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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 270, page id 845634801:0276
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=276
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.88
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0
Z aequalc. XC ex AB aBlcindatur AD aequalis dupIX CB. LraguE DB SErIXSUSMajOT qual
CB, quoniam AB mOT Cutriplo C B. Vnde in producta AC pOnAEuEBE ip A DB ae qua
lIS, _E PEFA AGAEUE AL IPH LB Parallela, cui OcCurraFBC in F. X cenero A, incervallo A
delcribarur circulus, quent AB lccer in C, II; FB vero lecer quoque in l. Frgo per ea qua
Osensa sUnE, eAuE GBad BF, ILa BF ad BI, de ica BI ad BHI. F s AUTCI ABOICTencia d
midia incer CB, BtI, _C. Detea C  L, BI. Ouare Factum est quoc
OpOrtuIE.
Si fuerine quacuor linex rectae continue proportionales: Dato adgresato
mediarum _ adoregato excremarum, dantur singula medix relextrema.
hyporenusa aequalis est compositae ex aderezato extremarum es duplo adgrecatome.
diarum, perpendiculum vero adcrecaro mediarum. Alterum cujus hypotenusa est
aequalis differentia extremarum, perpendiculum differentia mediarum. Est alt
tem basis in isto, eadem quae in triangulo rectangulo cujus hyporenusa est aequalis
adererato extremarum, perpendiculum adererato mediarum.
Itaque: Lrt ut quadrau composita ex adereeato extremarum es duplo ab
crecari mediarum, multatum quadraro aderecari mediarum ad quadratum adere
sari extremarum minus quadraso aderezari mediarum, ita quadratum aderecat
mediarum ad quadrarum differentiae mediarum. Vel ita quadratum composita
ex aderecaro extremarum es duplo adgre eari mediarum ad quadracum differen
tio extremarto.
LRDEOSFTTO ZIZ. Aedouvor.
Mdet duo ab iis constituuntur iitan aba pta rectanema. Vnum cus
Exponatur circulus ADBC, cujus liameter AB secer in(eripram quamcum que CD ita
E, ITA HEAE, FC, FD, EB line in concinus proporrione. Id enim teri porte lecundu
darimucua earum guxe in continua proportione sune lingula segmenra; diametri vide
ratIONEM quam CLHC CaCaH CS POHCUMI CIL. DiCO dramerro AB X inCcripra C
licet AL, EB; alcerius in (CrIPTA CE, ED. Cum enim CD secabitur perpendiculariter
eta CL Occurrence ip( BA in F, erir F A ipE C D aequalis. SItAULEM G CeNErUI PeE qu
secencur CD, CF ad angulos rectos in H, I. Suncigicur duocriansula rectansula 
liaFGI, CFH. Acrrianguli quidem FOI, perpendiculum CL aquale est ip H CHL, Leu
midia CD. CF rero hyporenula compolica est ex AC dimidia diametri AB, _L CX F A I
CACD. leaque datur criangulum FGI. Trianguli verOOFHI, hypOrenULA GF est ditra
rent dimidia AE, E. B, de perpendiculum P. FI aequale differentix dimidix CF, F
Balis poco C HI aequalis est balicrianguli rectanguli C O FI, cujus hyporenusa C 6 et
aequalis dimiata AB, perpendiculum C. HI aeguale dimidix CD. leaque dacur balis CL
Cum igirur duo lnclimilia criangula FCI, G F HI, quorum primilacera daveur: acqu