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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 814, page id 1815201908:0871
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=871
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.88
# 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.

814
APPLICA L
Ductui planorum in plana.
DVCEYS PLA
Vbrendat A A linea arcum quen-
adam circuli; e luper A A diamerio
lemicuculus LC aetciBatu, auccites
normalibus ad F C infinicis F ABCD,
46. 1o1uiu
hane rectis AL. aequales AB. SoItuI
crunclinea AB, hoceA A L, AC, AD
proporrionales, quoniam L AV re-
ctangulis xquancur L’A C rectangula,
hocest AC quadrata. O UarePerprE-
cedencem propolitionem rectangula
sub AC, F. D aquantur rectangulis
DABCInCD A F bis Cumpris una cum
rectangusis BC D. Consicut ergo ex propolirione rniverlalia huius li-
bri, corpus ex ductu plani AC in Cuperticiem F. D, xquari solido quod
sc ex mulciplicatione superticiei AB in F. D bis vna cum quantitate qua
reluleac ex ductu plani B C in C D. quare propolicionem apranimus ad
ductum planorum incer (c.
Scholion.
P Emodo reducendi corpora ex ductu genita ad quantitates solidas cerrae alcirudinis, hac
parce libri non intendimus mentionem inserere, cum particulari tractatu de eo arsumen-
ro in praecedenti parte actum fuerit.
PROPOSITIO CLXZXII
Duaria librinostri de linearum potentiis.
IF. eta SIE AB in C de D mecta d CACeMa Patione proportionali, et
B compolita e aea CaceMarum ee media bitariam secetur in F.
SCDLL Guamacu rectangulo DF. A xquale exlurgere.
alF2.LC AL2.
Nirculum CC ad extremicates
E. F diamerri continsane dux
rectae, quas secet A A parallela ad
F E, ductisqne AC, F. B parallelis ad
tangentes intinitis, FLABEFCCEX AB,
BD rectiS AC, CD proporrion.
les, erunebpuncta DD ad parabo.
laM.
Duoniam
homonsica
Dico semicirculi planum C P. in Le, aequari plano E. D ducro in P A.