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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 384, page id 1066518432:0412
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384
A P P E N D I X.
cademque omnibus competet celeritas jactus secundum A~. Nam,
quia V: = : T. AB = : L. AD:. AB: AD (CCu, quia AD2. AB est Coli-
dum constans) est; L: AD, erit V uer : L,: AD. Id est, in diversis
sectionibus conicis relocitates mobilis in alcerutra apside CxUINE in
composita ratione ex lubduplicata directa ratione laterum rectorum
sectionum, et reciproca ratione distantiarum apsidis a centro soli-
CIFaLIOMUM.
2. Si umbilicorum distantia Dd Fuerit infinita, sectio conica AOa
CA Parabola focum habens in d, ac proinde sublimitas IIA = Ad AF
xqualis quartae parti lateris recti L, ut Galilaeus, aliique post ipsum
plures ex aliis Fundtamentis demonstrarunt. In hoc ergo consectario
concinetur unirerla doctrina motus projectorum in hypothesi grari-
tatis parallelarum directionum.
3. Si mobile eadem relocitate V in A acquisita post descensum
in FIA circulum ex centro I, radiumque AI = : L. habentem delcri-
bat, conatus centrifugus mobilis in circulo eadem crit cum solici-
tatione centrali AB in apside A sectionis conicx AOa.
4. Graritasuniformis, qualis apud nos est, se habet ad conatum cen-
eritusum in dicto circulo, leu ad solicitationem centralem AB in A,
UE: AI seu : L ad TTA scu Ad. Adeoque in parabola ex Foco d et
vertice A deleripta mistilis graritas in vertice ejus A, aequabitur
conatui centrituso in circulo praedicto.
VII. De tempore Periodico in Sectionibus Conicis. VOCCHEUE LemDUIS
unius circuitus in sectione AGa, L, diameter Aa, D; ejus conju-
Satus 29, d; latus rectum I, distantia Peu altitudo AD, A, Coli-
citatio centralis AB in apsde A, C. Fruntque d =VID, e arcato-
tius ellipseos, hoc c, 2. AOa = ipDd, ubi p est exponensrationis cir-
cumferentia circuli ad radium. LA verO (5. 157.) I =2. AOaA: : AD.
V, erco Tubstituendo ralores analrticos locoareae e linearum AD, V;
habebitur P = pDd: An, CCu T = pp D. d: A u, eA vero dd = ID,
eE uW = : VCF, erGO T (= pp DI: :I AC) = 2pp D: A2. C. TIinc qua-
dratum ex tempore periodico est in composita ratione ex directa triplica-
ta ratione lateris transversi, e reciproca composita ratione duplicatae di-
stantia apsidis a foco, seu centro solicitationis, e simplae solicitationis Ct in
apside. Onde, quia Colicitationes graritatis lunt in reciproca du-
plicata ratione distantiarum mobilis à centro, rationes compo-
sitx ex duplicata distantixe apsidum a centro ex simpla gravita-
tis in apsidibus lune rationes aequalitatis, propterea sunt quadra
ca temporum periodicorum, uc cubi diametrorum principalium in
sectio.