# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1119
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1119?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1062, page id 1815201908:1119
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1119
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001119.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.92
# 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.

1062
GONOIDES BARANOLLEYM.
Demonstratio.
Ine dux sectiones DB P maior e mi
nOF F G TT, quarUI AXESHInE BK, F IT
factaque BI aequali FIY, POnAEuE IK
aequidistans F D: cric icaque BIR para-
bola aequalis FG FI, ve octensum est su-
pra 2: sed parabola BF. D ad BTR, p2
rabolam criplicatam haber rarionem eius
quam habec recta B F D ad TR, hoc est
FTO: Igitur manifectum est sectiones axi
Parallelas criplicacam habere racionem
suarum balium. Ouoderat demonttran-
dum.
PROPOSITIO CXLVIII
nonoides parabolicum (BAC) ad
conoides parabolicum (E DFY)
eandem rarionem habec, quam crian-
sulum BAC ductum in rectangulum
AC BI, adcriangulum FDF, ductum
inrectangulum DF F I, hoc est quam
prilma balim habescriansulum BAC,
alcicudinem C B, ad prilma balim ha-
benscriangulum F D E, alcirudinemF F.
Demonstratio.
DEr ea quae demonstrauimus prop. 129. huius.
conoides cs ad conoides, ve corpora qua
tunc ex ductibus parabolarum in sciplas. (cd
haecaquancur csolidis, quae hunc ex criangulis
BAO, FDE ductis in rectangula ACBI.
DF FR. Ergo conoidium ratio eadem est que
Tolidorum Factorum ex ductibus eriangulo-
rum BAC, FDE in rectangula ACBI,
DEFK. Duod erat demonstrandum.
Corollarium.
Arces conoideos parallelis ad balim planis abseisia, eam Peruane rarionem quam
Parces parabola per axemii(dem planis intercepeae, in se ductx, siuc quam parres
rianguli BC A duca in alcicudinem AI (Cu CB.
Demonstrabitur discurtu omnino simili.
ROPOSITIO CXLIX
des parabolicum ad conoides parabolicum rarionem habet
policam ex alcicudinc ad alticudinem, ee ex bali ad balim.
Demon:
14
hio
b1 12.