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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 238, page id 845634801:0244
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
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EEFECTEONYM GEOMETRTCARVM
LII. Lacus quadraci, aequalis differentia inter quadrarum perpendiculi es quadrarum la ricudinis
quam facit nculae quadrarum adplicatum basi. Oua in serie datur prima es latus quadrari, aequa
lis aderegat quadratorum a duobus reliquis. Itaque dabuntur duae reliqua per proposicionem X Y I.
Est autem Mechanice quadrato. quadrati, adfecti sub quadrato. Traque in canonicarum numerum
adscribitur. Dua de causa opus ipsum intesrum consencaneum est exhibere. Proposium icitur esto
Data base trianguli rectanguli, et media inter hyporenulam de perpen.
238
diculum, extubere ipu eastum.
sam ee perpendiculum. Oporrer extubere iplum Clatisl. e caeat et C. deplicerio
Sit cata A C balis erianguli rectanguli, et data quoque C F. media inter hyporenu
quadrarum ex C. P, Faciens larimmdinem C F. Deinde inclinetur C F perpendicularire
AF diameter circuli, e cujus circum terentia cadar perpendiculum BC. DicO A C BErIaH
gulum elle de quo quaericur, cujus ridelicer basis est ipla A C data. C Um aureM SIEUEA C
ad AB, ita B C ad BE, id est C F, uc opnsindicat, ee ancecedens demonstravir. CF ie
romedia (rinterA C _ C P, consequens est mediam quoque esse C. F inFeF A B ec B C
Duare factum est quod oportuie.
Daca meca erium proporrionatum, ee ea cujus quadeatum ae quale et
difterentixe quadratorum ab extremis; inrenire extremaS.
Vehic data AC _ C F, inveniuntur AB, BC.
PR OPOSFFTO XIZ
ad AC, sectaque A C bitariam in D, describancur proporrionales CF, CF, C G. FFH
Laem autem Problema poruit ita enunciari.
Si quacaCCAIX ITEF BaLin d perpendiculum ctianguli FeCtAHS
li, adplicetur ad hyporenulam: Oux oritur lacirudo, exie proportionalisiII
ter duo sesmenta hyporenula; quorum primi quadratum adjectum qua
deato lacicudinis, aequat quadratum balis; secundi vero quadratum cidest
quadrato lacicudinis adjectum, aequat quadratum perpendiculi.
Sic crianguli rectanguli tiypocenula quidem AB, batis AC, perpendiculum BC
media incer balim et perpendiculum B E, cujus quadearum adplicarum ad AB, Facta
lacicudinem BP. Cadar aurem CD perpendicularirer à puncto C in AB. Suncigil
proportionales AD Ccomenrum primum hyporenula, C D educta, et D B legmenu
hyporenulae reliquum. Dico DC eAC aqualem ip(i B F. Leaque BF ese proportion
lem inter AD, cujus quadrarum adjunctum quadrato C D equer quadracum A C b alton
e DB, cujus quadrarum eidem quadrato C D adjectum aequer quadcatum C Bp erpet
diculi, uc decernie Theorema.
Fs eniUEABadBE, ita BE ad BF ex constructione. FA quoque ut AB ad C B
ita AC ad C. D ex similirudine criangulorum ACB, ADC. Quadrarum aurem et
alet