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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 636, page id 1815201908:0693
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.80
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FY P ER BOL A.
eROPOSITIO CACHII
Acis A B, A D pro diamerris hypetbolae ad rectos anoulos constiru.
eis coniusaenssectiones delcribere
O3CGIMNI
a1. Sit C).
Constructio es demonstratio.
GOnanCUE P. L, TIC aequidictantes AB,
AD: Facto deinde parallelooramo ADC.
ductis quoque AR, AI hanc rectis AK X.
quales R, F F; rectis insuper AI aequales
recta I, IIG. DiCOBEF, DGC eAC hy.
perbolas coniugatas. quod sine hyperbola
quarum lacera eramluerta Lune AB, A D) de-
monstratum est prop. praeced. Ouod aurem
coniugaca, lic ostendo. Productis BC in C
 DC ME, POnaNCuT FNY, CMqueaequi–
distene AB, AB, dividentur ex constructio.
arectis AB, AD, Vpote diamerris, si vique ad sectio-
Ca luarum hyperbolarum ocenta tumc, x quidistancess igitur AB, = A D Cunc diameeri
Ex 40. coniusarx, ac prohs ipla etiam hgyra coniuxare sune secimus ixitur quod fyerat
Postularum. sin
e
ne hae bitariam in MI e P
nem verimque producta intellisancur. Cuncquerectis AD, AB quae lacera transuer-
frex AB, AF posira Sine ad quemcum que angusum L AB, IIIICA
IICXCVIII
huins.
ALid SIAG 12
Dico puncta DL. elle ad eandem hyperbolam cuius alympeoci lune
AB, AF.
que AB dinitâ sit recunque in C. C, de hac ve A C dd AB, itd BF
ad CD. Sineque BC, C D paraIlelA AF.
Demonstratio.
neu.
DVCanEUE EG _ DF, qux aequidistene A B: cum igicESE DC A C au AB, H
FB ad D C. parallelogramma C. D E. b xqualia sunc paralleloxrammo BE. 6,
Excon. pUnCtA ISITAE F. DDcad candem Cunchyperbolam.
ROP
5
F1O C XCIX
AB, AE linex quemcum que angulum constiMIEnEeS, ex B vero
colinca AB, ducacur BF parallela AF: e ducta quavis AC
dux LB lineam lecerin C, hane in continua analosia E. B, E F, E. H quE
Dalate lae Sinclinea AB.
exele.
uius.
bCo
Mt e  sit   t
11II
11III
111. M.I
 e  t  e i A e e at e  et   t e e  t t  et e te     e e   e