 1 5). One of the connecting comments 

 runs thus in the two editions. 



First Edition. Seeo?id Edition. 



Quinetiam duae aliaj D. Hactenus D. Leibnitius in 



Leibnitii ad Oldenburgum Arithmeticaversabatur,jamad 



Epistola?, altera Anno 1674' Geometriam se convertit, et 



Julii 1.5, altera Octob. 26 Anno proximo ad Oldenbur- 



sequente, Parisiis datse, le- gium scribit Epistolas duas 



