CORPORUM GRAVIUM CIRCA AXEM. 533

C O R o L L. 2.

1156. Si fridlio eflfet nulla feu — o, foret

da

h fin(p

igdt kk

Unde motus pendulorum fupra definitus facile eruitur, pro preJTionibus au- item E et F haberemus has aequationes:

2 (E + F) AAcof£=M C kk — hh fin<p* 4.et aFA 2 fina£= M QkCn^-hh fin£ cof(£-p) +

et 2EA 2 fin 2M (jtk fin £ -f hh fin cp cof(<f + (£>')

quarum utraque ut iit pofitiva debet efTe:

ta , P > —H h !l *' n ^ c °f<P + LL lintp

“igkk — 2 ghh lin<p 2 + hkkua cof<J>ubi notandum efi, efle kk > hh.

C O R O L L, 3.U57. Aequatio differentialis inventa ob dt —

— d<p

-abit in hanc

a

formam o = ada ({1 4- <W) kk cof<f— J/A (fin<£ + J cofip)) _ Sfhvadtp(coi (p — $ !>n <p)

+ 2 (1 + M) gh dtp cof^ lin <p — 2 Sfgdcpquae per (1 + < 5 $) kk cof^ — $fh (lin 9 + cof<£>) multiplicata fit inte-

grabilis, proditque

C' = as ((1 + <W) kk cofg- Ifh (fin Q-t $ co[q >)) 2+ 4 gf d( P ((> + U) h cof£ lin <p — <?/) (( 1 + kk cof£— tjfh (lin (p 4 - ^ cof (p))

SCHO L 1 O N.

11 58. Si hoc integrale evolvamus, repcriemus

C = 88 (( I -f <U) kk cof£ - 8fh (fin (P + <? c of<p)) z - 4 (j+ S3j 2 ghkk cof£ 2 cofip

— J(i + H) fghh cof£ ^ 2 <p - fin rP - eofvp) — 4 <J (1

+ (IJ 1 ) AA p C °1 £

— 4 Uffgh (cof<p - J 1 fm <p).

Xxx 3 Quare