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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 619, page id 1815201908:0676
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=676
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 recognised, mean confidence 0.80
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

cuTE
id II
Qu
Inet
1
b
eil
2C
lem
N.
lem
6
11.
15.
1
11III
EI Y P E R B O L A.
eaca est rarionis RH ad HO, igitur racio R N ad FTO, CadeM e cum rarione 275. Bs
IS ad FS. racio vero 15 ad TS, duplicaca b quoque est rats LS A RN: Bibid
igitur racio KV ad ITO, duplicaca cA racionis IS ad RN: igitur c segmentum cir g. hi
ISITK hoc cstI AK dimidium est scomenci RNOHI, hoC CA R AHI; _ IAHFeF - ius.
cia parci segmenri LAFI aequale cA. Duod tuic demonstrandum.
PROPOSITIO CEXZII.
D ECx AB, B C, ad angulos rectOS COIIOCAEX PONANEUE, qua LInE d-
LL Eympeocihyperbola CDII _ axes parabolarum BF D, B FD: (IF-
que L. F alymPCOTO AB parallela, PET CUIUSEXCTCMAAGanEUE BFG, B F HI
ducacurq; BD.
Dicotiguram CBD. Eisurae DBYt dimidiam eAte.
Demonstratio.
2 AliO TK ad LFd duplicara est eius rationis, quam
habet LL ad R L. Sed ve IK ad FR, GCDL est ad
NL. Pgicur racio DL Ad NI, duplicara est rarionis
BT ad KI, hoc est OM 3d PM, eA aurem ratio DF
ad NE duplicata rationis DT. ad FI R (quodD L, FTR,
NVE proporcionales inc) ec racio CM ad PM duplica-
caracionis CM ad DL, ob candem caulam. Igicur eriam
racio DL ad TTR, duplicata eAt rarionis GM ad DL.
Tgicur superticies cDL R FI dupla cA plani OML D,
hoc est DBHI, quancicas dupla quancitatis DBC.
Duod tuic demonstrandum.
11I
619
PAOEOSICIOBLKNII
d EX 170.
Vodlimanencibusislem recta F O contmcacur parallela BC e
midium forelesmenti D BI.
agancurtinex BOT, BFHI.
Dicoleomentum DBH di-
Demonstratio.
DrCISEMIHI AZ, DX, _ Y A qua
aegudistent alymproco BC, appac
bic ratio RO ad LS, hoc est X n ad
Z D, duplicatagrarionis R S adR F, hOC
eA XZ ad YH: sed rario X a ad ZD.
duplicaca est eius quam habech X X ad
A E; Cimiliter racio YZ 2d V FI, dupli-
cara estrationis YZ adZD; isicur Fa-
tio AT ad XD, duplicaca est rationis
XD ad Y II. quare cum quancicas
A TD X dupla sic quancitaris D Z YL
etiam TBD, dupla crir quanciraris
DB FI. Ouodtuir demonstrandum.
EX 170
huius.
n75. h1-
         u e   i   sse p