# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0530
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0530?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 510, page id 851387705:0530
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=530
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000530.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.86
# 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.

DF CY CL O ID F.
64. Cum igicur sicracio momenii hujus ad momencum illius, ut 3 A ABZ +
12 AABY ad = A ABY; hoc est (diridendo per A AB) uc 8Z + 25Y ad = Y, sive
(ductis omnibus in 12) ut 10Z F7Y ad 3~: Nempe, ut 10ZL + 7 2 Y ad
32 Y, (eadem scilicet ratio quae _ lupra 546,) Acque hoc ubique: Propter omnes
72  ad 3Z T, ponenda ratio 7 ad 3; e propter 102Z ad 32 l, eadem qua su-
Pra 546. Ec quidem eandem utrobique rationem provenire necesse elt, (utur variis
modis libuerit inrestigare:) Nam momentum lolidi ex convertione ejuldem E-
Surae, cirea A F respectu recta C F, atque circa C F respectu recta AF (proptex
marnimdinum ex diltantiarum reciprocarionem) tancundem exit. Adeoque hine
habemr tum distantia ceneri graritaris semisolidi ex Lemiereloidis femiconvertione
circa C. F, a recta AF; cum inceori iltius solidi iplictimum GTaVITatIS CeNEruM,
uepore quod in C F Cicum esse conttat.
65. Ouancum aurem ad distanciam cencri gravitatis ejusdem Semisolidi (ex se.
miconvertione semicycloidis cirea C P) ab ipla C F: Simili methodo investisanda
CTII. Cum enim Colidum ex semiconvertione Frianguliv Ep circa C F, sIc agGrC.
sacum seriei oby, TbY, 4 bY, 9bY, ec. ulque ad BY, (uE Cupra 562:) EF toli-
dum ex semiconvertione PrapezII V B, P cirea candem C F sit aggregatum CerICI
BZ +02 +0B +00, BL +, bZ + y B + by, BZ = 2bZ = 2y B + 4by
BZ = 3b2 = 3y B + 9by, etc. Luc Lupra 563.) Si uraque series ducatur in le
riem suarum respectire diltantiarum a recta C P; (nempe illa, in 0, y, 2y, 3y, ec
usque ad Y; _ hac, in Z f0, Z F Y, 2 f 27, Z F 37, dec. ulque ad Z. + Y:
habebitur series momentorum corundem Colidorum respeetu linex aequilitru C F.
Onde ee aogregati ad aggresacum racio; hoc est, momenci semilolidi ex Friangu-
lo, ad momentum semilolidi exi Frapezio (circa C F converto) respectu recta C. F.
Nempe
2t1s esC. uIque ac
BZ.Z 16DLL+0YBZ + obpZ FOpY B F Obyy.
B2.L + LbLZ+ 27B2 + 207Z = 2y y B + Fbyy
5LL F 262 L. + 47BZ + 8byZ + 4py B + 8bg7.
2. + 3bL 2. +6yB2. + 18672 +9yyB + 27617
Ac. in intinicum usque ad
B2Z + BZZ + 22B2 + 2BYZ + YYB Y BYY.
Summa: 1BTX ad Cumma ABZ 2. +: 1B~C +3 MBZ +: aBYZ + : a rB + = aBYY.
live AABYY
ad 3 +B2Z + 3ABYZ + B A BYY.
EdEut, 228 (∞.  a 2d 10511. 322 +. 3r2 + 1228. 1
Tire ut 3YX 1
ad 11 33F8Z Z = 2072 +1. 17YY.
FIoc est, uc3 quadrara rectae 2 P, adt 28 quadraca rectae Z Z una cum 20 rectangulis
Z2 Xy ec 7 quadraris 2 Y. Duod cum ubique tiae: ne hrabeatur ravio momenei 50.
lidi ex semiconrentione omnium Praperiorum, hoc est Setnicycloidis, ad momen-
tum Colidi ex convertione omnium Friansulorum, hoc elt Semicirculi, (oirea re-
etam CF;) quaerenda ratio cum omnium Ouadratorum 2Z Arichmerico proxortio.
Fis. Y. nalium cum omnium Rectangutorum Z Z L, in. Fespectra Friangula v F P, Sire
(.Proprer aequales ubique p.) in respectiras Alcitucines Y F; ad omnia Guadrata
2L in eadem respectira sive Priangula sive Alvitudines. Acque ilta demumrario
E dueaur in racionemes 8 ad 3, SIVO 6 ad r; aique haec quidem in rationem 20 ad
35 d uerisque randem (sie ductis) aejutsatur rario 7 ad 3: Flabebicur rario ea
quam haber momentum solidi ox lémiconvertione Semicyeloidis circa C F, ad mo-
mencum solidi ex Semicireuli sirca candem C P semiconvertione, respectu eju sdem
CF lineae aequilibrii. Onde si eximatur ratio magnicudmum; habebicur rario di
ltanciarum centrorum gravitatis.
66. Similicer Si Cumantur (in Lig. L, vol 8) omnes Z Y aequalibus incervallis dis-
Sica; ex quarum semiconvertione cirea Ci F fic Solidum Cyeloidale, Licur ex lemi-
conrextione semicirculi sire omnium in eo ordinatim applicatarum circa candem
rectam tic Femisphaerium: F ric momencum illius ad momentum hujus, respectu ejut-
dem C F recta, ut omnes cubi rectarum CY, ad ommes cubos rectarum 2Y: Hoc est,
uc omnes 2Z. C + 32L. 9X2. T F 3ZZXZZ9 F DY e, ad omnes 2 Z es Oux qui
dem omnia similibus mechodis ad caleutum reroeanda sunc acqie superiora.
11.
67. POrrO,
Ob