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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 79, page id 1066518432:0107
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DE VEREBOS ET NIOTTBOS CORBOROM. L IB. I. 79
hosce in aequatione generali 5. 168. circa finem, Substituas, era-
nelcent omnes coetticientes O2V, OAu, CCC. _OmnesO2V, 04V, 0613
_c. adeo ut hoc casu currae aequatio st SN =rZ. Jam quia A
(= 2m: am-) hoc calu cAt =aa: Z, atque adeo in A8. 38, Ordina-
ta FFI, quae alsumenda est aequalis difterentiae quantitatum e et A,
non summa, quia in ambisuo signo superius in formula retinuimus
quod indicat talem differentiam, atque inferius summam; ordina-
ta inquam PHT hoc casu erit = + e = A = + e F = = (+ eZ F 4a): Z,
atqui S, seu secans anguliM AL, est tertia proportionalis ad AC Peu
EFI, ec radium AM vel AI =r, er5O5 = rrZ: + ez +a4, adeoque
aequatio Sx = rZ, mutatur in
nEX = rZ, ex qua clicituE rX =
= ex F aa vel POTIUS eZ = aa = + YN, aUC eZ = aa F YN, QuXe CA X-
quatio sectionum Conicarum, in quibus abscissae ae sumuntur sursum
ec deortum a Coco. Ergo in hac hrpotheli centrum virium, seu lo-
licitationum graritatis, sunc umbilici sectionum conicarum, quod
jam omnibus constat egresie conspirare cum iis, quae demonstrata
Cunt ab TIlustr. Newiono, Leibnitio, Varignonio e aliis, circa
vires, quas rocant centripetas in sectionibus conieis methodis dire-
ctis.
20. Sitm = = 2, _ n = 2, at que e major quam r, ita ut Ss = rr = ee
sic quantitas negatira, crit ( = = 552: a, atque adeo solicitationes
erunt ut distantixe a OCnErO. Aquatio currae pro hac hypothest sic
indagabitur. Ouoniam n = 2, _E F: n = V : V Cxit v = 2W, atque adco
aequatio generalis (5. 268.) huic calui applicata mutabitur in hranc
sequentem Sax -Syy =r2Z. Peu, quia A (= 2m: a m- 1) hoc calu eA
= a: 22, _S = rY: e = A = rY ZZ: CZZ = a, Het (YYXNZZ - rYy )ZZ:
ez2 = a = rZ ~, at que ad co rXX - ryy = eZ Z = a = ex X + ey) - a
tinc a + r = e. XX = e + r. γ7. Jam quia e (secundum hypothelin)
major est quam r, quantitas r= e crit negatira, atque adeo aequatio
erit ad ellipsin, cujus axistransrersus est ad conjugatum (ICut V (e L r)
ad V (e =r); _ in qua abscissae a originem in centro habent. Idcir-
co Tolicitationes graritatis, quae in ellipsi sunt ut distantix a cen-
tro Policitationum, diriguntur ad centrum ellipleos, quod iterum
ex demonstratis errtonianis constat verum esse; nam II, ut LX-
cell. hic AUtOT, e postea CI. Varignon Fecemint, quaeratur qua-
lemgraritates mobilis, perimetrum ellipleos circumeuntis, lesem le
qui debeani, si carum directiones in centro eslip(eOS COnCUTranE, re-
DC.