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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 805, page id 851387705:0825
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la
ad AXem Aa, elta ArCuS; quae vero ad peripheriam ulteriorem continuetur elt
a FS =F; quaeque peripheria propiore intercipitur elt a - s = e, ditterentia ar
cus et linus recti linui verso AV conrenientium. (Puta, lig. 286, bB = a ]
F5. 185, bB = a = 5 = e; urrobique bV = a, BV = 5.) Adeoque LI exempro
illo Semicireulo, procruderentur illa intercepia rectae usque ad A a 2Xem; qua prO-
direr tisura esser figura Ditterenciarum arcuum sinuunque rectorum: Sicut, ex
Semicycloide, exempro Semicireulo, tigura Arcuum Formabatur.
Elis ita constituris; (Nempe Semieycloidem Semicireuli Priplam esse, de partes
parcium respectire sumpearum; vel quod eodem recidie, Semiereloidem Semicir-
culo e Fisura Sinuum versorum Areuumre (hoc elt, Frilineo restituto,) simul
Tumptis aequalem, ejusque parces partibus horum respectire sumpris:) ad caleu-
Lum sic procedimus: Rerencis Symbolis propolitionum praecedentium.
Est Senseneulus ADa = a L, (DerSB. PrOP. 15.) a Prilineum relticulum
= A D a (iltius duplum) Z R P; Der SB. prOp. 27. Ergo Semierelois (ejusdem
Friplum) TAV a =3 RY. Adeoque Parallelogrammi reliduum seu Semiercloi
dis complemencum A~ P = = RZ
Ecem Sector Ba A = Z a R F ZS R = = fR (per S II. Prop. 25.) Frilinei resti.
nuni portio bBa BA = a R F s R = fR, per SB, PrOP. 17. FrgO Porrio Cycloi-
ais b Ba V A = 3a R f. 35 R = 3FR.
Irem Sermentum Semicireuli residuum a B a = = R D - = a R - =5 R = = a R -
25 (E, (PET GC. PrOP. 15.) Ergo Segmentum Semiercloidis residuum bB+ = Z RP
3aR - 35 R = Z a R = 3 5 R.
Icem; Si ex illa porrione Semieycloidis BBa V A; auteratur cum parallelo.
srammum bBa B (= b Ba B H8. 270.) =aB, cum Friansulum aBV = ESB:
hoc est Fraperium bBa V = a B = Z sB =. 2a R = aV + 5 P = 5 52: Relinqui-
tur Semiereloidis segmentum ABV = = 5a R F Zs R + a 0 + 25~ =- - = cR +
a2 = 25V = ZfR = a B = Zs B.
Vel etiam; prOpter ABV = Z C R f Z S~ (per S F. PrOP, 45.) e ABB -
= c R + a 2, (per BB. prop. 17.) erie ABY = - he R + av + 1 50 = - 5 a R +
25R +
Eq speciacim, Seemencum AdC (prOPter a = 1 2, 5 - v = Re,) = R: + E A∞
Trem, si ex ParalIelogrammo AV bK = fV (ProPter A V = V, e bV = f, ) FI8. 166.
eximatur Scgmencum illud ABV = 3fR = a h = =sB: Relinquieur Frilineu
ABI (seu seementi ABV complemencum) fv - 3f R F aB + = sB; hoc clt
(reductione facta) Le R = 352; Nempe, cancundem acque Semicirculi scemen-
cum AB V, modo dictum.
Pic
50
170.
PFOD. XX. De Calculo Centri Cravitatis.
cuum) Si Diametro A e deseribatur circulus, quae d b puncto ordinarim applicatur
Sectoribus consticui, ut, AdL, La 2, C. rel eltam (quod in partibus intinire FiS. 167-
exiouis, propter inucar approsattoeu, Tautundem raler) ex intinitis nu. 168.
eet LFal uto a CCat CCpClibIS, uE D a H, P a t, dc. Eve ex
Porro, si incelligatur Semicirentus (juxta des. 2. cap. 4.) ex intinitis numero c
rotidem