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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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2.5C
PTTLOSOPMILE NATDRALIS
De Moropori atque adeo sectori huic provortionalis est; in Medio resisten-
Pouronon re est uc criangulum; ec in Medio utroque, ubi quam minima est, ae-
cedic ad rationem aequalitacis, pro more sectoris de trianguli.
FROPOSITIO ZIV. THEOREMA XI.
Tisdem positis, dico quod satium ascensu vel descensu descriptum,
est ut differentia areae per quam tempus exponitur, e areae cu
jusdam alterius quae ausetur vel diminuitur in proeressione A-
rithmetica; si vires ex resistentia es gravitate compositae su-
mantur in prorressione Ceometrica.
CapiatUE AC (in Fic. tribus ulcimis,) gravicari, _ AR RCS
sentiae proportionalis. Capiantur aurem ad caldem partes pun-
cti A si corpus descendit, aliter ad contrarias. Prigatur Ab quae
sIC ad D B ut D B9 ad 4 B AC: _C arCQ AbNVR augebitur vel
diminuetur in progrestione Arithmetica, dum vires CK in prO-
gressione Ceometrica lumuntur. Dico isitur quod distantia Cor-
Poris ab ejus alticudine maxima sIE ut exceNtuS arex Ab N R suPrA
aream D LT.
Nam cum AR EE ut resistentia, id eAt, ut AF9 + 2B AF;
altumatur daca quaeris quancitas Z, e Ponatur R aequalis
AP9+ 2BAF
; _ (per hujus Lemma LT.) erit ipsIuS AK mo-
mencum X L. aequale 2 AP Q + 2B AX Pd seu
ArCa ABNV K mOmentUM KL.O N aequale
BFOZBD cub.
2~ZC LX AB
BP4, et
EBFQXLO seu
Cas. T. Jam si corpus ascendie, sieque gravitas ut ABg + BD9
existente BF. T Circulo, (in Fig. CaC. I. PFOD. XIIL.) linca AC3
e
qua graritati proportionalis est, erir LBg + BDG
dc D P9 Ieu
AF 9 + 2B AF + ABg + B D g CrII AK XZ = AC XZ sCu
CKX Lis ideoque arca DV erit ad arcam D P Q ut D E9 vel
DBg ad C R X2
as