Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/461

 z, r']} '— 44f§ '}:z]z.} -\-J' Q.-\-Pi; But z. is a minimum; therefore rr]-zarr:z.]; confef 2 .3 4+r2 2   4'r2j  \  4'3r2

¢| ='§ Z f.'i; 'Q a J as B

quen y (z.) J “ +”

Hence J]—za]:rr; and making OQ: ClD
 * a; then(y—a~..:)Q S:.- (, /rr-}-aa:) Q C.

To the /hme Scbol. p. tzo. I. to. On the right-lineBC, (Pl. 19.FQ 3.) fuppole the parallelograms BGyb, MN v rn, of theeaft breadth, to be erected, whoe hi hts BG, MN, their ditance Mb, and half the um of their baes -}Mrn -|- QB 6: 4, are given: Let half the difference of » the baes iilflm—{Bb be called x: Let G and N be points in the curve GND; and producing b y, and rn v to g and n, (o that yg: v n: Q) the points tg andn may alo bein the ame curve. Now if the figure CDNG B, revolving about the axis B C, generates afolid, and that olid moves forwards in a rare and elatic medium from Ctowards B, (the poition of the right-line BC remaining the ame;) then will the um of the reitances againt the urfaces ge. nerated by the lineolaz Gg, N n, be the leat poible, when 52+ is to M4 as BGxBb to MNxMm. For the force of a particle on G rg and N n, to move them in the direction BC, is as 0% and Iéq; and the n

number of particles that flrikeingthe ame time on the urfaces generated by G g and Nn, are as (the annuli del'crib'd by gy and nv, that is, as BGX gy and MN Xn Va Or 25) .B G and M N; therefore the reitances BG

agaxnft thoe urfaces are as:-; to Q-(-lg, that is (put. Gg Nu °

ging J for af, and; fQrT143,) as? to Ag-V. \ 2 But

o