# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0841
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0841?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 821, page id 851387705:0841
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=841
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000841.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 76 lines, status machine
# Lines: 76 recognised, mean confidence 0.79
# 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.

vel
PFOD. XXI. DeCaleulo Centri Cravitatis.
52sBR = 495
14SR = 2055B; e d ra, 3 R + 525B R + 435
4415 R = 205 sB. Semritolidique Ciica TA, E, C. 166,
magnitudo 3f R P = Z5 BZ; mOmenEuM respectu TA, 52fR = 13SB R2 - , BS R;
Cenrique gravicaris inde distantia L28 R. 208 shR = 19653
2+~ 4+2fRP - 105SBZ
Trem, Ongulae Segmenti aBa, aciem habentis ra; momencum respectu ra, est
8a R3 = 35 R3 - 8sB R 2 f E s R, e respectu T A, 3a R3 - 85 R3 + + SBR =
iES R; per SY. prOP. 26. Ongulaque respectirae in Zrilineo Relticuco bB7,
momencum respectu + a, 34R = 35 R) = E sB R + ; sR; et respectu Y A,
Ea R3 - 35 R3 = 3 5 R; Det SD. PrOD. 19.
Ergo, Ongula portionis Semiercloidis bBr, aciem habentis + a momentum re-
spectu ra, 3 a R3 = 37 5 R3 = 8 5B R= = 28 5 R = 2b R3 ~ - 33 a R - 3 s R.
=35VR 2 = 353R; respectu T A, 3 a R3 = 33 5R3 + + sBR2 L 3+ 53R
= 28 R 3  - 22 a R3 = 2 5 R3 = 2+ sV R = 385 R. Adeoque (prOPteL magni
cudinem, Za R 2 = Z5 R2 = ZSBR, Per SF. prOP. PraeCed.) Distancia Cencri gra-
vicatis a 74 205 aN - 1055N- 63 sB R + 14 5
=3X.
900. R = 905R = 305B
T4SBR = = 5pV
45 a R - 4155R = 255B 3
25a R2 -755R = = 35BR = 24 52
90a R - 905 R - 305B
R-
=62
T4SB R = 7 53
45 a R = 455R - +55B
45 a R - 455R - 155B
=3.
F 15aR = 455R - 15 5B
Semi-
solidique correspondentis circa ra, magnicudo, 8 a R P = 3s R P - Z5BP; ejus
que respectu ra momentum 33 a R 3 - 325 R 3 - - 3 sh s E. H 18 s R; indeque Di-
Pancia Ceneri gravicacis, 24. 
 285B R Bn etum
32 45 a RY = 455RY = TFFBY.
Similiter; Ongulae segmenti aB a, aciem habentis F A; momencum respectu
FA, est 3a R3 - 35 R3 +  sB R  f 2 S. R; Der 8 Y. PrOB. 16. Ungula que
correspondeneis in Tcilinco Rellicuro b er, sa R) = 35R + 35b R F 35 R:
DET S D. PFOV. 19.
FrSO, Ongula BBF in Semieycloide, aciem habencis FA, momentum respectu
T A, 33 a R3 = 395 R3 = 12 sBR = + 38s R; et respectu ra (idem quod aciem
habencis ra, momentum respectu PA,) 37 a R3 - 34 5 R +  S B R= = 285 R. Ad.
eoque (propiet magnicudinem Z a R2 - 2s R + ESB R, Der S F. prOP. praeced.
Distancia Ceneri gravicaris a F A, 277 a R
=3ER
3P.
525BR + 495.
442 a R - 442 5 R + 105 5b
525hR + 495
44F a R - 44F s R + 105 sB
 1
5R + 57sBR + 145
126 aR = 1265R + 305B
lXd
25 a  - 75 5 R + 3sBR- 14 5
226 a R = 1265R + 305b
Semisolidique correspondentis circa FA,
magnicudo B a RP = 8s RP +  shP: Momenrum respectu YA, 33 a R
=225 R + 1 sBR F 1b 5 R: Cenrique Graricacis d T A diltancia L18 R.
20d 5BR2 L 29653 R
44T a RP = 442 5 RP + 1055BY
242
Eiem, Ungulae Scementi Semicirculis B V A, aciem habenis F A; momencum
respectu TA, cAt, SCR3 + 35V R = 3 s R = 4 53y; d respectu ra, dC R 3
+35VR2- 3 5 R +  siv; et respectu bBV, = 3C R3 + + avR - 5 sV R
1E5 R = 1 SV; per B F, PrOP. 16, tu
Et Ongula Frilinei BB A aciem icem habentis TA, momencum respectu FA,
est = 30 R + 3aV R + 3 5uR3-  3a 52R ∞ 55 R- 3 a sev; et respectu ra
L. IIL
ZC R
70
D
821