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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)
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De Calculo Centri Crravitatis. Cap. 1.
Eis. 201. CI (hoc est in a ductum;) dempris Omnibus Aecresaris ejulmodi usque ad re-
spectiros a arithmetice proportionales.
Estantem illud Sscreeatum Omn. a2 5, = - - a  R 2 f 2 a5 R 2 = a 2 V R-
2V R3, per 5O. prop. 29. Nempe, Insulae a B0 Fi3. 170. aciem habentis A a, mO-
mencum respectu Ra; cui relponder, in nostro calu, Ingulae M BVtig. 201. aciem
habentis PMI, Momencum respectu PM. ) Adeoque illud cories sumprum, hoc est,
in a =M B ductum, est - a 3 R2 + 2 a 25 R 2  a 3V R = 2 a V R3
Ouod quo rire intelligatur, contiderandum est; per s, incellisendum esse linum
rectum arcui a B fig. 270. hoc cA M B tis. 2Or. conrenientem; hoc cst, iplam BV
rectam; qua incerpretanda erir attirmacire vel nesative, prour citra vel ultra
M F A jaccat: Sieur de in ipso circulo Sinus Recti in contrariis semicireulis, con-
crariis signis aftici incelligantur; urpote ad contrarias diametri parres poliri: Trem
per V intellisendum este Sinum verlum arcui aB tig. 270. hoc est, MB AG. 2OF.
conrenientem. Si aurem B lumatur cura F; adeoque in primo Semicireulo; ni
hil cst quo quis haereat; (quippe hoc Caepius ostenlum cst, in proP. F7, de tigura
Sinnum Rectorum a rn fg. 179.) Si vero ulera P qui terminus est primi Semicie-
culi (cui convenit linus vertus v = 2 R, _ Sinus Rectus s=0) lumatur B;
(quod tancundem est acque s in Fg. 259. Post abtolutum semicirculum AD a, COn-
tinuandus csfer arcus, ulera a in Semicirculo oppotico, Turtum, versus A, Puta
ADaB,) Sinus Rectus contrario Signo alticiendus ellet; et decrelceret Sinus ver-
Tus (Tubducto ex 2 R, quancum eler linus vertus conrinuati areus aB, atia incho.
andus;) ulque dum, absoluro secundo Semicirculo, ad A tig. 169. Perrencum
tuerit, cranescence cum Sinu Recto, lecunda vice, in s=0, tum Sinu verso in
2R = 2 R = = 0. Sin porro procedatur, ultra circulum integrum, ad terrium
Semicirculum; ibidem Sinus Rectus ACtirmatire interprecandus erit, ee crelcet ite-
rum Sinus Verlus; Omi in quarto iterum decrescet, e Sinus Rectus nerative in-
cerprecandus: Et sic porro, alcernis vicibus. Ouippe eadem recta AV tig. 169
=Aa - a V = Aa - ∞ A F AV, ecc.) CM sinus vertus, cum AreuS AB, tum
Crelidui ad Circulum incegrum) AD aB, auc etiam (ulira Circulum concinuari
ADaBA B: TTeM arCUS A B, TinuS V B =s aftirmatire interpretandus, arcusque
ABaB, LinuS OppOSItS VD = -s negatire interpretandus; iterumque AreuS
AB. aD AB, sinus VYB = s; et Areus ABa. B ABa B, CinuS VB = - 5: FL Sic de-
inceps, si ad plures intcgros circuitus procedendum exit.
POrTO; PrOPIeT Aesresatum Omn. a S, = = a 2 R2 = 2a 5 R 2. = a 2 V R - 2VR
(utmodo oltensum est;) crunt Omn. Aecrecata a 2 5, ==Omn. = a = R2 = 2a5R
= a  v R = 2V R3; sumptis a arichmetice proportionalibus ulque ad a maximum,
noc cstMB
Sune aurem Omn. a 2 = Z a DeF pFOP. L. HujuS; FVBO, Omn. =a R, = - 2 a R
EF Omn. a5 = = e R = f a VR, per SO. PFOP. T7. (est urique Trilinei a B0
ti8. 270. momentum respectu Aay) FrGO, Omn. 2 a 5 R 2; = - 2 C R 2 = 2. a V R.
Et Omn. a2 V, = - 2 C R3 + 2 a V R 2 = Za3 R - a S R, Per S L. PrOB. 19
Nempe Ongula ABIE H3. 170. aciem habentis Aa, momentum respectu A~.
FrBO, Omn. a  VR, = = 20 R a + 2. a V R3 = 3 a 3 R 2 = a 2 5R =
EE Omn. V
=eR, per SB. prOP. 17. CF.lL urique Trilineum AbK H5. 270.)
ErSO, Omn. = 2. VR
a
FrCO, Omn. Aerecat. a2 S, = Omn. = a 2 R2 + 2 a 5 R 2 + a = VR = 2 V R3
=2C R a = 2 aV R3 = 2 C R a + 2a V R3 + 3a R = 42 5R2-
2CR4 = = 6CR + 4a DR3 = a 2 5R 2
Arque hoc demum subductum ex, Aesresat. a s, in a maximum, = - a3 R
F 2a2sR2 = a v R = 2a V R3; relinquit Omn. a3 5: = 6C R - 6 a V R 3 -
a3R2 + 3 tu da.
Fje. 199, Cum itaque singulorum Sectorum exiguorum Angulus siE, rexbi gratia, intini-
retima pars quacuor rectorum; cui respondeac. in Circulo primo, areus T = ∞ P:
adeoque in siis P F peripheriis conterminis, + = = Z; (DOTO a pro areu cir-
cuili primi qui respondene aneulo PM Y;) et propterea eorum magnicudines
GAE
884
00.