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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 20, page id 845634801:0036
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.90
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AD LOCZSTTCEN SPE C.
GONSECTARENM.
DEEFEREN EFA quadratorum hadplicetur differentix laterum, orietur adorega
cum lacerum: _ concra. Differencia quadrarorum ( adplicetur adorezato lacerum, orie-
cur differentia laterum. Ouandoquidem divisio resticurio est. relolurione ejus operis,
quod compolicione mulciplicario efticit.
PR OBOSIFTO ZV.
rB0 adgregati duorum laterum, cubum disferentix corundem
addere.
SEr lacus unum A, alEErUM B. OPOTFCAEA. + B cubO, A = = B cubum adderc. AC
vero cubus effectus ab5 A   B, ConAAE A cubO, i A quadraro in B FeF,  A in B
quadrarum rer, t. B cubo. Cabus aurem abs A = - B constac A cubo, = A quadraco in
BEeF, L A in B quadrarum rer,  B cubo. Finc igitur horum addicio: Cumma est A cubus
bis, = A in B quadracum (exICS. FLinC OrdinAtUE
T N E O R E M A.
Crors adoregari duorum lacerum, plus cubo disferentix corundem, aquatuE
duplo cubo lateris majoris, plus sexcuplo Colido à lacere majore in laceris minoris qua-
dcarum.
P R OFOS FF FO. XVT.
V B0 adgregati duorum lacerum, cubum differentix corundem de
ICEC.
SLF lacus unum A, alFerUM B. OPOTEAE A -F B cubo, cubum ex A- B demere
AbS Colidis lingularibus, quibus constar componendus abs A + B cubus, demantur (in-
Gularia Colida, quibus constar cubus abs A= B: orietur A quadrarum in B lexies, j. B
cubo bis. Hlinc
T H E O R E N A.
CY BVS aderesati duorum lacerum minus cubo differentix corundem, RquIATUE
sextuplo solido à lacere minore in quadrarum majoris, plus duplo cubo laceris mi-
nOris.
P R OPOSTTLO XVII.
EXPERENXFAM duorum lacerum in eria singularia plana, quibus
constat quadratum adloresati iplorum laterum semel sumpra, ducere.
SIF lacuSmajuS A, minus B. OpOrECAE A -B ducere in A quadratum, L A in B,
=B quadraro. Fint paeticularis ductio, et collixancur singularia Colida. Frunc illa A
cubus, - Bcabo. IIine
T H F OR E M A.
Or0D sic ex difterentia duorum lacerum in eria singularia plana, quibus constat
quadratum aderesari iplorum lacerum semel sumpra, aequale eA difterentix cuborum.
C ON SE CT A R FV M.
DEEPEREHEFA cuborum E adplicerurad differentiam laterum, orientur eria CIN
sularia plana, quibus constat quadearum aderegaci lacerum (emel LUMBTA. EF permu-
tim,
DIXFER ENZLA cuborum E adplicerur aderia Cingularia plana, quibus constat
quadracum adgregari lacerum lemet sumpra, oriecur disterentia lacerum.
PR OPOSTFTO ZVTTI.
CeTC.
DOR FC A Y V u duorum lace  tria linsularia plana, quibus
 constat quadratu cutterencix iplorum lacerum seme l Cumpra, du
5