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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 712, page id 851387705:0732
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De Calculo Centri Cravitatis.
ROP. ZIV.
Cap. V
A. B. Aecus. Circuli, Centru slaritatis, est in axis lui eo Puncto, cujus
distantia a Centro circuli, est ad Racium, ut expoliti arcus Chorda,
ad, Arcum suum: FF quidem, in Semiperipheria, ut Circuli Diame-
ter ad demiperipheriam; scu uc Duxlum Radti ad Peripheria Se-
missem.
(Adeoque; Data ratione Chordxe cujutris ad Arcum suum; datur AE-
cus Centrum graritatis: PE, Daco Arcus cujulris, tota Peripheria
minoris, Centro sraritatis; datur Arcus ad Chordam Puam ratiO:
EE, consequenter, circuli Quadraturam seu ratio Diamerri ad Peri
metrum.)
E. Estque Distantia Centri gravicatis, Superficiei Solidire, conversione
(perfecta vel impertecta) tactu ab Axe conversionis lux; ad Di-
Stantiam Centri graritatis, correspondentis Dneula (Superticialis
Solidaere,) a Plano per ipsius Aciem exanseunte (rectis in ipsius Cur-
ra suxerticie parallelo;) ut est, ad convertionis Arcum, Chorda (2:
Fit quidem, in Semiconrersione, ue Diameter ad Semiperipheriam;
seu, ut Duplum Radii, ad Peripherix semissem.
Acque hinc habetur, Superficiei spliaericae, Zonx dimidiae (aliutre im-
pertectae) Cencrum craritatis.
Sto Arcus circularis B A B, qui non lic major Semiperipheria, Chorda BB;
H12. La cujus exiremis punctis B, B, demista (ad parallelam Diamerrum DCD) Per.
156. Pendiculares sint Bb, Bb. Adeoque, l CirCa D C. D ut Axem, converri incelliga
D.
C.
tux D A D semiperipheria: qua d D B desexibitur portio suverticiei Spharicae,
aequalis erir tacto ex bD in Circuli Peripheriam, (atque hoc urinque;) quaeque
a B AB describicur, sequabitur facto ex bb, hoc est BB, in eandem circuli Peri-
pheriam: (per 8. C, LL, I, prOp. Praced. ) Hloc est, S Chordae seu Balis B B magni-
indo ponatur c; e inteorae Peripherix, P: eric, qua ab Arcu deseribitur curra
Superticies, cF.
Fst autem, quae ab illo Arcu describitur Superticiescurra; aequalis facto ab
Areu in Peripheriam Ceniro gravicatis deseripram; per prop. 12. hujus.
ErsO; Si per magnirudinem Arcus, ut a, dividatur sP; prodibie = P periphe.
ria centro gravicatis descripta. Adeoque pro Pcripheria P, substiiuendo Radium,
ut ; erit R (cui aqualis ponatur C5) Distancia ceneri praricatis d D CD dia.
metro.