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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 929, page id 851387705:0949
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PFOD. XXXI. DeCalculo Centri Cravitatis.
ErgO (PrOPteF HVD = ASX = AOV LOVHS = HDZ) ipsius H YD
relpectu Ao momentum Z A3 = Z F 3 - ABO - Z AXY + Z
Erso (propier Distancias momentis proportionales,) in DEI, Tumpta D.
quae SE ad AS uE : L. D 2 + , D3 ad 3 4 - , F = 4B0 - = A X 7 f 5 X72
ductaque OF paralleta A Z OCCUTrente SZ in R; erit in (juncta) AR (uepore
cujus lingula puncta in ea ratione diltant ab AD, A5,) Centrum graritatis IIVD.
Oux quidem AP est eadem policione recta cum ACI, quoniam ucraque cum per A
tran(Ic cunc per centrum graricaris HIV D.
Similicer (ob eandem caulam) in AFE, TUIPTA AL, qua Cit ad AS uE
22ad ; 2 - 5 F - 1B0 - = A XY + 5XZ2; ductaque L. K paralleta
AO, OCCUTTInL SK in K; eric in (juncta) AK (cujus urique singula puncta
in ea ratione diltane ab A∞, A0,) Cencrum grariratis. HVD. Prit autem hOC H
idem quod prius, ob caulam modo intinuacam.
22. Simili procestu urendum est in spatio exrerioriO V HIS.
Fst enim (ut jam ostentum) hujus respectu A0 momentum ABO.
Trem, respectu AZ, trianguli ASX =3 A elb (propter centri ab A X distan
tiam Z QVE) momentum aA VE; ee limiliter criansuli AOV momencum
5F3VE; criangulique HDX = = XY C propter dillantiam S LY) momencum
SXYFZ; iptiusque HY D (ur modo ) : L. D2 f = = D: ErGO (BEOPtETOVHIS
=ASX = AOV = HDX - HVD, ) iptius OVHS respectu A X momen.
cum E N VZ - EF3VZ = EZYHI =ZF D2.
∞
ErEO (proprex distancias momentis proporcionales) in DF, sumpta DL, quae
Sic ad AS, VES A V5 - EF 3 V= = 8XYIL = = L. D2 - q D ad ABO; du-
Ctaque LF paralleta A Z OCcUrreme SX in F; erie in (juneta) A F ( cujus pun.
Eta Tingula in ea rarione distant ab AZ, A 0) Centrum oraritatis O V HIS.
Idem obcinebitur comparando ejusdem O V LIS momenta respectu A∞, et AA:
vel A Z, _ AC; eande
eteta
cum per A, cum per ipLius OV FTS cencum graritatis.
F3. Simili icem procestu urendum elt in spatio exteriori A V HI A.
Fstenim (ur modo) hujus respectu A a momencum, L S FL + s, HL
Trem, respectu A X, rectanguli ADFLA momentum L R FF; unde Tubducto
iptius HYD momenco L L. D. +  F D; habetur iptius AVHID, respectu A X,
momentum ZXFZ3 - = L. D2 - = D3
FrgO, in AFI, sumpCA AMI, quae sit ad DFL, ut = S YP +, FL ad 3RFY
1 2. D -  = D3; exit in (juncta) A M, Ccujus sineula puncta in ea racio.
ne distant ab A A, AZ,) centrum graritatis A V FI 1.
Idemque obtinebitur, comparatis ejuldem momentis respectu AA, ec A∞; vel
respectu AZ, _ A∞: eandem autem AMI prodire necesle erit, ob causam ance in-
Finuatam; uenon lic spes inde ob duas hujusmodi rectas se muruo decustances, ipsum
Centrum obcinendi, ab (que plani magnicudine.
Si vero, in his omnibus, vel non sE S A∞ angulus rectus: ve) Foverbola nON
recta, sed Scalena, (sumprâ diametro quavis alia LocO axis AZ:) similis acthibenda
erit accommodatio cum ea quam de Scalenis insinuarimus ad GR. prOP. 3I. Cap. 5.
Multaque alia adjunsi polter, nisi sic nimius ellem.
Mistis icaque aliis; Unam adhuc de Hyperbola Speculationem subjungam, quam
Bbbbbb
Wrennio