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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 855, page id 1815201908:0912
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=912
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 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.

eRC
 PL ANV M
PROPOSTTIO CCXXXII
TIrculum AB C SeceEper centrum acta recta B D, cui AAFUIRCUEX-
souidistans AF. OpOrret aurem parei cynu habenci basim Ce-
Sudencum AFF, et alcicudinem BD  aliudxquale exthibere, qudd
SEal aceca fucadoaua Pacclula la Lechulcem.
Constructio e demonstratto
 EctiS AF AanEaequalestinca F, C. H, inparallelis F V, SecancibuS AF; ad
LSCeneur. Denique quoniam oltondimus Meas NOe I. M vircuales ello paca
rectos angulos; rectis quoque s I ponancur aquales P, C L, linca; Rmilicer li-
neis AV, aequales sacuaneur V, C+O, veicriam rectis F V, Xgnales V, CM, col-
Bolas, reducantur hx ad Formales aC veras RR, P1. e SS, F Y, prouc luperius
explicacum est, ostenden dum igirur superticiem TK, ductam in SP, qua amba
Tunc parabolicis lineis conclula, exhibere magnicudinem quancicaci parem illi, qua
resulcar exbasilegmenti AF F, d alcicudine BD. quod sc constabit. agaEUF X Y.
aequidistans AC, sedper circulicenerum: iungantur quoque Z A _t X P, vri criam
AF _E FF, criangulum A X F. cam rationem habec ad AF F, criangulum, quam
habec linea XZ ad F G, perpendicularem ad A F, sed crium criangulum A Z F.
ad A F F, criangulum habecrarionem compolitam exracione AX ad AB, X CXFa.
_ exratiONC ZF ad FL: lea ctau am AX F ad rectangulum AFF
tione X E ad F E, igicur racio X Z ad F C, composica est ex ratione A X ad AF
habecraltonem compolitam ex ratione A L ad AF, d exrarione X F ad F Fi igi-
cur eriam racio rectanguli A L C ad rectangulum ALF, eadem est cum rarione
X Z ad FO: rectangulo aurem A X F aequale est rectaneutum ZY, XZ; igitur
propolicionem quadraselimam quincam huius, luperticies s P, quam octendimus
ZX Y, cectangulum ad rectangulum AFF, eam habet rarionem quam linea XZ
ad F C, lincam; ergo rectangulo FC, XY vel BD, xqualecA rectangulo AF F
sedlincae AF aequalestunc ex constructiono rectis CN, _ linea FK, xquales sun
ex eodem capire rectis GL. Rectae vero GNY, e CL aequales sunt quoque lincis
SP, FKi igitur rectangulum S P, YR, aqualc est rectangulo F G, BD. quare per
palablis incerceptam, duecd li planci L R. (Gloa idem elt cum Se, linverracues
exhibeb corpusaale adimi luper bali legmenci ALiF, constirure habelt
 alcuamem aqualem MaMCErOCICUIBD. Suod erac extibendum
4944
Corot.
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