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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 12, page id 1815201908:0069
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=69
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
# Lines: 61 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.
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# After the first blank line: the recognised lines in reading order, one per line.

L IN E A R V V
Tisdem POstiS, POTCFUnE auFerrI
lineae, in racione F ad F, ve reldux
datam habeane rationem C FI act
III reciproce. Friganeur enim ex
C_I Parallela CR IL; Xquales
rectis AB CD; _E CK L PCF. X
AUCAEUELINCA PR MI, VEL M CC ad
MK, quemadmodum cst P ad F;
ducaturquerecta MFT, OCCUETCNS
ad MK; id cA F ad F; ee N C 2d OL, reliquam ad reliquam, ve C FI ad III.
y
Sit AB maiox recta CD, habCAEqUC F
ad F eandem cacionem, quam AB ad CD,
quae ex cadem sic cumratione G FT ad FI F. Ad-
di porerune lineae in ratione F adF, VE COm
Polica, rarionem habeane GFT ad FTT. addan-
TuT enim BK D L linex, Sccundum rationem
P ad F: Ouoniam igitur per hypochelin, AB
est ad CD, ve P ad F, id est perconstructio-
nem ve BK ad D E, Cxit ~ AR ad CL, VE AB
ad CD, id cA CFI ad FI1.
Tildem politis: demi pocerunelinex, irarione F. ad F, vereliquae racionem h2-
beanE GFT ad FTT. demantur enim BAI, DN; Ononiam isitur CAvE AB ad CD.
sC F ad F, id est per constructionem BMI ad ND, cric AM b ad C N, reliqua
ad religuam, ve AB dut C_ saCvE OTI ad HII. Duodcrac demonstrandum.
8. Sic ratio AB ad CD inxequalicatis; de
maior quidem, ratione OFI ad TIL; GIC
aurem racio F ad F, maior ratIONC AB
ad CD.
Diconddiposse lineasinratione P ad F,
vecompolex habeane racionem CFTI ad
TII. Facto enim RL ad NIT. vE F ad F,
CFISANEUE Cx R _ M ParaIICIa, R N, HIO.
aqualesips AB, CD; innetilque N, O,
AaCVE OTI ad HII, AC N P ad OP; QE CX
P per L linCAASAEUE PR qua (cum ratio
NP ad OP, id est OTT ad TIF, minor
AcrationC KL ad ML, id es F ad F, ad-
eoque PLnoxquidistec ipsi OM) cone-
niet cum OVI, NK lincis, in O eE R. Vn-
de paTCE MIO ad RR addicam ad addi-
FaM CAE, VE KE ad LMI, id est peF CON
Cructionem ve F ad F; _ OO ad NR,
cocam adtoram, ese ve NP ad O P, id est
OTI ad FTI. Tildem posieis:
Dico demi posse lineasin ratione F ad F,
vereX obtineane rationem OFT ad TIT. ProducatuE enim ON, donec cum
MK linca, conveniat in Z: Factoque OT ad NT, ve OTT ad TTI, _ sumper
LS aquaMipE ML, criE NT maior ipla NZ, X RS minor recta RZ, veosten-
dam; quare s ex T per S aZAEUE LinCA OCCUIEFeNS NK OMI lincis, in V dt Z,
factum crie quodperieur. Ouoniam enimratio OZ ad NZ, id est OM ad NR.
id estper constructionem AB ad CD, maior ponicur ratione GFI ad TTI, id est
29.6 C alt L L, erie diuidendo, ratio ON ad NZ, a maior rarione ON ad NT.
vnde NZ minor est linea N T. eodem modo cim rario F ad F, id cst MS ad
KS, exhypocheli licmaior, ratione AB ad B C, id eAt ONt ad NK, id est M L
2
Duod exat demonstrandum.
OK IT lineis in N et O. Patet LO ad NK ablacam ad ablacam CHC, VE L MI
Brbid.
M     e e.  i       1      et  e a t a       t  ta t   u            t  t u  p  .