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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 288, page id 1066518432:0316
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288 DE VFRTBUS ET MIOTTDUS CORPORAM. LIB. II.
Per punctum N ducta SIE lOg. miCa NTIT, cujus subtangenS AK
Dolito scilicet rectam NK iplam contingere in puncto N) aequa-
lis AN, acque in ea ad alrmptotam AR aptetur ordinata III aequa-
lis BD, eaque producatur in S; duetaque per logarichmicae punctum
II recta indetinita FICD parallelaO9, tangenrem l08 micx NVK in
C, rectamque NA in C secante, si in ca lumatur ubique CD ∞-
qualis CFI, interceptae inter tangentem NH et l0g. micam NHII.
eric lemper punctum D in scala celeritatum propriarum mobilis in
linea deterente NO.
Ducantur enim per punctum l0g.micx II tansens FIR et linea
FIE parallela tangenti NI, cruntque TII X IL, item LR _ TIS
vel DF. aequales, ductaque insuper dh alteri DFI indetinice vicina
lineola mh ec TR a media HIL proportionaliter secentur, critque
adeo FII vel BD aUC R F ad LR vel HIS TCU DE, Sicut TIm Ceu da
ad nh; adeoque F F. nh = DF. da. Tam, quia (consr.) DC vel R N =
CTI X Ne=ch, eritnh, differentia inter CTTI _ h, aequalis Re; nam
IIn est parallela ipsi 68. Ereo FF. nh = CF. Pe - DF. da. Quod
erat demonstrandum.
POrrO CAnh: L. R = mB: TR, atqui nh: LR = F C: DF (5. 128.)=
TEe, ergo tRe =Ii vel mh: TR; ergo omnia tBe, id eAt, tempus per
NVE = omnibus II: TR = AT: TR = l08. (AN: TTI) applicatus ad TR
vel ANV. HIOc eA, tempus absolutum, quo mobile percurrit spacium
NVE in linea deferente, exponitur l0g. mo rationis, quam habot celc.
ritas inicialis AN ad celericarem mobilis residuam IH claplo hoc
tempore, applicato ad log-micae subtangentem.
Elinc, quia (5. 489.) Spatium ablolutum, quod mobile M dato il.
lo tempore in aere transmittie, eAt ANI. +NF = NR, eric hoc (Pa-
tium AI = NR =CHI =OTI =CO = NC, quoniam (constr.) AN =
AK, ItCM ANR = AI: AN, X NE (conAr.) = OTI. Ergospatium
absolutum, quod mobile nominato tempore percurrit, in aere repra-
sentatur per eam lineam NC vel DH, quae relocicatis amistam par-
tem exhibet. Dux omnia erant demonstranda.
C O. R OL L A R Y u M I.
436. L.tG  Mobs celeritates actuales BD Ceu l umalicur In
progrestione geometrica, tempora respectira AI: AN erunt in pro-
crectione arithmetiea. et