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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 50, page id 1066518432:0078
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fO DE VERIBOS EF HIOTIBOS CORPORVM. LIB. I.
quo Facile elicitur ralor linca AD. Nam SI FF = a, AP = y, AF
=dy, FP = X, PP = dX, _E A2 = d5: Crit AB = ad5: du; e quia
angulus MIFE = a AF, atque adeo triangula rectangula FMF, et
Aat similia TUINE, inVenICtIE FM = ady: ds; XE NC = (ads- ady):
aS3 EUM CFIAMI ME = adX: ds; hinc quia MC: MF = AB: AD, in-
renictuE AD = ads: d5 - d).
Cl. Fac. Bernoullius (Aet. LipC. IOCO Fupra citato) calculo analy-
tico ulus, quemtamen illic non appoluic, reperit AD = xeds F adyds:
da ex qua Formula nostra paulo simplicior e nonnihil diver(a ra-
tione a Bernoulliana ex praecedentibus elicita, nullo negotio deri-
vatur, substituendo tantum loco du xqualem quantitatem ds.- dy 2
de numeratorem ac dominatorem dividendo per ds + dy.
DOsteaquam ca, quae ad reguoria Solicitationum, quibus unum
idemque mobile urgeri poun, spectant, excussimus: ipsi etiam
licicationibus continue replicatis, e uelibet rariabilibus, resultare
POTTUNE. Propterea in hac secunda Sectione NIOTUS COrporum aCCC.
leratoS _ retardatos generalistime contemplabimur tanquam oriun-
dos ex Colicitationibus continue quidem replicatis, non tamen uti-
que uniformiter, ut in Calilaei Erstemate, in quo graria in quacun
que distantia a centro grarium eadem graritatis solicitatione urge.
ri intelliguntur; sed quacunque ratione rariabilibus, sire corpOra
recta ad centrum grarium seu solicitationum acceleratricium Feran-
tur, sire in lineis curris incedant. Hlaec igitur Sectio complectetur
quacunque ad motus acceleratos, retardatos, ad motus projecto.
runi in vacuo, guxe ad ilochronismum motus corporum in lincis
quibuscunque curris, quae ad motus pendulorum XC. pertinent, in
omni possibili graritatis, seu solicitationum centralium, hypotheli, de-
monstrata, methodo non minus unirertali, quam perspicua atque Facili:
nam praeter Solutionem generalem Problematis inreniendi ex lege gra-
ritatis, utlibet rariabilis, semitam currilincam projectorum in spatiis
Generalem, secundum quam grablatem rariare oportet ad id, ut cur.
biles cractane, es saa ulla deinceps curiola atque utilia deducen-
tBEo
motus rasse accelerati dusue secaldati examinari debent, qui ex (0.
relistendi ri carentibus, tradet etiam haec secunda Sectio regulam
rae projectorum semper alsebraicae, atque adeo geometrica construi-