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published from the originals in the library of Trinity College, Cambridge; together with an appendix containing other unpublished letters and papers by Newton; with notes, synoptical view of the philosopher's life, and a variety of details illustrative of his history, by J. Edleston.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published from the originals in the library of Trinity College, Cambridge; together with an appendix containing other unpublished letters and papers by Newton; with notes, synoptical view of the philosopher's life, and a variety of details illustrative of his history, by J. Edleston.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.

    166/430 (page 60)
    be altered accordingly. And so must one or two of ye numbers in Prop, xn & xm. In ye 3d section of ye xxxvnth Proposition, I think my proportion is right, ffor the force of the Sun increases the force of the Moon in the Syzygies, diminishes it in the Quadratures & neither increases nor decreases it in the Octants: & therefore the distance of the Moon from the Sun must be doubled that the cosine thereof may vanish in the Octants. In the 3d Corollary of that Proposition lin 5, 6, the words should run thus [et cubus diametri Lume ad cubum diametri Solis inverse, id est, (cum diametri mediocres apparentes Lunse et Solis sint Si' 27 & 32' 12) ut &c.] But instead of the Moons mean diameter 31' 2? may be written Si' 161, & the Suns mean diameter 32' 12 may be every where retained, even in the Moons Theory. For 32'. 15 is too bigg. In the Scholium to the ivth Proposition, if the length of a Pendulum wch vibrates seconds in vacuo be put 3 feet & 8-|, the descent in that time will be 15 feet 1 inch & 2l lines. And in the xixth Proposition the vis centrifuga may be put in proportion to the vis gravitatis as 1 to 28.9, & then these corrections must be made. Neare the end of the Scholium of Prop iv. for the numbers 290I, 669 & -JL. write 289, 665, & g-^-5. Also pag 422 lin 9 write, ut 1 ad 289. lin. 13, ut 289 ad 288. lin 15, 289. lin 16, 288. Pag 423 lin 27, ut 1 ad 288. lin 28, pars -gj-g. lin 31, vis centrifuga gig-. lin ult. pars tantum gig-. Pag. 424 lin 1, ut 229 ad 228. lin 3, 19674224, seu millia jr| ium 3935. lin 5, 2£) x 1 x 5 pedum 86101 seu milliarium 17. lin 16, ut ad 1, F 5 x 228 seu 1 ad 8. lin 29, ut 229 ad 228. The xxxixth Proposition must be corrected by putting the semidiameters of the earth as 228 to 229 instead of 689