2 0 4 PHILOSOPHISE N A T U R ALTS
T>s M o t u L D q X T S A L B x T S
CüR.pottuM -pE xV T 'E xV ■' ut)I Pro V fcribatur ratio inverfi
vis centripeta, & pro T E medium proportionale inter T S Sc
zLT) \ tres rllas partes evadent ordinatim applicata; linearum totis
dem curvarum, quarum arem per methodsos- vulgatas innotefcqnt,
El- F. ft
Exempt, i . Si-, vis centripeta ad fmgulas fphmrss particulas ten
dens fit reciproce ut diftantia ; pro V fcribe diftantiam T E ; dein
z T S x LT> pro T E q , 8c fiet T> N ut S L — 2 LT) —
z L L '
Pone D N mqualem ejus duplo z S L — L D — — ^ : ¿¿ordinata;
pars data z S L dufta in longitudinem A B defcribet aream re.
ftangulam z S L x A B ; & pars indefinita L D dufta norffialiter in
eandem longitudinem per motum continuum, ea lege ut inter mo-
vendnm crefcendo vel decrefcendo mquetur femper longitudini
L<D, defcribet aream id eft, aream S L x A B ; qnx
fubdufta de area priore z S L x A B . relinquit aream S L xA B .
ytf fi '
Pars autem tertia dufta itidem per motum localem norma»
liter in eandem longitudinem, defcribet are- l\
am hyperbolicam ; qum fubdufta de area
S L x A B relinquet aream qumfieam A N B .
Unde talis emergir problematis conftruftio.
A d punfta L, A, B erige perpendicula L i,
A a, Bb, quorum A a ipfi L B , & B b ipfi
L A mquetur. Afymptotk L l, L B, per pun- xL A ------------- -
f ì a a b defcnbatur^hyperbola ab. Et afta chorda ba. claudet are-
ai» a b a arem qumfitm A N B mqualem
file applicatus ad planum quodvis datum • fcribe Ml Drn v
leciproce ut cubus diftantiae, vel (quod perinde eft) ut cubus
z A S q P
dein z T S x L D pro T E q -, 8c fiet T )N ut i f L x A S q AS q
t s JTDd - I t s
— a l b
j L B x A S g^ ,Qk continue proportionales T S, A S , SI)
H z T S x L -D q '
L S I I n j A L B x S I
Si ducantur hujus partes tres
ut ~j7ß z L D q
fn longitudinem A B, prima I B generabit aream hyperboli-
L'D
A B x S I ; tertia ~ —i t i —- aream
cam ; fecunda 1 S I aream N x i a x o x -, «*u* %LT>~q
A L B x S I A L B x S I efl- 4 A B x S I. De prima fubdu
T X A z L B
catur fumma fecund as & tertiae, & manebit y
area qumfita A N B . Unde talis emergiti
problematis conftruftio: Ad punita-
L, A, S, B erige perpendicula L i, A a, Ssì
Bb, quorum Ss ipfi SI aequetur, perque
punftum s afymptotis L I, L B defcribatur _______________
hyperbola a s ¿occurrens perpendiculis A a, T T 1 S B
Bbm a & b-, & reflangulum z A S l fubduftum de area hyperbo*
lica Aa s b B relinquet aream quaefitam AN B .
Exempt. 3. Si vis centripeta, ad fingulas fphaerae particulas ten-
dens, deerefcit in quadruplicata ratione diftantiae a particulrs ;
fcribe - ^ - ^ r pro V , dein L z T S x L D pro T E , & fiet D N ut
cub.
S lq x S L S Iq
d z S I x V A 2X z s / zS I VAX»
S lq x A L B r m __
- T WzS I V LSDq c°
Cujus