/V D L l C
11
U M Q U A R T U M
V'
<
tuntur in cadem ratione fecundus , & quartus , eritque ille exceffus ut
VH .
248 Vim autem effe proxime in ratione diftancix a centro pro cafu ho­
mogeneitatis , & pro cafu maflx in centro collocati , cujus maffx vis
mutetur in ratione fimplici direda H iHanti;u , diximus num. 24$ 3 & id
facilc pro iis hypothefibus cvincitur cx eo , quod ipfa vis fit direde ,
ut normalis
P L
figura: 28 , fivc rcciprocc ut pcrpcndiculum dudum cx F,
C
in tangentem . Id enim perpendiculum ica proxime xquale cft diftan-
cix
CP
, ut utriufquc cxc flus etiam ac dtfedus /inc proxime in cadcm
ratione . Duda enim
CV
pcrpcndiculari in
P L
, pacet cam fore paralle­
lam tangenti , adeoque
PV
xqualcm illi perpendiculo demillb cx C in tan-
gcuccm . Cum autem angulus
C P l'
fi exiguus , & angulus
V
rcCtus,diffe­
rentia inter
CP
,
VP
cft exigua rcfpcdu ipfius
C V
, adcoqnc exigua fe­
cundi ordinis , qux idcirco ciic exigua etiam rcfpcdu differentia: diftan­
tiarum CP ,
CA
, cujus idcirco rationem non turbabit ad fenfum .
249 Pro cafu nuclei folidi vis in
P
cric diverfa a vi > qux habetur >
ubi vis in maffam agat in ratione direda diftancix a centro, fed totum
diferimen erit in ca vi , qux pertinebit ad hujufmodi mafiam in centrum
amandatam; nam, vis. in fphonoidem > qux pro utroque cafu cft ad. fenfum
cadcm , & vis ccncrifuja , qux pendet a fola diftantia al> axe » mancbunc
cardcm . Id auc m diferimen cric & ipfum , uc eft dif erentia diftanciarum
C/l
,
CP .
Si enim dicatur C/J ^ r , & ca diffcrcncia
ZZZ t,
, cric
CP "ZZL
r
— x, , & fi vis in
A
in maflam in ccncro pofitam dicatui
\i
, ad haben­
dam vim in
P
, fiet in cafu rationis fimplicis diredx
r . r
—
tl
, : : tl
«
t l
—*
— , & in cafu rationisrcciprocx duplicaex fiec, wc
rr
—
irz, -j* t,t,
ad
rr
, ica
U
ad
r,r ' " - p * * >fivc divifionc inftituta
U
>
4
* ^ <
4
-
. Diffcrcn-
r r - i r z -t-iz
r
r r . j r j - f - * *
tia vis poflerioris a priore, contcmpco termino, in quo habetur z,1 ,
&
t,\
refpedu ejus * in quohabetur s,
evadit H-- ^ , qui cxc ffus ob j , i i j r
conflantes evadit , ut dif erentia diftantiarum x, •
250 Rcfcrac P H vim fecundum
P L
, & ducatur H6J parallela PC referens
ejufmodicxcefum ; cricquc
vis compofita , angulus vero HP6£ cric per­
quamexiguus rcfpcdu ipfius
five
§}PC
exigui , uc H ^ c f t rcfpedu.
P H
»
adeoque diredio
P§
1
_
cricdiredioni
P L
ica proxima , uc idcirco figura pri­
mo calui debita non mutetur ad fenfum in fccundocafu . Quod fi centro P in­
tervallo i>6JJiac arcus
QR
ulquc ad
P H L ,
fac ie paccc , ob angulum
QHR
x-qualcm incerno, & oppofito
HPC
exiguo, fore
HR
proxime xqualcm
adeoque
exceffus vis etiam compofitx
P § lfu
pra vim priorem
P H
cric proxi­
me , ut diffcrcncia diftanciarum
C P
,
C A .
Cum igitur & cxc flus vis dcbicx
pundo
P
in primo cafu fupra vimdcbicam -pundo
A
in utroque idem fit , ut
cadcm differentia , criceciam cxccflus vis in
p
fupra vim in
A
in fecundo cafu,
nimirum in cafu nucleihcccrogcnci, uc cadem differentia diftanciarum. Quam-
obrem cum hxc dif crcnciadiftanciarum fic , ut clt quadratum finus latitu­
dinis , fivc uc cft finus verfus lacirudinis duplicacx , cric etiam ubicunque
cxcelfus vis in cafu nudei hcccrogcnci fupravim in arquatorc, uc idem quadra-
cam , five uc idemfinus verfus, quo pado remanet accurare dcmonftratum idem
theorema etiam procafu nucleihctcrogcnci •
A a j
j j t Pa-
1...,381,382,383,384,385,386,387,388,389,390 392,393,394,395,396,397,398,399,400,401,...530