# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 251, page id 845634801:0257
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=257
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 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.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

reri el
elinqu
c
E O ML F. F R F A.
drato ex AC. Trague relolura analosia. ctiplum Colidum sub AC d quadrato ex AB, nH
nuscubo ex AC, aquale est Colido lub F. C dc quadraro ex AB. Quod erac oltendendum.
P R OPOSTFFO =YCII.
equalia, angulus aurem qui est adbaus Lecusuteplus anguli quielt ad
balim primi: triplum Colidum lib quadrato cruris communis ex dimidia ba-
seprimi multata continuatare longitudine ejus cujus quadratum aequale
elC criplo quadrato alcicudinis primi, cum mulcabitur eju (dem dimidix b2-
lis multata continuarare cubo, xquale est solido sub bale secundi et ejul-
dem cruris quadrato.
Siceriangulum primum BAC, habens ctud AB. AC LGIata, LC CMCHSC. VL, HavH.
loqueDC, DE crura aequalia. Ersinc AB, AC. iphsDC. DL. aequalia, le d ec angulus
DCE sen DEC Cerriplus anguli ABC (CU ACB. Excicecur aurem alcicudo crianguli pri-
Mi AF, ec in bale ponacur AC verlus B ipsius A F dupla; unde urraque BF, FC Acbalis di-
midia, _ quadratum ex CF eri-
plum est quadeari ex AF alciru-
dine; aeque adeo BG, aequalis
eA ipA BF muleara lonoicudine
GF; _ GC aequalisip(IFC, COn
cimracae lonoicudine CF. Dico
criplum Colidum sub BC de qua.
dearo ex AB, minus cubo ex
BC, aequale ese Colido sub CF
XE quadTATO ExDC LCUAB
GC _c quadrato ex AB, minus
cuboex CC, aequalc esse Colido sub CF e quadtato ex DC leu AB.
CumFerentiam in II, ex ex eadem circum Ferentia cadar in diamerrum ad punctum G per-
Pendicularirer recta IO. SHIHCIBIIHL Cresproportionales BG, GI, GC. Ouoniam aurem
AC est dupla sBius AF, ledamcet, angulus ACF eCtrriens recti: ideo criplum quadratum
 AB, aequale est lingulis quadracis absbb, bl, bC. Actecta ita que rtia lol1d a 9u d
lia Cune-
Primum, cabus ex D C, minus Colido eriplo sabBC de quadrato ex AB.
Sccundum, criplum Colidum sub BG _ quadraro ex AB, minus cubO ex BC.
Terrium, criplum Colidum sub GC de quadrato ex AB, minus cubO ex CC.
dedprimum, aequale est solido sub C E dt quadcaco ex AB, ex anrepenulrima propo.
cirione.
Ouace lecundum quoque de terrium; aeguanur cidem Colido sub CF et quacrato ex
AB. Vnde constac propolcio.
Si duoerianouta tuerineaquicrura lincula, ec ipsa alterum alceri curibus
Eccurtus eriplum Colidum sul
Cenro enim F incerrallo BF vel FC delcribatur circulus, de producatur FA ad cir-
PROPOSFT1O L14.
dejunctam concinuationi; licut quadratum lemidiametri ad quadratum
continuatxe diametri.
dub Aceurro, diametro BaC describarur circulus, de lumatur CD CCAS aIAMCELI, d
acus CErriens semicircum ferentia, seu aliter, arcuS HExABOMI. EFCONneCtATUIE F. D, cui
Sacur parallela Cemidiamerer AF, _C a pUIH CtO F in C B prOduCtam dUCATUEFG, (CCAnS
rcumterenciam in II, ita uE LIC sic semidiamerro AB seu AC aequalis. IpSI AUTCM FC
encalleta aGNCUC EI, Secans C. C in J. Dico tactum esse quod oporcuic, esse enim uc 1B ad
LA, it2
Cametrum circua oa, Coato da remscametrum