1
DE MOTU
CORPORUM
CORPORUM
Corol.1. Unde ſi Solidum
129[Figure 129]
Cylindrus ſit, parallelogrammo
ADEBcirca axem ABrevo
luto deſcriptus, & vires centri
petæ in ſingula ejus puncta ten
dentes ſint reciproce ut quadra
ta diſtantiarum a punctis: erit
attractio corpuſculi Pin hunc
Cylindrum ut AB-PE+PD.
Nam ordinatim applicata FK
(per Corol. 1. Prop. XC) erit ut 1-(PF/PR). Hujus pars 1 ducta in lon
gitudinem AB,deſcribit aream 1XAB; & pars altera (PF/PR) ducta
in longitudinem PB,deſcribit aream 1 in —(PE-AD) (id quod
ex curvæ LIKquadratura facile oſtendi poteſt:) & ſimiliter pars
eadem ducta in longitudinem PAdeſcribit aream 1 in —(PD-AD),
ductaQ.E.I. ipſarum PB, PAdifferentiam ABdeſcribit arearum
differentiam 1 in —(PE-PD). De contento primo 1XABaufe
ratur contentum poſtremum 1 in —(PE-PD), & reſtabit area LABI
æqualis 1 in —(AB-PE+PD). Ergo vis, huic areæ proportiona
lis, eſt ut AB-PE+PD.
129[Figure 129]Cylindrus ſit, parallelogrammo
ADEBcirca axem ABrevo
luto deſcriptus, & vires centri
petæ in ſingula ejus puncta ten
dentes ſint reciproce ut quadra
ta diſtantiarum a punctis: erit
attractio corpuſculi Pin hunc
Cylindrum ut AB-PE+PD.
Nam ordinatim applicata FK
(per Corol. 1. Prop. XC) erit ut 1-(PF/PR). Hujus pars 1 ducta in lon
gitudinem AB,deſcribit aream 1XAB; & pars altera (PF/PR) ducta
in longitudinem PB,deſcribit aream 1 in —(PE-AD) (id quod
ex curvæ LIKquadratura facile oſtendi poteſt:) & ſimiliter pars
eadem ducta in longitudinem PAdeſcribit aream 1 in —(PD-AD),
ductaQ.E.I. ipſarum PB, PAdifferentiam ABdeſcribit arearum
differentiam 1 in —(PE-PD). De contento primo 1XABaufe
ratur contentum poſtremum 1 in —(PE-PD), & reſtabit area LABI
æqualis 1 in —(AB-PE+PD). Ergo vis, huic areæ proportiona
lis, eſt ut AB-PE+PD.
Corol.2. Hinc etiam
130[Figure 130]
vis innoteſcit qua Sphæ
rois AGBCDattrahit
corpus quodvis P,exte
rius in axe ſuo ABſi
tum. Sit NKRMSe
ctio Conica cujus ordi
natim applicata ER,ipſi
PEperpendicularis, æ
quetur ſemper longitu
dini PD,quæ ducitur
ad punctum illud D,in
quo applicata iſta Sphæroidem ſecat. A Sphæroidis verticibus A, B
ad ejus axem ABerigantur perpendicula AK, BMipſis AP, BP
æqualia reſpective, & propterea Sectioni Conicæ occurrentia in K
& M; & jungatur KMauferens ab eadem ſegmentum KMRK.
Sit autem Sphæroidis centrum S& ſemidiameter maxima SC:& vis
130[Figure 130]vis innoteſcit qua Sphæ
rois AGBCDattrahit
corpus quodvis P,exte
rius in axe ſuo ABſi
tum. Sit NKRMSe
ctio Conica cujus ordi
natim applicata ER,ipſi
PEperpendicularis, æ
quetur ſemper longitu
dini PD,quæ ducitur
ad punctum illud D,in
quo applicata iſta Sphæroidem ſecat. A Sphæroidis verticibus A, B
ad ejus axem ABerigantur perpendicula AK, BMipſis AP, BP
æqualia reſpective, & propterea Sectioni Conicæ occurrentia in K
& M; & jungatur KMauferens ab eadem ſegmentum KMRK.
Sit autem Sphæroidis centrum S& ſemidiameter maxima SC:& vis