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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 808, page id 851387705:0828
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De Calculo Centri Cravitaris. C ap. V.
Fis. Es autem Frianguli BV a, magnitudo = sB; momentum respectu ra, Z sH:
266, respectu T A, ShR =- ZSB: per SMI. prOD. 15. Et Parallelogrammi bBaB,
270. masnicudo ah; momentum respectu ra, Za h; respectu Y A,, 2 a b R = Z a B:
per s f. prOp. T7. Erso Traperii bBaV, magnicudo, ah F Esh; momentum
respectu ra, Ea B F =SB; relpectu Y A, 2 a B R = sB R = = a B - 3 sB. OUX
relpectire lubducta ex Ouadrilinei BB∞ A, magniudine ec momenris SD. iradi-
cis: Relinquune Scomenri b V A magnicidinem 3 f R = a B - 3 s b = - 3 a 
F25 R + aV + = 50 = = ZC R F aV F Z5V: Momentum respectu ra, (vel cor.
respondens Ongula, ) 2f R = E sB R - Z aB2 = Z sh2 = - 2 a R= + 3 sR 2
+ 240R +  50R = 3 aV - 35v = = de A = + a 2 R + = 5V R = = a 5 + = 5:
respectu TA, 2 fR  = S BR = 2 aB R = sB R + Ea B = + 5 sB2 = - = a R =
1I.
=a5 R F 252R + 3202 + 55V2 = - = e R 2 + a V R = 3 5VR = = 4 52 - = 53
Unde reliqua deducentur ue prius. Praperiique Distantia Centri sravicatis
(momenco per magnicudinem dixiso) a ra, 3 a = 2 5 B; d FA, 2 R -
3a+
6a + 35
6a F 35
Si vero, ex Parallelozrammi A VBK momenis, eximaneur momenta lexmenri
ABV; relinguencur Momenca respectira Trilinei ABK.
EIL AuTEM, (DEOPter AV = ~, b V = f, Distanciamque Ceneri gravitaris ab
Aaq vel BR, Zf; ab AK, vel BV, ZV; adeoque ab a F, Z V = B = 2. R = ZV;)
Parallelosrammi magnicudo, fu; momencum respectu Aa vel DK, = f2V; re-
spectu AF vel bV, 3fV2 = fVR = 2F52; respectu ar, 2f~R = 3f22-
3FV= + fvB = = fv2 +f52 =fvR + 3s5.
LSI itaque ex ZfV 2 = fVR - 2f52 = a v R F 5V R - 7 a 5 2 -- 2 53, auFETALIIE
segmenci ABV momentum respectu T A (modo inrentum) = E C R2 + aV R L
35V = 2a5 = - 5 53; habetur Le R + asV R = 353, momentum Trilinci ABK
respectu T A. Fdeoque, propter magnicudinem (S B inrentam) Z0 R = 352, Di-
Mancia Centri praxicaris d X A, 3C P + 350- 25
30 k p
Oek + 652
3 150: Adeoque, d
i abY, 2R - b (= 0 - = R) + -
3
et (rellicuendo
magnimudinem) momentum respectu Za, 3C R= + 3 50 R F 553; et respectu bV,
ZCVR + 350= = ZC R2 = = 5V R + 553 = = de R 2 + 3aV R = = 5V R - 353
(DrOPteE ZC VR = = a V. R = = 5VR, _ Z5V2 =5 V R -- 353.) Vel eriam Cx mo-
mencis Parallelogrammi AVBK, fVR F 3f5= e fV R. - - = f5 (modo iradi
risy) hoc clt, ex av R F 50 R + Z a 5= + 3 53, e a v R = 5V R = = a 52 - =53
subductismomentis segmenti ABV, = 3C R= F av R + : 50 R + = a 52 + 35, et
ZC R= + 3aV R F 25V R = = a 52 = 553, modo inventis; TIabETUT MOmentuM
Prilinei ABR, respectu 74, 2C R = F 3 50R + 553; e, respectu bV, = =e R-
+7av  + 3 5V R - ,53; ut prius.
Acque tractenus Semieycloidis, partiumque illius, Momenta et Ungulas, conside.
ravimmus duncaxac prout ad rectas Ta, J A, aut huic paralletas respectum habent.
Oux quidem, (propier eandem d rectis illis distanciam P’arallelosrammorum DBE n.
sive uc inclinata jacene in Semieyeloide tig. 167, 168. Tire ut crecta in Trilineo re.
stiruco H8. 270. Ec Priangulorum Cimiliter, uc x ED seu Ba P, Ag. 167, 168. cir.
que aequalium Ba P, F8. 259.) alia non sunc quam asgresata partium correlpon.
denrium in Semicirculo, ee Frilinco Restituro, H8. 209, 1 0. Ft Momenia Ongu-
laque qua Semiercloidem spectant respectirorum Momentorum Onsularumque
aceresata, Semicireulum Prilineumque illud respectire spectancium.
Verum si ad rectam A a aliamre ipLis ra T A, non parallelam exisantur; sire
ut Ongularum aciem lire uc librationis axem: Ouoniam alia est inde distantia
Paralle logrammorum in demieycloide inclinatorum, alque erectorum in Frilineo
Retti.
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