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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 68, page id 1066518432:0096
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68 DE VERLBVS EF MOTTBVS. COR PO.RVM. LIB. L.
C A PD T IF
De Motibus curvilineis in Vacuo, in quacunque cravitatis
variabilis Hypothesi.
PROPOSTTIO ZZ. LENVA.
253. CT magnitudinis continue crescentis (cujus prima maenitudo AY
ea dicitur, a qua crescere incipit) incrementum infinitesimum FF
semper fuerit ad decrementum qr, alterius decrescentis Dq. cujus prima
maenitudo, a qua scilicet decrescere incipit, sit VR, sient crescens P F
ad decrescentem Dq, erit crescens F L ad suam primam maenitudi-
25. 35. nem AI, ut decrescentis prima maenitudo DR ad ipsam decrescentem
DC
In F19. 36. Circa axem DR descripta sit aliqua curra TF, cujus
absCINX DG, DR decrelcentem primamque ejus magnitudinem re-
Ferant, ordinatae vero FF X IA, crescentem ejusque primam maoni-
tudinem, ut adeo signa q; F ad idem punctum pertineant perin-
de ac Signa A, R. Per curra punctum S tangenS FO ducta lit axi
Occurrens in O, Factaque ordinata se alteri FP infinite ricina, crie
fa crelcentis FF incrementum, ex L’a vel gr Peu Fe decrementum
insinitesimum decrescentis Dg: Pritque adeo (secundum hrpothosin)
fa: gr = FF: D9. Verum triangula similia FaF, FFO praebent etiam
fa: gr = FF: EO, erSO FF: Dg = FF: F O, atque adeo D9 = FO;
hinc producta tansente OF, erit criam. OF =VS. FA CrOO pun-
ctum contactus P’ubique in mediorecex OS, angulum rectum SDO.
subeendentis, ut adco per convertam ProD. TII. Secundi Conico.
rum Apollonii curra IF FIyperbola ht intes a(YmptotaS SD _ DO,
acque adeo F. F sic adt AI, sicuF DR adt D9. Ouod erat demonstr an dum.
PROPOSTTIO XXT THFOREMA.
la celeritatum mobili, ex quiete in II in recta YID cadere incipientis
acquisitarum; atque hoc ipsum mobile in directione AR celeritate AF
propulsum, quam erave post casum ex altitudine TIA. in A acquirere
potest, urgentibus solicitationibus illis centralibus per ordinatas curvae
B sienificatis, curvam quandam AII in acuo describat. Frit FF
selb
254. Lxistentibus CBB scala) modationum centralium e AIF sea