# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0338
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0338?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 318, page id 851387705:0338
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=338
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000338.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 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 SECTIONTBOS PEOP. XZ.
reciproce proportionalis; ut sit ubique DBK AS = D Ax AL; adeo.
Que Latus rectum L. A = ∞ = AS, et AS = DB ~L A.
Denique (producta prius diametro D A, extra TErperbolam, donce
Opposito vel Trianculo vel Cono occurrat in a, ut habeatur Diame-
ter transverla A a,) exit (propter similia criangula) A2. AS:: Da.
D:
A a
est.)
Ad
A3
= E. A X D A, (quia nempe BD ~ AS = D A ~ P. A ut dictum
Hoc est, (substituris idoneis Symbolis, nempe c = A a d = D A,
c. F d = D an I = L. A, _ h = DO,) Duadratum ordinatim applicatX
in Hyperbola B =
d
=1d-
+d  a2
-1 = a1 + = a1 = 1a + - d (Om-
nes enim hae nocationes tancundem ralent.) Et quidem cam separa,
cim Ia = F D+ DB, _, a = FS= DB, quam conjunctim l a +; d.
= FDK DB + FS+DB =SDFDB =DO9.
Estque hoc quidem primarium acque estenciale Hyperbola symptoma, unde re-
liqua dependent omnia de calculo comprobari pollune. Reliquas Frperbolx aF-
tectiones post inreltisabimus, ubi absolucam iptius cractarionem (sine respectu
habico ad Conum) insticuemus.
Acque hactenus quidem Conisectiones vulso dictas, Parabolam, F.llixtin, acque
Eyperbolam, inspecto Cono considerarimus; ut quae d Cono. secto (quod et no-
men innuic) originem craxisse reputancur. Adeoque primaria illarum sympto.
mata ab iplo deduxi; quod ee de aliis illarum aftectionibus fecisse (si id Opus
CMet) non adeo esser ditticile. Duoniam autem carum natura masis abloluta est,
quam ut ad Conum solum percinere videantur; priorem contemplationem cousque
prolecurus tum, ut ee tontes aperirem unde Veteres doctrinam Tuam hausisse vi-
dentur, e quibus passibus ad abstrusas illas quas extribene demonstrationes aut
perrenerine aut salcem pervenisse pocuerint; Fc essentialia illarum sympromata
inde deducerem, ut randem licear illas etiam extra Conum Cuum intellixere, aut
etiam (si libet) de Cono in Conum transterre; cum carum affectiones reliqua ex
jam cradiis (etiam sine Coni auxilio) deduei possine, uc in sequentibus patebit.
Non aurem earum aftectiones omnes ea methodo prolecutus sum; quoniam illa-
rum cradicio ex absoluta, quae sequitur, tractarione (sepolico COno) et clarius e
Facilius perasi postic, nec opus sic rem candem iICratO aderC.