# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0578
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0578?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 558, page id 851387705:0578
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=578
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000578.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.86
# 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.

URVARUM FdirOM.
1e  F 3 Qlladrata parcicularum cuEVX
rer F C = C F) auctas extribett
ita Glaaca; eorumque radices AV
Cpla au
tem arcuut cc rentia = = AY. Adeoque ut ille om
nes ad omnes has; sic Plipseos exposirae peritmeter, FEF, vel ABC, ad peri
pheriam cicculi FZC, vel AP. (Quod et aliis FIliplium speciehus faerte accom
modabitur, ut mox docebitur.)
Sphaeroer. Detle, Si intellisancur cum Ellipleos illa, cum hae perimetri Circularis parriculae,
ais oblon-in iidem respectire a luis axibus distanciis conrerti, unde tiac illic, Sphxrocidis oblon-
Si; hic, Sphaera Superticies: Frir superticies illa ad
hanc; ut omnes AV: 2 R= a: ad cocidem
AR: lIve, ut omnes V: 2 R 2 - a: ad cori
dem R: Hoc elt, CE incellieatur in parallelo.
Grammo (Hg. 3c.) AB = R V2, e AR = R,
adcoque ar = a reliquaque ut in schemare
constructa,) uc RC B A quadrantis circuli seg
mentum, ad quadratum AR minoris lemidia-
mecri. Sunc enim omnia beb rectansula, hoc
elt. RV 2 F a In RV2 = a, hoc est, 2 R = a; ut rectarum rC quadrata: adeo-
que omnes rC rectae, uL V: 2. R = a. Duod eriam ex prop. 124. Apich. Intin.
Fulius patebit.
Fodem modo, ad alias Ellipsium species res accommiocabitur. Si hoc Falcem
adrertatur; In praesenti casu, propter FC. =CP Hg. 2. vel 29. aliguotas partes
cum rectae IC tum rectae CF, Eodem (ymbolo 2 detignari. Sin recta C’ F (quae
Potelt excellum quadrari axis lonsioris lupra brevioris quadrarum) vel longior
elter vel brerior quam FC. (circuli diamerer, rel E.Hip (EOS aXis MINOE,) DucA uE
FE ad R; Bolica A aliquota parte diametri circularis (uc prius,) erit = Academ
R A
P2
DarS recta CP: Adeoque pro p: + , sumendum eric
F
1 + 
R2- a
Adeoque Spharocidis illa superticies, ad superticiem Sphaera, exit VE omnes V: R.
F 772-
R2: ad coridem R. Ideoque ponendum eric, fig. 3F. AB = V: R -
es iliisii
+ ZP: _ AR = YY (semisti recta C F H5. 29.) quare d ax = 2. Fritque,
uc prius, VE A BC R quadrancis circularis sexmencum, ad coridem R, hoc est ad
LLXR: Sic suverticies illa Spharocidica ad Spharicam. (Et parres partibus re-
oecionales.) Est aurem, ut patet, AB, F. Mipleos semiaxis major;
RC, temiaxis minor; a R, distancia focid cenro, que recta quae porest disteren.
tiam quadratorum semiaxium.
Dicoisime, Si in cireuli quadrante cujus ractius A B ellipseos semiaxis major, or
dinatim applicetur RC. semiaxi minori aequalis, e complearur ARC rectaneu
Jum: Frit ut R C B A quadrilineum, ad A R C. rectansulum: sic Sphaerocidis ob-
jonsi supersicies, ad supersiciem inscripiae Sphaerae. d.  B ~t. ∞
Sphaeroei Incelligatur jam C plindus FFCZ Fis. 29, obliquus ette, cujus batis FCF circu.
dis lati lus5 e FZC Fliplis, axi recta, cujus minoraris FC. Cum isitur, divisa PF cir
upersi culi diamerro in parces aequales numero intinicas, quorum quaelibet dicacur A, e
parricule peripheriae (ue prius oltentum ) - vet.
Y. R. = a2 de harrmi pac.
ciertarum quadrata . ; unde si auserantur quadraca aequalium parieularum
recta
ABC; corunque omnium radices, curram ipsam: HloC eAt, (pr optec s = Y: N- a.
a h
sumpris a uerinque a medio, uE E, 2, 3, ec successire,)
super-
Fig. z
feres.