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# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 130, page id 1047377675:0146
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=146
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.81
# 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.

F3C
05, 04, O3, Ex intecedentes arque recta 92 luperat rectam
FP CxCCRU AO, e recta 05 superat rectam FN exccNu OF,
de recta OZ. superac rectam FSexcessu C O; igitur rectae O2
OSuf OZ. sUperanEreCtAS FP FN afLS CxCCNU AO uta OF.
 DC: recta quoque FY superat rectum OZ exceHuOD, de
recto FV superac rectam O4 excettu OB; _ ideoFY LFV lui
Perat 13,O4 excessu OD,OB; cumque in serie quancita-
tum C2.O5O2 F.P a.FN.FS, PY sa FV, 03.FO4, Tum.
a extremorum 021F, 65,,OZ f O3,F. 04 sic aequalis Cum
mae mediorum FP, F.FN. F. FS.FFY of. FV; eric differentia in-
ter primam ee lecundam nempeOA,, OF.FDC aequalis dit.
terenciae incer cereiam de quartam nimirum OB f. OB, quod
alemonctrandum erAE.
P R O P. 70. Y H E O R F M A.
Si circulus parabolam in pluribus punctis secuerit, e quibus in axei
eectua
ex vtraque parte rectae perpendiculares demittantur; erit ea ab
vna parte axis aequalis illis ab altera parte: quod si ab utraque
parte in duobus punctisillam secet: erunt similiter duae ab Vna
parce simul aequales duabus ab altera parre simul.
IEpara bola P ABC C quam secet circulus in punctisP,
 A.b,C: quorum nullum cst parabolx vertex. a puin-
AisP, A, B, C. demittantur in axem eidem ordinacim appli
CATX AFI, BX, MC, PH: dico ordinacim applicacas exrna
parce axisnempe AHI, PH, aequales ene ordinacim applica.
Eis ex alcera parte axis nimirum rectis BX, CM. Producan-
cur rectae PA, BC, donec concurrant in D; ericque rectansu-
lum BDC ae quale rectangulo ADP, e isitur rectae parabo-
lam PABCCtansenteS pATAIICla rectISDC, DP, aequales
erune, quae igitur se mutuo incersecent in parabolae axc, ta.
ciences cum cidem ordinacim applicaris triangula io(celia:
igitur DP, DC, illis parallelae Faciune cum eisdem ordi.
natim
sint puncta earum contactur E, T, Ergo guncta QY socabitur
a
ob ano parabala bitaria et ad augu. nietos. Et e erit
aqualat dimidio duuu AH, XN. EA TC aeque dimidio duam
3X, CM.
Ergo aissanet AH N, aquar PX, CM.
est
t. 1. e
ob circo
17. l.3. (on
A
EP
1