25 :

CAPUT IX. DE PRIMA MOTUS

ubi fi loco Q coQ- Pponatur -— ^ ^ ^ , fada redudiotie

J K noco^ 2 +bbfy*

pervenitur ad hanc aequationem

co [$ 2 (aa co 1<? cofyj — bb f 8 fn) (na cofjj 2 -f bb fri 2 ) + ccf$ t{aacoQcaCtt-bb/S/f,) = o. •quae per aa co(F cos^ — bbfSft\ divifa praebet

co 5 A 2 ( aa cofjj 2, + bbfy 2 ) -p ccfB 2 = oaequationem impoifibilem ob omnes partes pofitivas. Quare divilore uten-tes uancifcimur determinationem anguli r\ feilicet tangjj = a ° C °^

(Q coff? — P/<J) aabb

bbf$

ex

vel ne am-

otio porro colligitur trmgA =■ -----—

J V 5 h KccJ^a* coi$*+b*fp)

biguitas ligni radicalis dubium relinquat.

. (Q cosF _ P/«J) aa cofjj (Q eoU - P /i) b bfr>

tangit = -- —

unde angulus

R ccf$ ' R« cofd 1

Hoc jam axe invento fi pro Q. cosF — P valor fi,perior fiibflitttatur,colligitur momentum virium follicitantium refpedu illius axis =\ihf(J + yj) (aa cofp 2 cof 5 z + bbfq 2 col'5 2 -f- rr/A 2 )

(aa cofj; 2 -f- bbfr\ 2 ) eoIZ-

dementaris da tempufailo dt circa axem genitus eritj __ Rj ghdt 2 f^ + yt) _ Rghdt*f(a*coCS* + b*f$ 2 )

M coi B (aa cofyj z -f bbJy \ 2 ) M aabb coFZ-

fi in /0 + jj) loco anguli t\ valor repertus fubfiituatur.

C O R O L L. u

Hg. 82« 640. Ex pnndo ergo V, in quot, diredio vis follicitantis planum

AIB trajicit, fiatim invenitur in eodem plano reda IE cui axis gyratio-nis IF imminet: pofito enim angulo AIV — i, erit tangAIE = tangjj =

^ : neque a diredione ipfitts vis pendet,

C O R O L L. 2 ,

647. Quare fi vis folficitans per axem principalem IA tranfeat, an-gulus AIE fit redus, axisque gyrationis IF erit in plano ad axem IA nor». . Qbb

mali. At ob £ = o et ti = 90° erit tangEIF = tangS- = --

CO -