# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0875
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0875?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 855, page id 851387705:0875
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=875
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000875.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.88
# 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.

PxOP. XXII. De Calculo Centri Cravitatis
dempris Omn. 2 BY 2V R, Cumpiis a arictumerice proporcionalibus; idem est ac. Fi8. 177.
que Omn. a BY = =; lumpris v ariitimerice proporcionalibus. (Nempe idem 283
Colidum ABV. ) Ec (dividendo per B,) 2 AV ZY R = Omn. 2 Y 2 v R: Sump.
cisa acictmetice proporcionalibus; idem acgue Omn. a Y = =, sumpris v arictr.
merice provorrionalibus; (cu Omn. an Lumpris Ab = 2 c arichmetice propOrtio.
nalibus; hoc est, Trilincum ABB tig. 182.
Porestque idem (si Opus est) Colidum considerari tanguam ex planis ipsi ABV
Parallelis conslatum. Et lic alibi.
Similiter; Divita, ut prius, Aa in minutas parces aequales; cum quae his re-
spondent particularum b x momenta respectu Aa, H3. 277. Teu Ongulae (aciem
habentis Aa) Parcicula, sine (ue dictum est) uc coridem =  Y 2R, seu a V
E +S Y =; sineque iplarum a T A diltancie, AV = v respectirae; eric
omnium respectu F a momentum, toridem a V 20R. F sV 2V R; sumpeis v aricti.
metice proportionalibus.
Fequidem asgregatum Omn. 5Y 2V R, (hoc est, omnium rectangulorum DV p
Fix. 185.) facile habetur. Cum enim sinc Omn. 5. Y 2 , idem acque coridem  V FiB. 179.
F8. 179. erunE Omn. SY 2V R, hoc est Omn. V SV =; vet etiani ( propter
s = Y VB,) Omn. V V 2BR; idem atque earundem  V momenta respectu H A
rectae. Flt autem (per prOP. 6. hujus,) Semiparabola a M A diltancia centri gra-
e
vitatis ab a7, Za A = ER; adeoque ab A Y, 4R; e (propier magnicudinem
ER2) momentum ejus respectu A P, 32 R3. F semiparabolx a n V, diltancia cen-
eri gravitatis ab a5, Za V =- ZB; adeoque ab AY, 2 R - 3 B; _ (PTOPIEE mae
nicudinem ZB V 2B R,) momentum respectu A F, 3B R V 2BR = Z h= V 2B R.
ErgO (subductione facta) Nomencum portionis H A V  respectu Y A, cst 23 R:
= Z BR V 2B R F Z B= V 2B R. TTOC CIL (DFODHEE Z B R = X 2, e V 2BR = X,
P. Tancundem Scilicet acque Omn.
sumpris AB = 2c arichmetice proportionalibus; ut S F. octensum clt.
5c
E. X
Sunque Omn. a Y 2V R, tumpris v arichmetice proporcionalibus; (hoc e, Fir. 177
omnia rectangula BV D H5. X85.) idem atque Omn. =, sumpris AB = 2C a-
richmetice proportionalibus. (Ocrumris urique est Ongula ABAG. 277. quantum
ad alticudines bB, momencum respectu T A; ungulaere Ab aciem habemis Y A
momencum quancum ad dillantias b B. ) OuodsFL. deprehendimus 2c
F 18X R, + 352. Acque hinc reliqua deduceneur ut ad S I.
Sed ec idem solidum Ab V P tix. 285. (quod complent omnia b V P rectangulam
Teu 0
alia plana rectis ur insistentia; hoc est (ue ex constructione parebie, si incelli-
BatuF Aa F semipnhZ ad angulos rectos erecta, e Tuper A a Y plano mota, (0-
lidum describere,) coridem semiparabolae AV p, dempris omnibus AOP, quarum
alcicudines A0 =gX sine sinus versi arcuum arichmetice proportionalium: HIoc
est (DOTito AR = BV = A, ee AV =V, ) ZAV 2V s dempiis omnibus
a V 2V R, sumpris a arictinetice proporcionalibus. Quod itaque cancundem
etiam valet acque Omn a5 sumpris AB = 2. c arictimetiee proporrionalibus.
Porestque idem solidum (A opus est) considerari canquam ex planis ipsi ABV
parallelis conttatum: Oc anre monitum ett.
Similicer;