COROLL.

Designet CK (_Fig._ 3.) lineam intersectionis planorum æquatoris

planetæ et orbitæ satellitis, et resolvatur vis SD = 6_kbc_ ⁄

5_l_³, quæ agit perpendiculariter ad planum æquatoris, in vim DR

perpendicularem ad planum orbitæ satellitis, et in vim SR jacentem

in eodem plano. Producatur SR donec occurrat CK in K, eritque SK

normalis ad CK, et planum SDK normale ad planum orbis satellitis;

ac proptereà ob similia triangula SDK, SRD, si _m_ denotet sinum ad

radium 1 et _n_ cosinum anguli SKD, inclinationis scilicet orbitæ

satellitis ad æquatorem planetæ, erit DR = SD × _n_ = 6_kbcn_ ⁄

5_l_³, et SR = SD × _m_ = 6_kbcm_ ⁄ 5_l_³, existente 1 gravitate totâ

satellitis in primarium suum. Jam quoniam vis SR jacet in plano orbitæ

satellitis, hujus plani situm non mutat; accelerat quidem vel retardat

motum satellitis revolventis, sed hæc acceleratio vel retardatio ob

brevitatem temporis ad quantitatem sensibilem non exurgit: vis DR eidem

plano perpendicularis continuò mutat ejus situm, et motum nodi generat,

quem sequenti propositione definiemus.

Philosophical transactions, Vol. L. Part II. For the year 1758. Giving some account of the present undertakings, studies, and labours, of the ingenious, in many considerable parts of the world. · 第 93 / 119 题