4 3 *
L I B E R D E C I M U S .
Concipe propterea de punito quolibet, axis
Flexibus educlara redis dilcedere redam
1725 ~
Parte ab utraque v iam , nimirum infraque fupraque ,
Verum infinito diftendi tramite fupra,
Parte repellentes etenim fimul abi mus cx hac
V ires , ex alia contra inferiore trahentes.
Parte ex hac ergo crus quoddam extendere debet 1730
Curva infinitum v ia , quam nos quaerimus, atque
Illam infinitam propius corradere redlam ,
Omnibus ufque locis propius, fed tangere nunquam:
Dcfcendcnfquc locis magis ufque recedet ab illa
A ltis ; jamque axem veniens fecat, & fugit ultra 1735
Praeteriens, aliamquc in partem labitur infra ,
dicularcm * ad q u e m accedit in
infinitum crus c u r v x a fy m p to ti-
cum , quin u fq u a m in ulla finita
diftantia c u m e o c o n g r u a t . Id
tendit fu rfum , q u a m p la g a m ad
h ibeo pro rcp u lfio n ib u s , fivc v i
ribus rcpulfivis ita , u t a r c u s , q u i
abeant fu rfu m , fin t o m n e s p ro
viribus r c p u l f iv i s , o m n e s , q u i
d eorfum „ p ro a t t r a d liv is . H ic
arcus , d um d ifce d it ab a s y m p to -
to illa p rim a , a cced it ad a xem ,
quem fecat in d ifta n tia p e rq u am
exigua ab it>fa a fy m p to to , five a b
origine abfcifTarum : p o ft fc£ tio -
nem , in q u a tra n fitu r ad attra-
ftio n em a rc p u lfio n c , arcus ip fc
primo recedit a b a x e ,
tu m ad
ipfum r e t o r q u e t u r , et ip fu m ite
rum f e c a t , ac im m e n fo fle x u u m
num ero c o n to rq u e tu r circa ip s u m ;
q aem in im m e n fo p u n & o r u m n u
m ero f e c a t , a n te q u a m d even ia
tur ad d iftan tiam a b o r ig in e n o b is
fen sibilem . In p o ftrem a . fe ftio n c
abit d eo rfum ad partes pofitiv^s ,
ubi p rim o q uidem reced it in im -
m enfurri', tum re to rq u e tu r verfu s
axem , q u em fere l a m b i t ,
Sc
v e l
ipfum h ab e t pro a fy m p to to , v e l
non nifi in im m e n fa d iftan tia in
ip fum r e c i d i t . Si gravitas ge n e ra
lis in in fin itum exten d itur im m in u
ta in in fin itu m >axis ipfc c r i t a f y m -
Tum
p t o t u s , & a t p rim u m c u r v x cru s
e ft a fy m p co ticu m re p u lfiv u m , ita
erit
Sc
u ltim u m a f y m p to tic u m fle d
a ttr a ftiv u m . Q u o d n in d ifta n tia
m a j o r e , q u a m fit d ifta n tia o m
n iu m p la n e t a r u m ,
te
c o m e t a r u m
n o b is a p p a ren tium , g r a v ita s d c -
fi n a t , & r e p u lfio . fu c c c d a t ^ t u m
v e r o cu rv a in illa im m e n fa d ifta n
tia fecabit iterum a x e m ,
Sc
a b ib it
ad partem n e g ativ am .
Et q u id em cum ju x ta ea~, quae
d ixim u s , vis in m in im is d ifta n tiis
fit r e p u lfiv a , lex a u te m u n ic a v i
riu m p e rtin e at ad o m n ia m a t e r i x
p u n ft a , & ad d iftan tias q u a fc u n -
q u e 5 g ra v ita s n o n e rit a c c u r a te in
ra tio n e recip ro ca d u p lica ta d ift a a -
t ia r u m .q u x lex e x h ib e re t in m in i
m is d iftan tii^ vircs a ttr a d liv a s cre -
fcen tcs in in fin itum : h in c fieri d e
b e b i t , u t ' n cc in m a g n is f e r v e t
a c c u r a te ra tio n em ca w d e m , f e d
p r o x i m i c u m v id e a tu r d eb e re e x
p r im i p e r un icam c u r v a m u n i f o r
m is n a t u r x , q u x e ad em q u a p i a m
co n fla n ti lege p r o g r e d i a t u r . P o r
ro nullus a rcu s c o n tin u u s u lliu s
c u r v x a ccu rate c o n g r u it c u m u llo
ateu c o n tin u o ullius a lteriu s: p o f -
fu n t q u id e m fc m u t u o f c c a r e , v e l
tan g e re in p u n & is q u o t c u m q u e ,
fed n o n c o n g ru e re . H i n c fieri p o f -
f e t , u t p o ftc a q u a m s * r va v ir iu p i,
