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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 921, page id 851387705:0941
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PrOD. LLSI. De Calculo Centri Cravitatis
ceris ad D. Vice comitem Brouneker, (Societatis Regix Londini Praelidem dignisti. Fig. 210,
mum, ex harum rerum sciencistimum,) datis, Julii 8. _ Aueusti 5. 2668. acque IN ZLY.
Transactionibus Philosophicis Condinensibus. lub idem tempus, intCFLIS, PrO Mense
Aueusti 1668.
Eabica vero, ut dictum est, Figurae Fyperboliex Fixceriorismagnicudine: Friam E.
Incerioris magnieudo facile obcinetur.
Incellisatur urique ab V vertice, recta VO, ip(i A∞ parallela; portionem ab-
Scindens SFIVO. Cujus plani magnitudo, (sic ut jam craditum est inventa,
dicatur P L. FAtque AVO = Z AOV∞ = = AB. TIem AZS = Z  (RemDE
li sic Friangulum rectansulum; adeoque Z5 et S A ipsi A, figurae alcicudini,
aequalis;) vel salrem (polito SX =. F,) AZS = 3 A F: ErGO HVZ = AX5
AVO-OVIS = = 2 = = AB = PL, Teu = AF = = AB - PL. Sed et
hinc etiam, s OpuS LiE, abscindi porerit (per HI D ordinarim applicatam) LI D X
criansulum; ue habeatur porcio FIDV
Si vero, non quidem ad Axem, Sed ad aliam quamris Diametrum, ponatur hy.
perbola: Menluram ejus non minus alsequemur.
Nempe; Sumpto, ubiris in Flyperbola, verrice L; cui respondeat Diameter
AIdX. Ouippe hie timilirer habebicur Magnicudo Triangulorum AC,L, ASX,
Eldx et sparui SCLHI: Adeoque e LHIX, LFId.
Sed _e, propter cognira triangulorum ASX, AOV, EDX, vel ASL, ACL,
FTdZ cum Plaonitudines, tum Centra gravitatis, horumre momenta re(DCCtU re-
CtX A∞; (per prOP. 6. HujuS:) AEque etiam (per jam iradita, 5G.) Sparii
SOVHI vel SCTMI magnicudinem, Cencrique pravicaris ab A0 distantiam.
ejusque (respectu ejusdem A5) momentum: Flabebitur etiam portionum FIVX,
EDV, rel TITX, HdI, momentum. Cunque (uc jam octentum est) habea-
cur e harum, magnicudo; habetur (momencum per magnicudinem dividendo)
cacundem diltancia Cemtri sraricaris ab A0.
Porro: Si contideretur eadem V HD semi hyperbola, tanquam ex rectis ips R.
HID parallelis, ad axem VD ordinatim applicaris, contlata. Manifeltum clt, Lin-
sularum FTD ordinacim applicatarum momenta, Peu Priansula iplis inliltentia
Semiquadrantalem Ongulam complentia, aciem habentem VD; carundem Semi-
ladracis esse aequalia. Adeoque Temilumma quactracorum IIIOPUM, CrIE FOEiS
VHD semi hyperbolae respectu iptius V D momencum: (seu semi quactrantalis
Ongula aciem habens V D.)
Polito iIagUE PTO AXe FranIVerIO, Z; pro Lacere Recto, L; Sumpris Diametris
interceptis, a arichmerice proportionalibus, uc F, 2, 3, ecc. ulque ad maximum
D = V D: tirunc quae his respondent ordinatim applicacarum (lemi hyperbolam
complencium) Ouadrata (uc in tractatu meo De Conicis Sectonibus, PrOP. 33.
ostensum est:) cocidem d L. +  (eu 
Z, Tumpris d arictimetice. pro.
porcionalibus, usque ad maximum D Y + D L. = Duadr. H D. Adcoque (PrOP.
tex Omn. a, = = D 2: e Omn. d2, = = D3; per prOP. T. hujus;) Omnium qua-
deacorum summa 
+3 F, seu 3
plani momencum, 3F + 2 2 ∞. 2.
L 2
D2 L: _ Semi Summa, seu
Acque hocMomenium, per plani magnicudinem (modo extribicam) divisum;
exhiber ejusdem ab V D diltantiam Cencri graritatis.
Sed ejusdem Centri distantia ab A0, jam extibita cst: FrGO (propter A0,
AVD, non invicem parallelas,) exhibetur iptum Plani V FD Centrum Gravita.
tiS; DeT PrOP. 26. Cap. praeced.
EE consequenter; (propter data etiam criangulorum ASX, AOV, FIDX,
Magnicudines et Centra praricatis, per prop. 5. vel 6. hujus; iptiusque SOV H
magnimdinem, jam oltentam;) datur etiam plani SOV HI C entrum sravicatis; Per
PECP, 27. Cap. praecect.
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