Correspondence of Sir Isaac Newton and Professor Cotes : including letters of other eminent men, now first published from the originals in the library of Trinity College, Cambridge; together with an appendix containing other unpublished letters and papers by Newton; with notes, synoptical view of the philosopher's life, and a variety of details illustrative of his history, by J. Edleston.

  • Isaac Newton
Date:
1850
Catalogue details

Licence: Public Domain Mark

Credit: Correspondence of Sir Isaac Newton and Professor Cotes : including letters of other eminent men, now first published from the originals in the library of Trinity College, Cambridge; together with an appendix containing other unpublished letters and papers by Newton; with notes, synoptical view of the philosopher's life, and a variety of details illustrative of his history, by J. Edleston. Source: Wellcome Collection.

    128/430 (page 22)
    velocity in D, tis evident y4 the arch CD will also be as x, & the Fluxion of ye space BD already described will be as • • — x. If therefore t be put for ye moment of time in which the fluxion of ye space - x, the fluxion of ye velocity v, the fluxion of yl resistance z are generated; You will have 11 ^ * 11 — — * II * 11 * 11 ^ || —7—, v || cc — z x t But % || vv & therefore z | vv | t — x x x — z || zx - xx. Assuming therefore the determi- nate quantity [a] of a just magnitude You will have this • • • ./Equation az = zx - xx. To construct this [equation I introduced another indeterminate quantity [y] putting * * * • • % = p + qv + ry & z = qx + ry ; which values of z & z being substituted in ye former sequation I obtained this other aqx + ary = px + qxx + ryx — xx. Then putting q = 3, p = a, I had the two following aiquations — = x, y z = a + x + ry & ye construction of these two ^equations agreed intirely with Yr own Solution of ye Problem*. Being satisfied by this Analysis of ye truth of Yr conclusion I easily saw yt my former difficulty lay in ye ambiguity of ye word [data] in line 1 & 5, & ye word [detur] in line 6. which I think may be remedied by the alteration which I propose. Page 312. 1: 21 I would leave out ye word [quamproxime]. Page 313. 1: 29 f I would conclude the Demonstration thus — et ex aequo perturbate Fh seu MN * The analysis and construction of the problem will be found in Cotes’s Lngnmetria, (Philos. Trans. Jan.—March, 1714, pp. 40—42. Harmonia Mensurarum, pp. 36—38.) t In Prop. xxx. Lib. 2. This Proposition contains the geometrical construction of the equation — (a2-62) = k / vnds (b being the first arc of ascent), which is ob- vdv p* tained by one integration from the equation of motion — —— = -. s — kvn. Cotes’s sug- d s t gestion leads to further correspondence (see the next five letters). This and the preced- ing proposition may give us an idea of the trouble that Newton would take to exhibit his results in a synthetical form.