# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 41, page id 845634801:0057
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=57
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 recognised, mean confidence 0.87
# 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.

YOF A PR FOR E S.
(is B, perpehdiculum D. OpOrteaEFacere quod imperatur. Sumatur F majoripia L.
lum. Traque hE limiliS HBBOTenUCA F L D quadratO, I B quadraco. BalIS VCFOF F D
quadcaco, = B quaataco. Perpendiculum F L D in B 2. Cui secundorrianoulorectan-
sulo aliud constiruatur simile, cujusperpendiculum (rD, Faciendo
D in~, = v qu
Latcraaclinue camillio
cum exposci crianguli rectanouli aucantur in F + D. in B 2. Duossm luncrriangula
in F + D quadrato - = B quadraco. BalIS D iN F + D quadrato = B quadTATO. PCF-
rectangula, hyporenulae videlicer Hane
crura alceriuserianguli, adgregarum ve-
robalium in dircctum policarum, ba(IS.
Alcicudo igicur mavel caac. Cale-
rum ur balis primi ad alcirudinei, Ila
alcicudo ad minorem bale secundi. Fs
enim
de abs P i. D vr radice una d B urradice altera, eAtingarur aliud eriangulum rectangu-
CIEF + D in B2 2d F L D quadr. = B quadraco, ita D ad ba(In, quae ideo erie,
 EC UEF + D in B2 3d quadraTUM ex F + D + B Guacat
ita D ad hiyporenulam, GuX IdCOCHII,  
rectangula. Primum, cujus Cimilis hrpocenula Z in F F D in B2, basiS B in F + D
in B2, perpendiculum D in F + D in B 2. Sccundum, cujus similis treporenuszD
Pendiculum idem ac supea in priorieriangulo rectangulo.
Coeancioitur in unum duo ciangula
V26D
in L
re B in F + D in B 2 ad D in
F = D in B 2; ita eadem magnicudo
dd D cubum 2.- + D quadearo in P2.
Ac ipla balis secundi similis est D in F
t. D quadratum, = B quadraro; hoc
est, F quadcatum in D, + D cubo, = D quadrato in F2, = B quadrato in D. CIITIB-
lolida dividantur per D. IIlIc remanet D quaoratu Y L Guacato. Hlic D quadra-
EUM, J F quadraco. Praestat aurem pet HpothchnF, pn L. Cetur alcicudoproPOr
F LN LS N O F A R EI M P N YO R E M.
que abdicatur F in D quadratum 2, X aadacur B guaaratum in D. Kchqua aenque
cionalis incer basimprimi, de minorem bale secundi. Iaque ansulus quem lubrendie
balis secundi, major est eo quem subrendir perpendiculum primi. Angulus itaque este-
ctus ab hyporenulis (cu cruribus est obculus. Ouod Faciendum erat.