# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0738
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0738?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 718, page id 851387705:0738
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=738
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000738.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.89
# 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.
FI itaque Sectoris BCB A magnicudo a R, (nempe Z BA BK G A, per proP. T2
Fis. 159, hujus;) ejusque demiltis BC A, La R. Ei, spcciacim, iocius demiciiculis (propter
Trem Frianguli BB C magnitudo : BBx CV (per PrOP. 6 hujus;) hoc est SX:
(Nempe, SR = - 5V, A V HCrIE CuPEa CentruM; vel 5V = 5 R, si intra:) Adco-
que BC.V = 55 ∞: HIOC CA, Z 5 R = Z 5V, S luPrL; vel Z5V = = s R, Ei intra
Adeoque, Si a Sectore BC. B A = a R, Auteratur Friangulum B BC = 5 K
=52; vel Addatur Friangulum BBC =5V -s PP; (prout tuerie V supra in-
Frave Centrum:) urroris calu habetur Segmentum BB A = (a R F 5 N =) a R
=sR + 50 = e R F 5V. Adeoque BV A = = a R F Z 5 N = = a R = 2 5 R + = 5V
ZC R + = 5V
Hoc clE: Si inCeripro (in Circuli Sermento) Friangulo aequialto A B B (= 52)
addatur Friangulum aliud (a R = s R = e R) cujus nempe Balis sic aequalis C ir
culi Radio (= R) e AIcicudo (= 2a = 25 = 2e) equalis excelII AreUS LUI-
pra Tubrentam: Flabetur Segmenti B B A masnicudo; a R 5 R f 5V =- c R + 5V.
Ejusque Semistis, Semilegmentum B V A = = a R - 35 R + 3 5~ = Z C R L 2 5V.
Adeoque, duo timul Scgmenta abscista AB, AB, (qua, cum interipro Frian-
sulo, complem Segmencum BB A, ) aequant a R - s R = e R, e corum utrumris
a R 2S R = ZCR.
Hoc elt; Si (a = 5 = e) excestias Areus B A supra suum sinum rectum B V.
ducatur in (= R) semistem Radii: Elabetur magniudo Scemenri BA; = 2 a R
Si vero Semenros BB A (= e R. F 5v,) adjieiarr Feianeulum BB a (= B 5:)
Hhabetur Sector B a B A (angulum habens B a B in peripheria, et B A B arcum,)
eR + sV F sh: hoc et (propier v + b = 2 R,) e R F 25 R; vel (propier
e= a sy) a R + 5R = fR. Adeoque Ba A = Z a R F 3 5 R = 3 f R
(Idem proreniret, si Sectori BCB A = a R, adderencur duo Friangula B C a,
BCa: quorum communis Balis ett C a R, e urriulris AIcitudo BC =-5: adc0.
que simul urraque sR. HIOc elt, BaB A = a R + SR = fR: EF Ba A = = a R
F25R = 3
R.)
HOc est: Si (a F s=f) aggrexatum ArCUS BA, e Sinus Recti BV; ducat
in Semiltem Raci (= = :) Hlabecur Sector Ba A = 3 a R F Z 5 R = 3 f. R.
Similiter de Centro Craricatis procedendum.
Nempe, (per jam demonstrata ad hanc propositionem S A,) Sectoris BCBA
(sire Semicireulo major sic, live minor, sire ipli aequalis) Cenirum graricatis clt
in CA recta, supra Cenrum C, quancum elt = = R. Nempe ea raione ad 3 R,
quae est Chorda BB = 2s, ad arcum B A B = 2a; sive ut s ad a:) Adeoque il.
lius, a puncto e seu ra tangence, distancia est R. f 2= X = 3a F 25 R. Ad.
eoque d P A (cangente verricis) R - = X = 3a= 25 R. Fademque est, ab
cildem ram T A, diltantia Ceneri pravitatis semisectoris BC A; Propier dimidias
B V ec hruic parallelas semisectorem complencibus, toris B B et huic parallelis com-
plentibus Sectorem inceorum, proporrionales, ee in eisdem cum illis distanciis sire
d ray sire a Y A. (Quod ee similicer incellixendum crir de Semi conis, Semi-
sexmentis, sc. quorum Centra pravitaris sive a Balis plano, sive à Plano verricis
bali parallelo, cancundem distant, quantum inde distant C’entra graritatis integro-
rum luorum sire Conorum, sire Sesmencorum, ec. Ouod semet monitum csto
ne opus sic idem Caepius repetere.) Li speciarim, Semicirculi ADa, Ceniri pra.
vitatis (urpore in DC jacemis) distancia Ere d ran sire dTA, est R = C. a
C A.
Adeoque (proprex magnicudinem Scctoris BCB A = a R, _ BC A = ; a R,)
Momencum (respectu rectae ra uc axis Libra) Sectoris B C. B A, est 3 a + 2 3 p
Cmenivdine seilicet ia distantinme ducta; ) et Semiletoria BC a, 3 a + 25 .