Ca afcenfu defcriptum, & area I E F ad aream 1L T ut Oj^ad OS,
Dein perpendículo M N abfcindatur area hyperbolica P IN M qu$
fit ad aream hyperbolicam P IE ^ j x t arcus C Z ad arcum BC de-
fcenfu defcriptum. Et fi perpendículo R Grabfcindatur area hyperbolica
P IG R, qu® fit ad aream P I E ut arcus quilibet CD
ad arCum BC delcenfu toto defcriptum ; erit refiftentia in loco D
ad vim gravitatis, ut area — I E F — IGH ad aream P 1NM.
Nam cum vires a gravitate oriundas quibus corpus in locis Z, B,D,
a urgetur, fint ut arcus C Z ', CB, CD, Ca, & arcus illi fint ut areas-
PINM„
D E Moxu
CORPORUM
P R O P O S I T I O XXIX . P R O B L E M A VI .
Pofito quod corpori in-cicloide ofcillanù refijìitur in duplicata
rañone velocitatisi invertire rpfifientiam. in locisfingulis.
Sit Ba arcus ofcillatione integra defcriptus, fitque C infitnum
cycloidis punftum, & C Z femiflis arcus cycloidis totius, longitudini
penduli aqualis ; & quseratur refifientia corporis in loco quo-
vis D. Secetur retìa infinita 0 §^ in pumftis O, S, P, <£, ea lege.
Ut (fi erigantur perpendicula OK, ST, PI , QE, centroque O & a-
fymptotis OK, defcribatur hyperbola T IG E fecans perpendicula
ST, P I , §FE in T, 1 8c E, & per punéìum I agatur K F parallela
afymptoto O^occurrens afymptoto OK in K, & perpendiculis ST
& §FE in L & F ) fuerit area hyperbolica P IE Q ad aream hyperbolicam
PITS ut arGus BC defcenfu corporis defcriptus ad arcum
301
, cDins\ ‘P IG R PITS- , e x p o n a n tu r turn arcus turn vires
f lN M , P I L t infuper D d fpatium quam minimum a
per has areas 1 e p j Pfrr;ntum & exponatur idem per aream
^rpore d efcend^te ^ comprehenfam ; & prou
tfin I a B i s , R H n K H K V
M decrementa.
R r
L iber
5 E C U N D Ü.S»
* H G - ^ I E F , e rit ad are®
turn Gm nh t>o,g — — I F F , feu R>
P IGR decrementum RGgr, feu R r x R G , ut HG -
■ ¡¡9 i e F
OR
ad
/A F a d O R x G R feu O P x
RG ; ideoque ut OR X HG
PI, hoc efl * HR
OR
OR *GR , ORHK
t i g r + i g h .
O /? , n r TLT i ofltnr ^
2 1 I E F ad OP IK. Igitur fi
at^e are® P I G R decrementum. RGgr detur, ent incrementum
C© p r o p o r r i o ^ a » * f Eft t.aque
■ ¡ H - V ; U p ^ . £
faftum eft conjunftim. e ¿ ire¿te & partícula eadem terncontemporawum
fp> >■ P fiftewi, per hypothefii. fit ut qua-
H reliftentise (per ■ ■ ent |
c o n t a in , , id eft, I B E f c
H H H H I atque ideo, ft momentum fpant
turn fpatu & V v fcrib>tm ejus exponens
T g itu r a te , 9 IGR pet datomm —
formiter decrefcente, cretont ate,^ ^ to u t
■ H i — H moaentorum pergent effe atquales, & * q u * t o