The first three sections of Newton's Principia; with copious notes and illustrations, and a great variety of deductions and problems. Designed for the use of students / By the Rev. John Carr.

  • Newton, Isaac, 1642-1727.
Date:
1826
Catalogue details

Licence: Public Domain Mark

Credit: The first three sections of Newton's Principia; with copious notes and illustrations, and a great variety of deductions and problems. Designed for the use of students / By the Rev. John Carr. Source: Wellcome Collection.

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    Note to Prop. 4.—Cor. 7. 75. Let ^ = absolute force, and the law of the force be 1 then if bodies revolve round different centres, accelerating force will (Art. 61) a Pc A P oc and V oc 9'^ 9^ 1 Introductory Articles to Prop. 4.—Cor. 8. 76. Let P Q E be any curve (Figs. 48 and 49 J, and S any point within it; take any point 5, and from it draw any line sp \ suppose the radius vector S P of the curve P Q E to revolve round S, and at the same time let the line sp begin to revolve round 5, with an angular velocity always equal to that of S P, and so that sp may always be to S P in a given R°.; then will the curve, traced out by ^7, be similar to the curve P Q E (Art. 27). The points S, 5, are called points similarly situated; and if p s q.^ p s &c. = P S Q, F 8 C, &c. respectively, then p, q, c, &c., and P, Q, C, &c., are called similar points; sp, 5 5 c, «>;c., and S P, 8 Q, SC, Sac. similar or homologous lines; p q^ p q c, &c., and P Q, P C, Q C, &c. si¬ milar or homologous arcs ; and p s q, p S c, q S c, &c., and P S Q, P S C, Q S C, &c. similar areas of the similar figures respectively. 77- From the definition of similar figures, it fol¬ lows, (1) That if S, s be points similarly situated, the chords of similar arcs P Q, p q^ make equal Z® with the radius vectors S P, sp; and are to each other in a given R°. For since PS : S Q s : s q, and Z P S Q = Z j) s q^ A® P S Q, p 5 5' are similar; Z Q P S Z .s, and P Q : p §' .* I P S : p 5 in a given R°. (2) That the tangents to similar