Universal arithmetick: or, a treatise of arithmetical composition and resolution. To which is added, Dr. Halley's method of finding the roots of aequations arithmetically / Translated from the Latin by the late Mr. Raphson, and revised and corrected by Mr. Cunn.
- Newton, Isaac, 1642-1727. Arithmetica universalis. English
- Date:
- 1720
Licence: Public Domain Mark
Credit: Universal arithmetick: or, a treatise of arithmetical composition and resolution. To which is added, Dr. Halley's method of finding the roots of aequations arithmetically / Translated from the Latin by the late Mr. Raphson, and revised and corrected by Mr. Cunn. Source: Wellcome Collection.
300/310 page 268
![[26871 | when the Signs are different, e is z— V/ TE — i; But after itis found that it will be — e, let the Powers 20 au £', Cc. in the affirmative Members of the /Equation be made Negative, and in the N-gative be’ made Affirmative ; that is, let them be written with the contrary Sign. On the other hand, if it be + e (let thofe foremention'd Powers) be made Affirmative in the Affirmitive, and Negative in the Negative Members of the /Equation. | Now we have in this Example of ours, 10450 inftead of the Refolvend 10000, or b= +450, whence it’s plain, that 4 is taken greater than the Truth, and confequently, that ‘tis —e. Hence the Aquation comes to be, 10450 — 4015€ 7r 597ee — 4€ -Fe*—1coo0. That is, 450 — 4015é-F §97¢€ =o ; and fo 450 —4018Se—«27ee, or 45s—bDt $ b=—se—tee, whofe Root PIRE EY oat I eran po 2t ss b Peas en — — -3 that is, in the prefent Cafe; Ath] E 200713 — Y 2761406 $ £L 30$ from whence we have the Root 597 | fought, 9,886, which is near the Truth. -But then fubfti- tuting this for a fecond Suppofition, there comes 4 4- e — x, moft accurately, 9,8862603936495..-. fcarce exceeding the 7 Truth by ‘2 iB.the laf Figure, viz. When f/i:5 + bt | t —-$fz£ And this (if need be) may be yet much far- ther verify'd, by fubtracting (if it be +e) the Quantity Zuei>+ie4 2 TE j QXTUETP from the Root before found or (i£ it be —e) s 5 het ig ae or ae E ‘by adding AP Gee pane: - j to that Root, Which Compendium 3 Md ATTI ! e 3sfo much the more valuable, in that fometimes from the firft Suppofition alone, but always from the fecond, a Man may continue the Calculus (keeping the fame Co-efficients) as far as he pleafes, It may be noted, that the fore-menti- ond /Equation has alfo a Negative Root,viz. z — 10,26... . which any one that has a Mind, may determine more. ac- curately. : | AD EXAMPLE](https://iiif.wellcomecollection.org/image/b30538579_0300.jp2/full/800%2C/0/default.jpg)
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