Volume 1

Arithmetica universalis : sive de compositione et resolutione arithmetica liber / Auctore Is. Newton. [Anon].

  • Newton, Isaac, 1642-1727.
Date:
1722
Catalogue details

Licence: Public Domain Mark

Credit: Arithmetica universalis : sive de compositione et resolutione arithmetica liber / Auctore Is. Newton. [Anon]. Source: Wellcome Collection.

    55/346 (page 47)
    VIFISORVM. — 7, &— 13 inferius, ac tento ii fubdudlis his de numeris 27 ac 12 qui flant e regione in quarta columna differentias dividunt iflos 170 & 190 qui flant e regione in columna fecunda. Et quidem differentia inter 27 & — 7 id efl 34 dividit 170 & differentia 12 & — 7 id efl 19 dividit 190. Item differentia inter 27 & 17 id efl 10 dividit 170 fed differentia inter 12 & — 13 id efl 25: non dividit 190. Quare pofleriorem progreffionem rejicio* Juxta priorem f C efl — 7, & * B nihil; terminis progreffionis nullam habentibus differentiam. Qua¬ re divifor tentandus All ± B l£ C, erit 377 + 7. Et divifio fuccedit, prodeuntey*— 277 — 27 + 2. Si nullus inveniri potefl hoc padto divifor qui fuccedit, concludendum efl quantitatem propofi- tam non admittere divi forem duarum dimenfio- num. Poffet eadem methodus extendi ad inven¬ tionem diviforum dimenfionum plurium, queren¬ do in prediclis fummis differentiifque progreflio- nes non arithmeticas quidem fed alias quafdem quarum terminorum differentie prime, fecunde, tertie, &c. funt in arithmetica progreffione: At in his Tyro non efl detinendus. Ubi in quantitate propofita dua funt Utera, & omnes ejus termini ad dimenfiones aque altas afcendunt; pro una ijlarum literarum pone unitatemy dein per regulas pr ace dentes quare divifor em, ac diviforis hujus comple de~ fidentes dimenfiones reftituendo literam illam pro unitate. Ut fi quantitas fit 6y4 — cf — 21 ccyy + 3 cy + 20 c4 ubi termini omnes funt quatuor dimenfio- numj pro c pono 1, quantitas evadit <5y4 — y* — 2177+ 37+20, cujus divifor ut fupra efl 37+4, & completa deficiente dimenfione poflerioris termini per dimenfionem c, fit 37+ 4C divifor quefitus. Ita fi quan titas fit x4 — b x3 — 5 b b x x + 12 x — 6 b* y pofito 1 pro b, & quantitatis refultantis x4 — — 5 * x Hr 12 x ~ 6 invento divifore x x +