Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/462

 But the fhrnof their refifhnces (T -1- -24) rs armr-U O nimum. Therefore—B Gx J- — MN>z fl = o, ar r  J] 1* MNX 5'-:-'-BGX-I-2 But:(f}'-z:- .gt-7g?D r'|—aux-|-x.x'+b5; and z.: (19:13: M rn + vn =) an-\-:ax + xx -|- H; therefore;:ul-uxz, 2ndf.=z4.§ +zx.§ :confcquentIy 'aff.v X 2 Q ZZ - G . .  MN ... xr; -|-x:- %-x; ¢x¢-x; or(-1;-:Tx 4 -| x 2) MN B ...—»- G zz' * Mm 2(-ig x4—x:)% X Bb. Therefore (U) EF# (lb) -I-V714:: BGXB5:MNxM1n. C°“'°°l“°f“|y, that the um of the reitances againt the f\l\'fiCCS generated by the lineola G § and N rn, may betbt lcaf¥poHiblt»Gg4 muff be to Nur as GBb toNMnr. Wherefore, if yg be made ' nil tn 9/G, o that the a\o EE, -: z;,, md-6'4'°- -:; 4§ then '-'z N rg*:: G Bb:gNMm;gand G1'1cegGR is paggg to Nn, and BG, BR paraIle\ fb nv, Nv; alo nv:gy
 * 1) Hgh 753 may be 4f°, andegt angle BG; 155°;
 * yG'; it f0ll0W$ that (nv: yG:) B5: (Nvz)

Mm:: BG: BR; therefore B6 s a1fo(nv:) yG: Nn:: BG: GR. Z Confequcntly —+ —.4 - }g5, '*) gf* “(NMf»°')  Thad” g 3 4573 xB£ is to (§ '§ aGR to MM \ 'FINIS.
 * "ZZ  - i*f 'l -¢- 6511- BG