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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 614, page id 851387705:0634
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Crarcum Descensib
Idem similiter ostendetur: Si in F P CE plano ad Florizontem obliquo Ferendum
intelligatur Grare; propter punctum P omnium in illo plano intimum, per 20
hujus: ductumque circuli, maxime Dectivem, per 24, 25, 26. hujus. Duod erat
alrimo demonstrandum.
SC +FOL LVH.
COpponic haec Propolicio, Filum non Ratensile, led non et Inftexile; adeoque
dilerre procedit de Crari Pendulo; quod itaque humilius incellisicur, Palcem
non altius, quam F punctum tixum. Verum quidem clt; Si estet in eadem P C
Deripheria, lupra Iorizontalem rectam. PC concinuata; descenderet hoc adt Per-
Dendiculum; at non Ctarim hac de caula, neque stacim secundum peripheriam; Sed
sccundum Pexpendiculum, uc Cirare adhuc absolure liberum, (non cantum libere
Pendulum,) per 22 hujus: donec, extenso ad Tuam longitudinem AlO COCTCCTCTx
ne diurius recta descenderet, sed sccundum Peripheriam, Vi Proxositionis hujus.
Sin Filum illud eriam Inflexile incellisatur; ubicunque in ea peripheria (ex.
era perpendiculum) ponatur; (sire lupra tire intra Horizontalem lineam:) sceu
dum veripheriam delcendet, circa Cenirum motus rorando. Verum illud hujus
loci non est; sed ad Libram spectar, ee intra demonstrabicur.
PROP. XXXII.
Crare pendulum, in Pexpendiculo consticutum, Vis quantumris exigua,
a Perpendiculo dimorebit.
Idem de Perpendiculi Succedaneo, in Obliquo plano, intelligendum.
Deque aliis motibus, mutatis mutandis.
VX punctoF, in Perpendiculo FP, dependeat ex Filo Pondus D: Ouod, ex
perpendiculo morum, describat P SC Circuli quadrancem; Cui circum seritr
TuT FFI quadratum. EF exponatur, Secundum directionis lineam P IL FLOrizon-
talem. Vis quancumris exisua: pura, quae lic ad Vim Ponderis P, uen ad F (hoc
Cst, s incelsipatuE Vis V, Ponderi P in perpendiculo aequipollens, sit expolica Vis
nV. ) EE POnatUT (ex PeXexIpIO PrOP. 28. hujuS.) PO recta, ita declivis, ut
Ponderi P in PO morendo aequipolleat Visn V. Nempe, Tumatur, in HG recta,
recta FO quae sic ad P HI in ratione virium expolica n ad T; dt jungatur PO. Cum
enim (IC, ue Vis ad Pondus, lic Altitudo HO in perpendiculo (qua elt Directio
Ponderis) ad FTP lineam directionis Vis Nloventis: Expolico Ponderi per PO
morendo, aequipollebit Vis exposita; adcoque aucta rel tancillum Obliquitate,
Morebic. per 28 hujus. Elt aurem (propter S P HI angulum contactus, minorem
angulo rectilineo OP FI, Per 16 Flem. 3.) Obliguior AsCenSIIS per PS quam per
PO. Morebic ixitur datum Pondus, Vis Exposica in P S peripheria. Ouod etat
probandum.
Aia Demonstratio.
Idem demonstrabitur ex 25 hujus: Proprer candem PS peripherixe in puncte
P decliritatem, acque Contingenis rectae PH; qua cum Florizontalis licu consta-
bic proxolicum, Der 27 hujus.
e R OP. ZXXTTT.
Crare Pendulum calum, quousque extra perpendiculum, data Vi
morebitur; determinare.
18. 4
Cap. II.
Onstructis uc prius: BICo; Per areus P A (quem ableindit PO recta) SC
millem PS, Hec ulera, Fxposica Vi motum iri Pondus P.
Lrat, quae P A aC (adeoque d LubtenIam, PeL 3O Elem. 3.) bisecat e Cen-
tro recta LS, Secat Lubientam P A ad angulos rectos; per 3. Flem. 3. Huic ioi
tur subcenta, hoc elt PO rectae, parallela est quxe Circulum in S cansit SP re
etam
E18. 43