# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0757
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0757?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 737, page id 851387705:0757
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=757
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000757.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 67 lines, status machine
# Lines: 67 recognised, mean confidence 0.80
# 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.

et
1TA
PFOD.XVI. DeCalculo Centri Cravitatis.
Aeque haec momenta, momeneis Spharici Segmenti, Semilesmenti, et Correspon. Fie
dentis Unoulae, BB A, BV A, respectire addira, exhibene momenta, relvectu insi.
aS 7a, Sphaerici Sectoris B a B A, 3VR = Z = 352 RX = 1 52~Z; SemilectOris
Ba A, SV R = P = 55=RZ =  5222; e correspondenis Ongula, JV R3. 
Exrespectu TA, momencum Sectoris Spharici Ba B A, ; V R 2 D F ; ) s2 VP; Sc.
misectoris Ba A, SVRZ∞ + +52VD: Ongulaeque ZV R3 F 1552V R.
Vet etiam; Incelligacur, luper BC a Priangulo, Ongula Semiquactrantalis,
aciem habens Aa: Oua Pyramis erit verricem habensa; et balin J riangularem
Tuper BC rectam. Fujusque Balis Friangularis (in rectam CB projectae) Cen-
trum gravitaris puta B, distabit a C. (vercice Priansuli) ZCB, (per 6 hujus;)
ejusque ab A a (plano) dictancia, B7 = ZBV =35; e, in recta inde ad a ducta,
Frianguli centrum graricaris ut S, ablcindet a8 = Z a B; Cujus itaque ab A a di-
lancia BC = 2B7 = 3X35 = =s: PjuSque d r a ditantia, (7a = 2y a; Hoc est
(PrOPter 70 = R L3 V = 3R = 30,) Z R = =y; adeoque ejuldem d l A distancia
X F ZV.
Oux quidem distancia, in 55 R (Pyramidis magnicudinem, per prop. praeced.
55.) ductae; exhibene momeneum Pyramidis; (seu Vngula B Co, aciem hrabencis
Aa,) respectu iplius ra, s 2 R= -  52D R; e respectu iptius LA, 85 = R 2 ]
SVP. Adcoque Solidi (seil. Coni; conice excarati,) convertione Prianguli
BC 2 circa Ra tacti, momentum respectu ra, Z5= RP = E5 = VX; de respectu
TA, 252RD F - =S2VP: Semisolidique momencum respectu ra, ads2 RF -
+s2 VD; e relpectu L A, 16S= RP + + 52~F.
Acque haec momenta, momentis Sphaerici Sectoris, Semilectoris, et correspon.
dentis Ongulae, BCB A, BC A, respectire addira; exhibene momenta Sectoris,
Semilectoris, Ungulaeque, Ba B A, Ba A, respectu ipLiNS Y a, 3 V R 2~ L = 52 R4
252 V2, 5VR= P + 352 RD  52VP, 3VR3  362 R 52V R
F respectu Ip(uS PA, 3D R =P + 5= VE, 6VR2P +  5= VZ, LV R +
2S= VR. VE PrIVS.
Ouxe quidem momenta, per magnitudines dirita, (prop. praeced. 5 S. Tradicas)
exhibent dictanciam Centri graritatis, a ra,
252R - 520
42 R = 25 i d d F A, X = 25 R - 5v
40  25
VR +Z52R = 2 S2VR
EVk + 5 s X
252R - 520
B52
DC, quR t 25 quR f25
R1
Similiter; Coni incegri B AB, (Trianguli B A V convertione cicca A a de.
scripes) magnicudo (Dex S R, PrOP. praced. ); Semiconi VF
22 X; e Semi-
quadrancalis Ongulae 5 5 2V. Centrique graritatis distancia d F A, 3V (per 6 hu-
juS;) atque a ran 2 R -32. Ouxe quidem distanciae in magnicudines ductae, ex.
Si Semiconi
16 pi Ungulaeque tsv
= : s vR - 5 52: Respectu ra, momentum Coni 5 s2 v X - s V Z
552 DD = sv
8 X3 Semi cons
Ongulaeque 3S2 VR = 5 s2V = 3 S V R + 3s
Oux quidem momenta, ex respectiris momentis segmenti, semileementi, Vn
Bulaeque, BBA, BV A, (S F. tradicis,) subducta; relinquune annuli, (conver
tione segmenEI A B A cirea Aa) momencum respectu Ta, ZV R = P - Z5 2 R ~ 
2s= VF: Semiannuli 5V R 2 P =  S2 P + a 5 ~~; EF correspondens Vn.
sulae ZV R3 =65= R2 + 252V R = V R2 + 12S = V R. AIque, respectu TA.
momentum annuli 30 R= P - 55? RP = 12 S = VD; Semiannuli 5VR = ~-
35  R~ - 25 2 vF: Ongula que ZVR3 = 65 R 2 - 1 5 = V R =  2 X = 3 5 VR.
Adeoque (propier Lncula masnicudinem S B, R. proP. praced. JV P = 5 V X.L
55 R,) distancia Cencri pravicais est d F ∞ R + = R + iB; a T A, R - :B;
acque a DC, 3b = 2
159
260.
A 2 d d 2
101t0