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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 711, page id 851387705:0731
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O
PrOD. LLIII. DeCaleulo Centri Cravitatis.
istius cui intistic Sinus; sirque ipsum Triansulum (uri jam ostensum est) Semiltis
Ouadrati; FrIt (pTOPteF ZX Z = 3) Cujusque Prianguli Momencum, Cubi Friens:
Adeoque Priens Cuborum sinuum illorum omnium, elt iptum Onsula (Semi-
quadrantalis) Momentum.
Atque hoc Momentum, per Magnicmdinem (modo invencum) diritum, extri
bec Centri sravicatis Onsulx, ab iplo, in Aan crecto Plano.
Cum vero, pro invenienda Summa Ouadratorum, Omn. s; e Summa Cubo-
rum, Omn. 5; habenda Crunt Omn. OR, e Omn. o R, (per SV. hujus: ) hoc
elt, Summa Ordinatim applicatarum, e Summa Ouadratorum ex illis, (in R du.
cenda:) Hhaec quo habeantur nihil impedit; cum et jam nocis mechodis, haberi
Postint; et methodis a nobis intra tradendis.
SCTZOL TV M
DOret quidem hac Propolitio, pront Supertieiem curram ex cireumducto Areu
Circuli ortam spectar, ab illa qua lequitur (aliunde demonstrata) inferri.
Nam data Arcus Magnicudine, ejusque Cenero graritaris; habetur cum Ongula
superticies curra, (live, quod eodem recidir, Summa Sinuum Rectorum;) cum
Superticies curra illius convertione facta: per prop. LT et +2 hujus. Sed perinde
est sire haec ab illa, sive ab hac illa, interatur; dummodo harum Palcem altera
aliunde probetur. Fgo hanc pocius praemiti, propter sequentis ex hac demonstra-
tionem perspienam, et quidem simpliciorem quam apud alios hactenus riderim.
Illa enim (mea mechodo) directe lequicur de immediare, a demonttraris olim ab
Archimede, ee post illum aliis.
Ouxe autem hic tradica sune de Curra Superticie Ongulae Semi cylindri, aciem
habencis Diametrum basis circularis; Peu, quod eodem recidit, ArCUS MOmentO re-
Spectu iltius Rectae: tacile (per ea qua ad prOp. TF. cracidius) EraNSTCrrI POTC.
rune ad Ongularum aliarum Cotindricarum Superticies curras, alios habentes
AXeS; Peu Arcuum Momenca respectu rectarum aliarum. Cumque omnes in siL
perticie Cylindrica Pisurae, planorum sectionibus terminata, relolvi poltint vel
in curras tiguras Cylindraceas, vel Caltem Ongulares hujulmodi: Poterunt propter-
ea ejulmodi Pigurae omnes in Superticie Cylindracea, hac methodo, ad certas imen-
Turas revocari. Ouod cum Colius calculi opus lic; acque etiam in sequentibus ali-
qua
Ea vero Linea Curra quae Ssuram Sinuum rectorum (MOdO MCMOTATAM) Fje
terminat, ACia As. 255. alia non elt quam Semielliplis, sectione Semi Cylindri
facta, in planum expanta. (Ouod olim docui in meo de Cyeloide Tractatu; et in
Tubjuncta ili Epiltola, Pa8. 99.)
Ouippe si Tuper A a D Semicirculo (f8. 254. ) erigacur Semi eylindrus, alricu-
dinem habens, in D, aequalem ipsi DC; perque punctum iptiD (in ea alticudine)
imminens, Balisque diametrum Aa, tranlear Planum (Onsulam Semi quactranta.
lem abseindens;) Sectionem illam, Plano secanti ee Superticiei Cy lindrica commu-
nem, Semi elliplem esse constat. Eadem vero abseista Onsulae curra superticics,
in planum expanta; estipsa quam Fisuram Sinuum rectorum vocatus, A a C.
Iptaque AC a illam terminans, eadem elt linea jam in planum expansa, quae, in
Superticie Cylindri, tueral Semi cllip(Is.
Sin porro, Planum idem (quod Ungulam tranc ex Semi cylindro abseindic)
concinuetur per tocum Cylindrum, inceoram FDiptin sectione perticiens; caque
inceora FIliplis, eodem modo quo haec semi ellipsis, expanta in planum superticie
curvan expancatur: Continuata curra A C. a in A et a exhibebic (urrinque d C)
curvam eam (quam F.llipsin expansam pridem nominarimus) quae Fieuram Si
nuum versorum terminabir. Ouod in Practatu de Cyeloide tusius oltendimus;
quaeque in ictius Tractatiis FI8. 7 et 30. extibetIE: EF in sequentibus ulcerus
contiderabieus, ad prop. 27 hujus.
255