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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 19, page id 845634801:0035
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 recognised, mean confidence 0.88
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# After the first blank line: the recognised lines in reading order, one per line.

 proportionata lex plano. Lolida.
A quadraco cubus.
A quadcaco-quadacu IM B.
Acubus in B guactatum.
A quadracum iM B cubum.
A in B quadrato. quadracum.
Bquadcaco cubum.
N OF A PR TOR E S.
Exproportionalia denique conrinue leprem Colido. Colida.
A CHb0- Cubus.
A Gitadraco cubusHB.
A in B quaacato. Cubum.
A quadrato. quadratum in B quadeatum.
A cubus in B cubum.
A quadracum in B quadraco- quadrarum.
Echc deinceps.
PROPOSFFTO ZII.
VADR A XO adgregati lacerum, quadeatum differentix corundem
SEX lansunum A, alcerum B, OPOrteAE A - F B quadrato, A =B quadrarum adde-
re. AC vero quadearum efectum ab5 A F B, constat A quadrato, F A in BbIS, +. B
Quadearo. Ouadeatum aurem effectum abs A = = B. ConsTAE A quadrato, = A in BbIS-
F Bguadraco. Fiac ioicur horum addirio. Summa erie A quadrarum bis, = B guadraco
bis. Ouare factum es quod oporruir. Iinc
T H E O R E W A.
OVA DR A TVu adgregati laterum plus quadrato differentix corundem, XquaFUE
adgregato duplo quadratorum.
P R OPOSTFFO XTTI.
Dr ADRATO adgregati duorum lacerum, quadrarum differentix co-
Lcundem demere.
Sic latus unum A, alceruM B. OpOTECAE A F B quadraTO, A ==B quadearum auterre.
Abs planis lingularibus quibus constat eftingendum abs A. F B quadTATUM, aUECTCNEUE
cngulacia plana, quibus constac quadrarum abs A =- B: ex exi ditterencia B in A qua
Ter. HIinC
T H E O R E M A.
OTADRAErM adereenri duorum lacerum, minus quadrato diftetemix corun-
dem, aequatur plano quadruplo lub lateribus.
C O N S P C F A R F V M.
DL a vrM sub duobus laceribus cedic quadraro dimidii adpregati laterum. A qua-
licatis enim percheorema ordinacx vrraque pars lubquadeuplicetur. Ouadcatum adere-
saei dimidii lacerum praectabic plano sub lareribus per quacrarum dimidiae differentia,
aur non erune lacera diverta. le d aequalia. Ouod animadvercisse Tuir opetaeprecium.
PR OPOSTFZO ZIV.
DTFFERENXTAM duorum laterum, in corundem adgresatum du-
CeC
S1xlacus majus A, minus B. Ducatur A = B in A f. B, e cingularia plana colligan-
tur. Frunc illa A quadracum, -B quadcaco. Flinc
E O R B M A.
Qr0D sic ex difterencia duorum lacerum in aderegarum corundem, aequale est
differencix quadcacorum.
OX
B cubo- cubuS.
adcte