# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0871
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0871?run=74
# 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 851, page id 851387705:0871
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=871
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000871.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

PEOP. XXII. De Calculo Centri Cravitatis.
Superest tandem, ut suxerticialis Snoulae AF vel AB, aciem haberitis Aa, m0.
mencum respectu A a inveltisemus.
I
Fis
Dirila itaque, ut prius, Ar in minutas partes aequales: Adeoque Tumpris AB 182, 183
=26 fiy. 177, 182. arichumetice proporcionalibus: Frie cujusque b puncti, Pey 170.
Partis minurae, ab Aa distantia, bB V Hg. 277. hoc cst Bb  tig. 182. Adeoque
omnes rectae punctis b inlistentes, Ongulam complentes, lunt tocidem Bbo rectae
crilincum A a 70 tig. 182. complentes; hoc cst, bis Omnes orv Hg. 183. hoc est
tocidem a-  s. Subtensis c’arichmetice proporcionalibus respondentes. Oua icidem
in a f s diltanciam ductae, exhibent earum respectu A ae momenta, rotidem a 2 +
2a5 = 5
Sune aurem, omnia a; seu omnia quadteata 70 lig. 183. Duptum Semiaus.
drantalis Ongula, seu momenti crilinei An a, PCU A07, (pront rel tocum vel parS
consideratur,) respectu Aa tig. 183. Hloc elt (propier figuras similes A n a. (i8
283. _c a _ F fig. 170.) Sexdecuplum momenti crilinei a r P vel a0y, fig. 170. Ic
spectu rectae a P, (nempe in eriplicata ratione laterum FTomolosorum, Aa = 2. R,
ad aT = R.)
Fstautem, Momentum Frilinei 403, Fg, 170. hoc Ct, 4E07 =E0a, (respectu
aF,) Ea = S, minus, = e R F aVR; (DeF BO. PrOP. 79.) Seu 3B =5. + e R2 -
avR, hoc elt = a 2 5. = a R = - 5 R - a 2 R, (DolitO a = a EHi8, 1, O. PTO AiCU AN
A8. 279. Temiste arcus AB; adeoque s = AM, et 2 =M N = C N - ; a B = R
=EX:) Adeoque Momentum crilinei Aoy EB, 183. ( uipore istius Octuplum,)
425 = 8a R2 = 85R = 8 a V R, (Tumpris an s, 2, eodem sentu:) Hoc est,
(DOlito a = AB, = 2 AH; _c = 25; _ R = =X = v;) 3a2C + 4 a R2-
4cR - 4 a R = 2a 7 R = = a 2 6 - 4c R2 = 2 a X R: Adeoque Omnia a  c0
spectantia (uevore momenti duptum) a = c = 8CK = - = 4 a X R; hoc est Omnia
quadrata 70 f18. 183. Adeoque (proprer A r Hig. 182. = 2 A a tig. 283.) Omnia
quadrata BB F9. +82. Peu Omnia a 2 (eo spectantia) = 2 a = C = 16CR = + 8aXR.
FEprOPIerCa, SI EOtaM AF SpectemUS; (PrOPter a = ZP, 0 = 2 R, 8 X = 0,)
CFIE RP 2 = 32 R3 =OMn. a 2
Trem, omnia s, hoc est, omnia quadraca bo fi. 282. seu tis Omnia quacrata
70 f8. 283. IdeM TUNE C PFOPIeT 30 = b0-EV: 4L
R
cl) acque coti.
dem 4 2. = . Sune auceme (sumpris e avichimerice proporcionalibus, usque
4 R
ad maximam C. = A B,) Omm. 62: = = C3; et Omn. 54: = = C3 (per PrOD. T. BujuS.)
FreoOmn.   = : == Omn. c2 -
+
4 R2: = 3C
20 X Nempe Omnia
quadtaca 70, seu Omn. 52: (15. 183. Fi∞O (proprer A, = 2 A 0y) Omnia qua.
drata bv f5. 282. Omn. 52 = 3C3 - - . Et propterea, Si toram A + specte.
20
muS, PrOPIET C. = 2 R, ) Omn. 52: = 15, R3 - 18, R3 = 32 R3.
Irem, (propter s= V. + Rc
) Omnia as, sune roridem = cV: 4. N - 2
2R: Adco-
que (propter oy = aq e 9) = V: 4 R= = c 2: de Ay = c: Omnia a5: hoC
est, Omnia Rectangu la oy v fi8. 283. Tunt Momencum, respectu As, omnium gyo
rectansulorum, (tolidire ex his conclati,) per 2 R divitum. HIoc est (propter
sixuras similes A n a H8. 183. _can F seu dr S, fig. 270. item AO 40. H8. 183. 8
DEa Fx. 269. rationemque lacerum homologorum A a ad aF, ut 2 ad 1;
Sen decupt
habentis respectiris E. Z H∞. 269. aequales, respectu rectarum a. d vel dc.
Festaucem portio solidi hujusmodi brB, Tcu e TE, Hg, 170. = +  R - = s R, Per
SKE. PrOP. 18. (BOLIIO ~C = a;) HOC eA (Dosito e8 Pev 28 =- E, adeoque a = = P - E;)
22 R = dE= A 1 aG A = qd A. A deoque d TS (PTOPterE =0, et 5 = R,
_,  R. L proprerea decd. l drs = er.) = 1E R = i6i s +
PDD