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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 721, page id 851387705:0741
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PFOP. ZV. DeCal aadta.
Suippe e omencium Sesmenti aBa, respectu Fansentis oppotii FA, eris
a R2  2 A  83BL; _ respectu Tangentis concermini 7 a exit Z a R 2-
5R= 6
ANEetiam, ex LP R momento rocius Semicireuli ADa, respectu Paripentis
uexiulris ra vel T A, auterendo =a R3 = 3s R2 -5sV R momentum scctoris
Ba A respectu ip(ius Ta, (Der SM. ) habetur relidui ad semicireulum Segmenti
aBa respectu ejuldem + a momencum + P R2 = = a R 2 - 35 R 2 = SSV R; hoc est
DEOPTCF = Z = a = a, _ V = 2 R - B, ) Za R 2 = Zs RZ = ZsBR: Acque limili-
cer inde subducendo ejuldem Ba A lectoris momencum relpectu T A, Za R 2 1
5s AE = 35 R; habetur legmencia B an respectu ejusdem P A, momentum ix p2
22 R2-
5R= - 550R; hoc et (PrODICE Z P = 4 = a, _ v = 2 R = B,
Fx simili racione, mucaris murandis, corundem exposicorum omnium Planorum C
momenca respectu alius rectae iptiS T a F A, BV, paralletae; cujus diltancia intra
vel supea harum aliquam dacur.
Ouodque de horum Planocum Mamenris respectu rectarum Fa, F A, BV, aut
hisce parallelarum, dictum est; paricer incellisendum est de Ongulis luper cadem
plana crectis, qua plano ablcindantur per ealdem respectirera, TA, BV, vel
hisce parallelas, (quae expolicum planum non secent,) cranseunte. Nempe; Si
secancis plani ad expolicum, inclinacionis angulus sic Semiquadrancalis seu eracl. 45,
quam demiquadrantalem Ingulam dicimus;) eadem erie (per FF hujus) Ungu-
La atque Momenti delignatio. (Rric enim Ongulae alricudo, super quodris expo-
sici piani punctum, eadem arque ejuldem puncti ab illa recta quae est, communis
planorum incerseetio quam Onsula aciem dicimus, distancia.) Sin major fuerit
minoxre lnclinacionis Angulus; major exic minorre illa Ongula; ee quidem in
ratione Tansencium Ansuli Inclinationis. Nempe Solido Prilmatico seu Colum-
nari aequacur; cujus Balis, sic expolicum Planum; Alciindo, aequalis alcicudini
rectae Centro graricaris inliltenris; (ur ad prop. rr. oltenlum eft;) HOc ett, (A
ansulus Inelinacionis sic Semiquadrantalis,) aequalis distancix Centri gravitaris ab
illa recta quae concipitur rel uc Axis mocus, vel uc planorum, expolin ee secantis,
communis sectio, seu Acies Ingula.
Denique; Eadem quae diximus Momenta, extribent etiam Magnicudinem 5o-
lidi, quod expolicorum Planorum circa expolitas rectas conversione deseribitur;
per T2 hujus.) Nempe, in ea racione ad momenta ut jam delignata, vel CIngu-
las Semiquadrantales, quam habet Periphoria (incegra, vel dimidia, eec. prout con-
verlio illa estincegra vel dimidia, ec. ) ad sui Circuli Radium. F.A enim distan-
tia Ceneri graricaris plani, ab exposita recta, Radius iltius Peripheria (sive per-
tectae, sive impertectae) quae convertione Ceniri gravicaris cirea illam rectam de
Scribitur.
Pnta, Sectoris BC. A, respectu rectae Ta Momeneum, vel Semiguadrantalis
Ongula, est (uc supra, SI.) Za R7 = 3s R2; e respectu rectx TA, =a R2
Es RZ tirso Solidum Annulare, illius incegra convertione cirea r a Factum, est
Za R P = 35 R~; e leniconvertione, +a RP + SS RP: EL, Circa T A, ine
Era convertione, Z a R P - 35 RP; et semiconvertione, ̀ a RP - + 5 p4
Trem, Sectoris Ba A, respectu rectae r a Momencum, vel Semiguadrantalis Dp
Bula, (ut BM.) cst  a R = + 8S R = = 35VR = 3f R2 + 6sB R; _ relpectu re.
Eta TA, Za R2  SS R = + 35V R =3f R2 = EshR. Erso, Solidum illins inte
eia convertione circa r a deteriprum, cst, L a R P +
165h4; e convertione anmidia, = a R P = 3S R.
Acque, circa TA, ConVeTHOLC Incegra, Za RP + 55 RZ
SR
2507
55V
5
2
S RP + insBZ
EFRP EstZ
Tiem, semiscementi BV A, respectu iPlius ra Momencum, vel Semiquadrancalis Vn
ad A F Z5VR
= 25 R2 + 35V R-
=ZC R 2 f 35VR + 353; F.L
= ZC R2 = Z5VR = 353. H. LGO
Solidum illius incepra conrettione cirea ra deseripium, cst, La R ~ = = sR ~ +
i e convertione dimidia, + a RP
25 X
20 R2 = = 5 R + Es B R. UE priuS.
Scta Ct (Per D L.) = a R3
relpectu l A, Za X
150 P + p  6a L + 150 +
et couvextione dimidia, = a RL f 12 R P + 12 sV P = = fRP = = 5hZ