DE MOMENTO INERTIAE, , 79
(aa — cc) fi AE 3
^ aa — bb+ (J)b — cc)cofCAS z *
Sin autem augulum ACS introducamus, repenemus/?CS 2 - ( aa-cc)fiCE 2
bb — cc-\- (aa — bb)cof ACS Z ’
angulus CAS usque ad redum augeri pote A, dum (aa — cc ) fi AE* non
i „ _ . aa — bb
excedat aa — bb, hoc efi fi fuerit fi AE < fi --; at angulus ACS
aa — cc
usque ad redum crefcere potefi, fi fit fi CE < fi - feu fi AE > fi
aa — cc
aa — bb
———, Quare pundum S erit in curva, quae ex E adurgens per qua-drantem AB tranfibit, fi fuerit Ji AE <, fi —-; curva autem ilia.
aa—cc
per quadrantem AC tranfibit, fi fuerit fi AE > fi -. Cafu autem
bb aa — cc
quo / AE = fi - curva per ipfum pundum B tranfibit, omnia*
aa — cc
que momenta inertiae erunt = M bb. Hoc igitur cafu erit Ji AS 2 =s
aa — bb
aa — bb + (bb — cc) cof CAS
Hinc ob cof AE — Y~ -
aa-»
fAE z
bb—cc aa — bb fi AE 1 _
—, et - — --, fiet/? AS 2 =
cc bb—cc • cofAE z ’ 1
„ _„ ideoque tang AS =: unde intelligitur
fAE* + cofAE* cofCAS z 1 6 ro/CMS °
loca pundorum 8 fita efle in circulo maximo per punda B et E tradudo.
aa —bb
Cafu quo fin AE < fi -- , fcu pundum E propius ad A fu 7
mitur, fit id in e, et in quadrante AB dabitur pundum/, in quo mo-mentum fit aeque magnum
„ . - (aa — cc) fi he z. Erit ergo fi Af z = --—-; unde
aa — bb
aa—cc
fi ponatur Ae= e; Af~=f : AS = / et angulus eAc — <p, ob
aa — bb
finf* bb — cc Jif z — fine z , , ,. . ,
5= — et- —— - L -, habebimus inter / et © hanc aequa-le* aa—bb ficf .
Z a tionem:
Fig-49*