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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 762, page id 851387705:0782
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DeCalculo Centri Cravitatis.  Cap. V.
ut 2 ad 2, (Incellige, in parribus intinice exiguis, dum Friangula Sectoribus, e
69, Parallelosramma respectiris Ouadrilineis coincidere reputaneur.) Forunque
270. Friangulorum cencra graritatis in a B polita, ab a distane Z a B; ideoque, ab A a
3BV; hoc clt ZB0. ErgO (propter EX Z = 5,) Momenta linsulorum a B Frian-
sulorum respectu adjacentis aa; hoc est, Friangulum a B = Z bB, in ZBY = 3B1.
elt ad BB in B0; NE F ad 3. FC, consequenter, omnium Friansulorum, hoc est
Sectoris Ba A, momentum respectu A∞; ad momentum omnium DB Parallelo
Grammorum quadrilineum bBa A complentium in respectiris distanciis eo Tuspen-
TOrUM; UE F ad 3. FH autem (per S S. prOB. 25.) Sectoris Ba A, momencum
respectu Aa, seu correspondens Ungula, = V R 2 f ES2 R: ErgO, omnia BB.
Rectansula; seu Omnia Bs, aut omnia 25 R -~5, eo spectantia; (hoc ell,, 50-
lidum Ouacrilineo BBa A incumbens, alcicudinem habens super singulas rectas
XE, 26, _c. aequalem respectiris Eo Cv, _c.) V R 2 fZS R. Ft de aliis iltius.
modi Solidi porcionibus, mucatis mutandis, timile fiet judicium. Puta, (propter
Seomentum AB A = Z a R = = s R, ejusque respectu A a, momentum : V R2 = ES R
per 8B. prOP. 15.) quae porrioni Ab K incumbic ejuldem Solidi concinuati pOr-
cio (hoc eltu omnia vs eo spectancia,) exit D R 2 = = s R. Et, Similiter; qua
trilinco rbB incumbir ejuldem Solidi porrio (hoc est, omnia hs hruc spectantiam)
BA2 = = s R. EF Sic alibi.
Acone his ita in Fisura Sinuum Versorum A ra absolutis; idem eciam in
Fieura Simuum Rectorum (corius Semieirenti) arn ab(olvetur. EM utique hu-
jus ucerque Semistis a s un rdn cadem, plane fieura acque dCi A, (figurX A7 a
Leomentum,) vel de 2; alio sicu Dolita. Cum enim bB hoc est V a (et de reli-
quis similiter) sit arcus Ba = =B, suus vertus; erit ptopterea (ejusdem à Ro-
dio differencia) bk, hoc CA V C, arcus BD linus rectus. FL sic ubique. Fs
isitur, cum dCi A, cum der, fgura Siruum rectorum tocius Ouadrantis, (puta
quadrantis DA, vet Da AI8. 169. urrinque à D inchoando;) adeoque cadem
plane figura cum a d  vel rd u, qux iridem (per constructionem) lunc Fisura
Sinuum Rectorum unius quadrantis incegri, acque ad cundem Radium. Cum igi-
cur cum ipsius dC A crilinei, cum partium iptius, magnicudines, momenta et Cen
era cravitaris determinantur: Etiam fisurae a rn utriusque Semittis, adeoque e
rocius, ejusque partium, masnicudines momenta et Centra srarucatis derermi-
MaNEUE.
Exempli Bratia; e, d n = 7 8 n = dC A = = a R F 5 R F a V (per SB.) id est,
noc casi, (prOpter D = A C = R, _ 5 = DC = R, _ accum a =D A = 2 7.
P = R= F = R~ = R2. Fjusque momencum respectu batIS as, vel dC,
(hoc elt omnia Semiguadrata Sinuum rectorum unius quadrantis,) 2 a R2 =35 p
F25V R = 3 a s (per S F.) id est, in hoc Catu, 16P R 2 - 3 R3 F ZR3 - 3Y R
SP R2; (Adeoque, Summa quadratorum sinuum rectorum, Peu omnia s’, t0
tius quadrancis, 5R2 P; uE Supra S V. PTOP. F3.) Cenerique gravitatis à balC aS
seu de distantia (momentum per magnicudinem dividendo) is P
Similiter; porrio n d BV, HoC cst (Lumpta C l =dB) ACIZ, est (ut SB.
Ss, SuMptO arCI XO hOC CA Z A, ==a. Nempe Factum ex Radio R, in s Si
num rectum arcuS Z A = =O; hoc cAt, in Sinum arcus DB = s B; hoC est, (BO-
sito aB= AB =a; adeoque BD ejuldem complemento,) in x = VC. HOc est,
1 dBV =
Ex consequenter, a P, = a. 8 n = S uv B (prou minor majorre quadrance tuerit
arcus a B Teu AB) erit R F ~ R; hoc Cst (PTOPTCF N = R = v E AB tiv qua-
drance minor, et x:
= --R = v E quadrance major; adeoque, urcunqueu R F N = 2,
aBV= R F _ R =
atine item deducetur Momentorum ratio in Frilinei as n. vel rsu porrioni-
bus; ex momentis portionum Frilinei dC A; sed perplexiori aliquancum calculo
ob concrarium Pixurarum scum. Cum enim, in priori Titu, areus ab A inchoa
rimus, (utu recbi graria, arcum AB diximus a; cujus linus rcetus s, et verlus v.
adeoque BD eNet ejuldem arcus complemencum, cujus linus rectus VC. = v:
jam mutaro Titu, areus inchoantur ab a hoc cst d D; (ad eoque arcus a B, HOC
elt DB, dicetur an cujus lnus rectus s = V C; et linus complementi BV = X, etC.)
Verhi gracia, sii
Ex Pacalleto eramoni ALC A momenco respecta Y A, hoc ell, (volico L X,
H0c
Fip
1.