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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 733, page id 851387705:0753
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PrOD. XVI. D Cm Sentri Cravitatis.
FNTcellIZatuIE B C B Sector SphaerieuS; (inect-
lise Piguram Solidam in Sphaera, quae con-
vertione Sectoris Circularis BC. A, ICu BC a
Circa AC a deseribitue:) Fx intiniris nume
ro Prramiculis limilibus ee aequalibus (juxta
det. T. Cap. 4.) componi: Ouarum commu-
nis vertex sic Sphaera Centrum C; Balesque
componant Sphaerica Luperticiei sesmentum Se-
etori sphaerico conveniens. Frit saque, Pum
Timul omnium Magnicudo, aequalis Frienri
Radii (communis Alcicudinis omnium) in
Sphaericam superticiem B AB, vel B a B, lecto
si convenieniem, (upore Balium Agpreea
cum) ducto: (Onod ex = vel 6 hujus pro.
Babitur; Propter Parallela Pyramidum Plata similia, atit etiam parallelas Sectorum
sphaericorum curras superticies similes, in ratione Secundanorum:) Tum Centra
craricaris omnium, in Simili Supertiere Sphaerica, deseripea, Ractio Cb- CB =3X
proprer Cencra graritaris Pyramidum, in Axe Tuo polita, eres quadrances ejus-
dem ad verricem abscindentia; per shujus.) Cujus quidem superticiei D ab, ra-
dio Cb deleriptae, cum lingula puncta incellisantur aeque onusta, (UE qua aqua-
lium Pyramidum Cencra gravitaris Cultineant;) idem erir hujus Centrum gravi-
cacis, acque expoliu Sectoris Sphaerici. Puta (in sectore BCB A) in C, medio
puncto recta a v (Cinus versi arcus ba) per FZ hujus. F auTeM, (PTOPTCK
CD =ZC B = 3R:) recta a v = 3AV = 30: Adeoque 2C == Z 2 V = 3V, _ CO
V = 8h, (DTOPtErE R = V = B.) ECB
milicer oltendetur, in oppotio Scctore BC Ba, a V =d a V = 3B; e 2C = 3 a
8B;  CC == C. a-
8V, (propier 2 R = B = v.) Hoc est.
Dutancia Ceniri graricatis Sectoris Sphaeriei (in Sectoris AXC DOlit) d̀ Centro
Sphaera, aequalis Pribus Muadrancibus Radii minus Fribus Oetancibus alcicudinis
Tuperticiei Curra lectori convenientis; aut etiam (quod eodem recidic) aequalis
Fribus Octantibus alticudinis religuae superticiei sphaerica. Ouod crat propoluum.
Hoc cl, speciatim in Hlemisphaerio, (PrOpter V = B = R, ) 3 R-
Corollarium constat, ex prop. 3. Cap. praced. ITam Scctori BCB A, dempio
BBC Cono, habetur Sesmentuim B B A; e Sectori BCBa addico eodem BBC
Cono habetur Segmentum BB a. Cum icaque cum sectoris lphaerici (per jam
oltenta;) cum dempri addicire Coni (per 6 hujus;) magnicudines et Ccurra
sraricatis altignantur; habebicur et Relidui, vel Aggregaci, Segmenti Sphaerici
cum Magnicudo, rum et Cenirum gravicaris. Ec similucer, (muraris murandis,) in
aliis Sphxrae porrionibus.
Exempli pratia. Ceniri pravicatis Sectoris inceeri BC B A (convertione se-
B
misectoris Circularis BCi A, circa C A, desexipei) diltantia a C, (per modo de. Pip
monstrata) est Z C. A - 8 AV = 8A a = 3AV =3V a, in ipIO AXC AC
Hoc elt (policis ur in demonstratione propolicionis pracedencis, Radio C A = 160.
CD = Ca = R; inceera Peripheria = P; ArCU BA = a; Chorda B A = c; Finu
recto BV = 5; ee verso AV = v; vertique reliduo ad Diametrum V a = 2 R -
e = B; d Centro Dictancia Y C. = ~ = R = v vel V = R; Tiem a - 5 == e; a 7
=f; _cc.) 2R - 3V:
Adeoque ejuldem Cencri cravicaris ab a vel ra, lincellise; a plano in a
Sphaeram Fangente,) R = 8b = Z R - 30. AIque d F A, R
is
Eademque est ab nildem ra, vel TA, planis; distantia Ceneri pravicacis semi-
sectoris, (puta, qui plano per Aa transeunce, incesrum bilecante, decerminacur;)
aur Sectoris Ouadrantalis; aliulre impertecta quaris conrertione deseripii, (adeo.
que duobus ejusmodi planis, quorum communis sectio AIC A a, interjecti;) prOpTOK
omnia plana, Sectorem incegrum complencia, iplorum partibus, Sectores partiales
complencibus, proporrionalia, acque in iildem d ra, T A, planis Tansencibus
distanciis. Ouod de lemi conis, vel semilermentis Sphaerieis aliis, atiisve Solidis
impertecta convertione deseriptis, es correlpondencibus Ongulis, dec. Similiter ob-
tinet. Ouod semel monco, ne lapius Lic Opus idem repetere.
bZ. Z. Z