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.

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    — 2yy'&y6 — 4toy'> -r 400y*: = o. Etpermul- tiplicationem idooj5 — 20800y5 —p 67600y4 = o. Ac reducendo 4^ — 52 jy + idp = o. Sive (ra¬ dice extrada) 2^—13 = 0 feu ^ == d4, Id quod etiam brevius alia methodo fed minus obvia fupra inventum eft. Porro ut inveniatur x fubflitue d4 pro y in aequatione x x ^ ^ x + )) = °. Et ex¬ urget xx — 134* + 424 = °) feu x x = 134x 4- 42 4. Et extrada radice x = d~ + vel —V^-V- Nempe df + V 3-nr cft maximus qua? fi torum trium numerorum-, & d-f-—Vy-r? minimus. Nam x alterutrum extremorum numerorum ambigue de- fignat, indeque gemini prodeunt valores, quorum yy alteruter potefl ede x, exiflente altero —— y y Idem aliter. Pofitis numeris x, y Sc — ut ante, x y y ^ v erit x + y + = 20, feu xx= ^ x— yj&ex- x y 20 trada radice x = 10 —- \y + V100 —10 y \yy ^ y y primus numerus: Hunc & y aufer de 20 & reflat — = io — ^y — V100 — 10y — y tertius numerus. Eflque fumma quadratorum a tribus hifce numeris 400 — 40 y, adeoque40o — 40 jy — 140,(1 vejy = d4* Invento medio numero <54, fubflitue eum pro y in primo ac tertio numero fupra invento; & evadet primus 6i + ac tertius 6\ — V3-rV ut ante. PROB. XIV. Invenire quatuor numeros continue proportionales quo¬ rum duo medii fimul conftituant 12, & duo extremi 20.