A reply to a critical and monthly reviewer, in which is inserted Euler's demonstration of the binomial theorem / by Abram Robertson.

  • Robertson, Abram, 1751-1826.
Date:
1808
Catalogue details

Licence: Public Domain Mark

Credit: A reply to a critical and monthly reviewer, in which is inserted Euler's demonstration of the binomial theorem / by Abram Robertson. Source: Wellcome Collection.

Provider: This material has been provided by Royal College of Physicians, London. The original may be consulted at Royal College of Physicians, London.

    11/42 (page 9)
    multiplicemus ut feriem obtineamus huic produ&o [in] . [«] aequalem, quam facile patet hujufmodi fonna expref- fum iri: I -f- AX + ex2 + CX2 + D.t4 + EX5 etc. cujus coefficientes A, B, c, D, E etc. quemadmodum per binas literas in et n determinentur ut pateat; ipfam mul- tiplicationem faltem inchoemus. r i m [m] = i H . + a n— i x2 + etc. \n\ - i + —. x + —. . x2 + etc. L J i i a M • 0] m in m — I i -4- — 4 x ■ • • xx etc* i i a n + •—.x + I in n ' • 1 I i n ii —i XX &c. XX &c. Quod ft jam hoc prodiidtum inchoatum cum forma af- fumta i -f- Ax -f- bat2 + cx2 etc. qua idem produ&um ex- primi ponimus, comparemus, fiatim intelligitur, fore A = in in — I • m n nn — »,+ net E = —. ( . 1 . i a 111a five B = mm—m nn — n . in + n m + n—I + inn + unde fit b = . . a a i a §. 6. Quemadmodum hie duos primos coefficientes A et B, per literas m et rc-determinare licuit, ita manifefturn eft, ft fuperior multiplicatio ulterius continuaretur, inde etiam fequentes coefficientes c, d, e etc. per eafdem lite- ras vi et n deffniri poffe, quamvis calculus mox ita fieret moleftus, ut maximum laborem requireret. Interim ta^ men bine tuto concludere poffumus onines plane coeffi- cientes A, b, c, d, e etc ; certo modo per binas literas m et n determinari debere ; etiamfi ipfam rationem, qua quifque per has literas definitur, adhuc ignoremus, hie autein imprimis obfervari convenit, hanc compojitionis ration vein non ab indole literarum m et n pendere, fed perinde J'e ejje habituram, five ha liter# m ct n denotent numeros inte- gros