# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0840
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0840?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 820, page id 851387705:0840
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=840
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000840.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.84
# 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.

De Calculo Centri Cravitatis. Cap. V
Fir. 266, cum Magnitudines cum Diltancias utrobique aequales. (Si vero vel Ongularum
acies, vel rectae ad quas momenta altimantur, tinc Aa; aliare quae ipsis ra, TA,
Parallela non tic; lecus erit: Propier vel Magnicudines, vel Diltancias, rel utral.
que rariatas. Or post dicendum exit.)
EA auem, rori semicirculo insiltenis semiquadrancalis Ongulae, aciem ha-
benris ra Momentum respectu ejusdem ra rectae, 3R3 Z; e respectu rectae
PA, 2 R3 P; per S T. PFOV. F6. Porique Frilineo insistentis, aciem icem ha-
bentis za momentum respectu ran eltu Z R3P; respectu T A, Z R3 D; Der SB.
PrOP. 19.
tergo Semiercloidi insistentis Ingula aciem habentis ra momentum respectu
70, 28 R3 P; e respectu FA, 25 R. P. Adeoque (propter magnicudinem S R2 P.
Der S C. proP. Praeced.) Diltantia Ceneri graritaris Dnoula d re 6R; a JA, 3R.
Semisolidique circa ra, Magnicudo (quippe ad illam noulae, uE = P ad R, scu
P ad 2 R,) E RDZ; Diltancia Ceneri gravicaris a ra (quipre ad illam Ongula,
ut 2 R ad L P, seu 4 R ad P,) 2 P; semitolidique momentum respectu axis
sui ron ad illud Vneulae ut 2 ad L; (propter maenicudinem uc P ad 2 R; ee di-
Canciam ve 4. R ad X: per PrOP. 12. e 24. elque R n  = 7:) hoc est,
23 R. Y.
Similicer; Semicireulo insistentis Ungulae, aciem habentis F A, Momentum
respectu ran 16 3∞; e respectu Y A, 1 R3 P; (per 5F. prop. 16.) Trili
neoque Relticuro insistentis, aciem habentis TA, momeneum respectu ra, Z R34
(idem urique acque aciem habentis ro Momencum respectu TA, propier magni-
iudines _ distantias reciprOcaTAS,) e respectu TA, IE R3 P; Per SB. PrOP. 19.
Ergo, Semiereloidi insistentis, aciem habentis T A, momenium respectu ra
2R3 P; e respectu TA, 28 R3 P. Adeoque (propres magnicudinem, 3 R2
per SC. prOP. praeced.) Diltancia Centri. a r an 23 R; e d TA, 22 R. Semiloli-
dique cirea TA, magnicudo, i R D=; Diltantia Ceneri sraricatis ab aXC ConVer-
tionis TA,
(18X
2 ∞i Momentum relpectu ejuldem F A, 3 R3 P.
irem Ongulae Sectoris BaA, aciem habentis ra momenium respectu ra,
8FR3 = 3 SBR2 - 3 s R; respectu L A, 3F R - 2 sB A = 12 s R; Der B W.
PrOD. 16. Ongulaque porrionis Trilinei resticuri bBaBA, aciem habentis ra
momencum relpectu ro, EF R + E 5BR = 3s R; relpecta YA, 3F R + 35 R
Der SC. PrOP. 19.
Ergo Ongulae Portionis Semieveloidis B Ba V A, momentum respectu ra, 27 f R:
+85BR = 2b5 R = 32 a R) + 3sR = 85VR= 65 R; relpectu TA, 3 s R
3 SBR2 + 2b 5 R = 37 a R3 + 3 5 R +  50 R + 23S) R. AdCOqUO (PTOBIT
magnicudinem Z f R2 L E sB R, pPerSD. prOP. Prxeced.) Distancia Cencri Sravica.
15FR + 155B1 e a, F A, 3R 4 sBR - 7
45FR = E5 5B
rIB 2 78 Z R + =4SB R =  5.
dique circa ram magnicudo EF PP +  sBP: momencum relpellu ra, 3 f R.
+3 sB  =  . R; Centei erabicatio L ru dillania, (4 R  56 5B F. - 28 S R
37
45fAP F 15 5tZ
Similicer, Ingula Sectoris Ba. A, aciem habentis Y A; Momencum respectu
T A, elt 3fR= 2 sB R 2 - 2s R; pex S W. PrOP. 16. Ongulaeque in Frili.
neo correlpondentis bB a BA, i FR3 = = 5B R 2 = 3 s R, pet 5C. prOP. 10.
Ergo Ongula portionis Semiercloidis BBa V A, aciem habentis L A, momen-
tum respectu iptiuS TA, 3 fR3 - 22 5 B R 2 = 365 R = 2 a R3 + 35R F 32 5V R
=3sR; _ respectu ra (idem quod aciem trabentis ra, momentum respectu
PA: Propies magnicudines et dictantias reciprocatas,) 34 S R . L  a 5B R2  , 35 R
=3 a  + 2 sR. = 2 52 R 4 1. s R. Adeoque (propter magnicudinem 25 R
 Sb_ per S. D, BEOP. pracect.) Distancia Ccatei pravicaio 2 F A, 3 R=
52 5 B R
320
170.