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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 840, page id 851387705:0860
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840
De Calculo Centri Cravitatis.
Fis. 177, tione r ad R2:) Eric proprerea V P (= AB = Y 2VR) = Y 4 =21: Lt
78, 17.
Va (= BV ==) = BV-
BL
) = 2r B. Fujus ilaque duptum Ar B, eric ipsa A V cco interminabilis.
CNa qua rationC AaO co el CIIa MHHICIIEI pataLLCLOSTAMMII AaOO; eadem
id .1.
.Adeoque Rectangulum AYa ( = v BY
est A V oco incerminabilis, dupla huic inseripet pacasselogrammi AV co; nempe
DeF PTOP. T. HujuS.) Est aurem (PrOpCL Aa = 2 R, _ aO = B,) Rectangi-
lum AaOO = 2 RB: hujulque propierea cuplum AaO∞o = 4 RB. Lrga
AY cocoq ad A aO con (adeoque e AB, alt L7,) uc Ar B, ad 4 R B; hoc ett,
ut r ad R.
Cum itaque Sivus verti AV ad Aa, (hoc est v act 2 R;) LII L duplicata
ratiore subientarum AB ad Aa; (hoc clL, V 2V _ ad 2 X Ieu V 4 R2; vel
Vo ad V 2 R:) Cincque item eadem A V ad A a in dupLICaLa Faltone Curvarum
Ab ad Ar, (ut modo demonstrarum est: ) Fadem erit ratio AD currae ad cur-
vam Ar, qua et rectae AB ad A a rectam. Adeoque, ut Ar curva ad rectam
A a sic eurra AB ad A B rectam. Fs aurem (vri jam demonterarimus) curra
M dupla recta Aa; ergo _ A
curra, dupla est rectae A B. EF sic ubique
HOc CAt, A7, = 2 A a == 4R; 8
b = 2 AB = 2c = 2Y 2vR = V8VR.
Fis. 177, Vel CtiaMI, AL HaDCLME CAEVX AF dirs M TactosC Caca. Sa SCMICCLH
180.
in ratione data, in 7; aptetUT AB = A 7: Ductaque BB rectae A F parallela, in
eadem ratione diridetur A7 in b. OF ex aetiS PateI. DemDe H. Y:: 1d.
A2 = AB:: AT. AD.
PorrO; rectarum V ay hoc cst, BC, b8, vel GHI, 3h, hoc est, (in parribus
fi5. 177. intinice exisuis) b x, vel Xd; a Fansenre vercieis YA, distantia, sunt iplie
AV = ~, respeclirae. Oux ilaque in magnicudines BY = = (modo inventas)
ductae; cxhibent carundem respectu T A momenta, B Y 2VR (Teu cB.) Adeo-
que (Tumptis v arichmerice proporcionalibus) currx A~, vel AB, momeneum
respectu AF; vel Semignadrancalis Ongula superticialis iph Ar vel AB CurrX
insiltens, aciem habens PA; est asxresatum omnium BN 22 R eo spectancium;
vel (omistis B) omnium Y 2 2 R, hoc est, omnium Vp rectarum, Semiparabo.
lam AaP, vel AV p, H8. 1, 8. complentium: (est enim B, uc ex iptius origine
paret, nihit aliud quam ipsius A a vel AV pars intinicesima; quae omnes limut
sumpeae iplam A a vel a V. conticiune; acque hic nihil innuit aliud quam recta.
rum illarum, planum complenciu, eralsiciem.) Ft propcerea, Cuperticialis Vn.
sula ipti AF vel AB currae insistens, (aciem habens A L,) aequatur ipli A a P,
vel AV p, Semiparabolx; hoc ost (propter latus rectum 2 R, axemque Aa = 2 R,
vel AV = 2,) eric Ongula AT, = A a P =3 R2; e Onguta AB, = AV P
=ZVY 20 R == 3V6. DeT DEOD. E, vel. 6. hujus. Adeoque quae convertione CUT.
X A + vel Ab cirea F A, deteribicue superticies; cM 3 R P, vel  vY2VR
259
 e semiconvertiones 1. X P, vel  0 Y 2V R = v C
Iudgue