This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1803 Excerpt: ...or is = 1-2 + z-23, &c. 1 + 2 but although 1 arithmetically added to 2 is 3, yet we cannot put-= I-2 + 2-23 + &C 3 for fbr1-2 + 2', &c. was produced by dividing by 1+2, the numbers preserving that arrangement and being kept distinct in the same manner, as if they were algebraic symbols; neither is to be put by putting ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1803 Excerpt: ...or is = 1-2 + z-23, &c. 1 + 2 but although 1 arithmetically added to 2 is 3, yet we cannot put-= I-2 + 2-23 + &C 3 for fbr1-2 + 2', &c. was produced by dividing by 1+2, the numbers preserving that arrangement and being kept distinct in the same manner, as if they were algebraic symbols; neither is to be put by putting for 1 + I, i +-)+-- (i+-)+-, &c, but-cannot striUy be called the symbol or generating function of such a series, since the series is produced by an arbitrary process of which all traces are destroyed. Waring speaking, p. 355, Miscellanea Analy. of the series produced by the expansion of, &c. fays, ' revera forsan hisce seriebus haud assijinari possunt summae' mistaking I + II + I + I or-o either the meaning of the word sum, or the real nature of the operation by which the series were produced: he falls likewise into the same mistake as Euler and Leibnitz and makes, --;;--, r I + I 1 + I + 1 1=-, for is symbol of, or (employing the connecting sign = ) 1s=----+-----&c. 2 2 zs 24 I.... r II I I aga1n, 1s symbol of, or=. +--.---, &c. 5 3 + ' ' 3 3 33 34 and =1-7 + 2-?3 + &c. 1+3.'22 (1 + 2)t is symbol of, or is = 1---+ &c. (2 + 1)t = a +-+ &c. 2.2 8.2 and consequently, although 2 added to 1 is 3, yet cons1dering (1 + 2), (2 + 1)t as symbols, (1 +2)- is neither = 3 nor = (2 + 1)$. 26. It would appear strange, did we not know that clearness, and accuracy of conception, were not the characteristical excellencies of Euler's mind, that this great mathematician should have given an accurate definition of thesum of a series, yet confounded together the parts of the expression representing thesum: for he puts 1+2 + 4 + 8+ &c. =-1, P. 97. Institutiones Calc. Diff.: ' Dicamus ergo seriei cujus..
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Add this copy of The Principles Of Analytical Calculation to cart. $19.72, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
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Add this copy of The Principles Of Analytical Calculation to cart. $42.59, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
