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 theſeaft breadth, to be erected, whoſe hi hts BG, MN, their diſtance Mb, and half the ſum of their baſes -}Mrn -|- QB 6: 4, are given: Let half the difference of » the baſes 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, (ſo that yg: v n: Q) the points tg andn may alſo bein the ſame curve. Now if the figure CDNG B, revolving about the axis B C, generates afolid, and that ſolid moves forwards in a rare and elaſtic medium from Ctowards B, (the poſition of the right-line BC remaining the ſame;) then will the ſum of the reſiſtances againſt the ſurfaces ge. nerated by the lineolaz Gg, N n, be the leaſt poſſible, 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 ſame time on the ſurfaces 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 reſiſtances BG
agaxnft thoſe ſurfaces are as:-; to Q-(-lg, that is (put. Gg Nu °
ging J for af, and; fQrT143,) as? to Ag-V. \ 2 But
o
