# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/826605435:0045
# Permalink to this reading: https://leibnizlegible.com/page/826605435:0045?run=74
# Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmarks Leibn. Marg. 84:1, Stück 2; Leibn. Marg. 84:1)
# Folio 25, page id 826605435:0045
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=826605435&page=45
# Source image: https://digitale-sammlungen.gwlb.de/content/826605435/jpgs/default/00000045.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.90
# 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.

DF CYCFOLD
vero Sectoris cujusvis ZC C, X7 C O crianguli, cum magniru.
dinibus cum ceneris gravicoris, dacur etiam cenerum gravicatis
seomenti Z C. Vacis aucem cum segmenei ZC, cum crianguli
2C Y, mignicudinibus ec graviracum ceneris, datur etiam cen-
trum gerritacis dggregatI Z Y C. Ec limilicer de SectOris2FC,
aliutre, centro sravicaris conteabi.
70. In porcionieus Sphaera, cenerum gravicatis sic colligitur. Centrum
Ouadracum rectae 2 X fg. 6. 2quat ubique quadrarum Radii mi- Gravitatis
nus quadraco (7 X, (quod patec.) Dicamus aurem, uc alibi, Ra- dutoris, 206
dium R, ejusque parrem aliquocam infinire exiguamr. Frune i- demn
sicur quadeata omnium Z Y (quadranrem b C C complencium) Spharici
R =, RZ n, 2 R2 = 4 p _ R Z = 9 p = _C uIque dd R = = X 2
(quod est punctum verticis C.) Sin pro Duacraris hisce substi-
cuamus ubique circulos, laceribus quadrarorum ut Radiis deseri-
PrOs, (adeoque quadraris illis proporcionales:) pro omnibus R2
habebimus circulos Cxlindri, hemisphaerio circumscripei: pro
omnibus 00, r=, 4r =, 9r = _c, Circulos C’oni, cujus verrex (i
cenerum Sphaera, balis eadem cum base Cylindri, in plano quod
Sphaeram in C cangic; proucrorumque vero differenciis R20,
RZ- p = R = 4Y 2, R= = 9r 2 ec, Circulos hemisphaerii,
(quadratis urique rectarum 2 X proportionales;) qui proprerea
aequales deprehenduneur planis annulis cxlindri conice excavaci
Sed ec eadem habebune graritaris cenrra, (nempe respectiva
puncta Y, in recta C C:) aequiponderabune itaque cum lingula
singulis respectire, cum omnia omnibus; idemque erit cen
erum graricatis cxlindri hujus conice excaraci, acque hemisphae
rii: Nempe in eo axis hemisphaerii puncto quo ica dividicur, ut
DAES Ad CeNETUM SpHXFX SIE ad FelIquaM uC 3 2d 5, Sve Z COTIUS=
Id enim ob dacum cum Cylindri, cum exempei coni, magnicudi
nes et gravicatis cenera Facile colligicur.
72. Velsc. Cum circuli hemisphaerium complences, CinE
(quod modo dictum est) uc RZ - r a, R2- A p 2, Z= = 9r L
Scc, (hoc est, juxca noltram Arichmecicam Tntinicorum, uc se-
ries Aqualium dempra serie Secundanorum, quae ad correspon-
dencem seriem Aqualium, ett uC L = 3 ad F, hoc eA uC 3 ad L,
sire uc 2 ad 3; quae icaque est racio Hemisphaerii ad circumseri-
peum Cplindrum;) Sincque eorundem Circulorum distantix a
CenErO SphXTX, UET, 27, 3r, ec, nempe series Primanorum :
HaC