# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0043
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0043?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 27, page id 845634801:0043
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=43
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000043.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.88
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

NOT A P RTOR F S.
Ex operemulciplicationis Acubi, F A quadrato in B3, A in B quadrarum 3, PusL
cubo, per A - + B - + D
lblatete, caccesus tuo guaaraco, a radice binomia adlcitis conoruen-
ter lublaterali coefticiente lolido ex lubquadrarico coesticiente plano,
COPOHETC.
draricum C planum. Oporreat quadraco. quadracum abs A- t B adFectum adjunctione
duplicis plano-plani, unius (ub A F B e D Tolido, alcerius (uB A - + B gnadearo e C pl2-
nO Componere EHingatuE quadeacum abS A = + B, Rin illud superaddico G plano, ducarur
A - + B, X in efecta lolida superaddiro D Coldo, ducacurruilus A - + B, _ CollIgANCUE
Cingularia effecta plano plana, quae quidem CruDE
A quadedto quadrarum. AClBO in B 4, -+ A quadrato in B quadrarum 6,-F A
in B cubum 4, =F B Guaacaco- quadrato, t A quadeaco in C planum, -+ AIn BbIS
in C planum, + B quadraco in C planum, -+ A in D Colidum, - + B in D solidum. IlaC
icaque plano plana aeguanEur guadraro quadrato abS A - F B, adFC Ctoadjunctione pla-
no plani lub A  B quadcato et C. plano, et plano planisub a =+ B cadice, et V lolido.
Flinc
draricum, alcerum vero lublaterale Colidum Frie
Ouadraro. GuaaC TaLCHIS PEME, PIuS CDO TateS P Tacus ICC qua
druplum, plus quadraro lareris primi in laceris se cundi quadrarum sextuplum, plus lacere
primo in laceris secundi cubum quadruplum, plus quadraro-quadraco laceris secundi
plus quadcaro laceris primi in coëtticiens planum, plus duplo plano sub laceribus in ec et-
Aciensplanum, plus quadraro laceris secund in coefficiens planum, plus lacere primo in
coesticiens Colidum, plus larere secundo in coefticiens lolidum, aequole quadrato qua-
draro adgregacilarerum, adFecto adjunctione duplicis plano plani; umius lub quadiato
aderegat laterum, ec coëfticience plano, alcerius lub aderegeo laterum, ee cvesticiente
Colido.
COPONCLC.
povere quadeaco- cubum abs A -+ BadFcctum adjunctione plano. lulidi (ub A- t B, 8
Dplano plano. Componaneur quadraro quadracum abs A- + B, de in illud, lipernddi-
20D planio- plano, ducacur A. F B, de colligintur effecta Cingularia plano. Solida. FrUBE
cuboabs A = B, adtecto adjunctione plano. Colidisub A F B, _ D plano plano. Flinc
concipitue
Eiciensplano. planum, plus larere secundo in coefticiens plano planum, est aqualis qua-
deato
R 0 P 65+ L1O XZR.
Vadraco. quadratum adFCCTUIMACMMCHONE AMPHCIS PTAHO.PLALII, CLIIdS
Sicradx binomia A - + B, coeficiens sublarerale D ColidutH, CocMMctens lubquadra-
E O R E M 
Si Fuerine duo latera, et praeterea cu efticiens duplex; unum quidem planum subqua
PR OPOSTF1O XXXI.
)Cladraco-cubum adfectum adjunctione plano lolidi sub lacere aradi-
ecbmomia adlcitocongruc uaaee Plaho-Plano,
Sit Fadix binomia A -+ B, coesticiens (ublarerale D planO. planMM. OPOTFCAF COM-
A quadearo. cubus, Y A quadraco- quadrato in B5,  A cubo in B quadraTuM 10,
 A quadraro in B cubum 10, + A in B quadcarO- quadraTuM S, F B quaa1at 
A in Dplano-planum, i B in CPa PraI. Oua ideO X quabUnEUE quadraTO.
T E E O R E M
Si Terine duo latera, ex praeterea coefticiens sublaterale plano. planum: quadcato. cu-
buslaceris primi, plus quadcato quadraro lateris primiin latus e pn
Pluscubolaceris prim in laceris secundi quadrarum decuplum, piets eeacato laceris pri
im in laceris secundi cubum decuplum, plus lacere peinre ta lateris se cundi quadraro-
quadrac sincuplui. Prus sueace cubo laceris secundi, plus lacere primo in evet.