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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 124, page id 845634801:0130
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=130
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 recognised, mean confidence 0.88
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124
DF RRE COGNEFTONF
Sunsolatera L. 2. lD- F lN, aquarur 2. ex fit L NL. Rursus + O = L N, aequabitur 2. 8 fit
+ 2.
P A B O R E M A II.
EF A quad. quad. + B Colido in A, aquetuF Z plano- planO, _ TUPIIS F
quad. quad. = B Colido in F, Xquetur Z. plano. planO: TUINE QUAEIOFCON
tinue proportionales, a quibus cubi alterne sumpei differunt per B Colidum.
Fic aurem Z plano. planum, ductu alterius extreme in disterentiam cubo-
rum a reliquis alterrie lumprorum: e est Aprima minorinter extremas, L
QuarFa.
Sunto coa proo I. N C. 2. NC. 4. 2.
e fit LN F. RursuS 1Q O =SN, aequabitur 6. e fit 1N 2.
F I E OR EM A ITI.
29Q =5N, aequabitur 6.
CTA cubo. cubus =+ B plano. lolido in A, aquetur Z Solido. Colido, et
Prursus P cubo. cubus = B plano. Colido in F, Eequetur Z Colido- solido:
Cunt lex continue proportionales, a quibus quadcaco-cubialcerne lumpu.
differune per Bplano-Tolidum. Fic aucem Z Lolido. lolidum, duetu ilterius
extreme in ditterentiam quadraro. cuborum à reliquis alcerne lumoro-
rum _ est A primaminOFInEeF CxErCMAS, P (eXFA.
Sunco proporcionales continue 1. N OC. 2. N OC. 4. N OC. 8. N OC. 16. 2
2CC = 2I N, aequatur 22. 8 fit LN L. Et rursus LCC - ZLN, aequabitur 22. 8 fit L N2.
Y H E O R F M A IV
OF A quad. quad. F B in A cubum, EquetIE Z plano plano, e rursuS F
quad. quad. = B in P cubum, ae quetur Z plano. p lanO: LIINE GULALIOF CON-
tinue proportionales, quarum alterne lumpearum differentia est B. FF AE
Z plano. planum ex ductu veriulris extreme in cubum differentig reliqua
rum alterne sumpearum, _ dum incelligitur prima mInOF INEeF exEremaS,
eAt A difterentia alcerne sumpea trium primarum, P difterentia erium po.
Aremarum.
Suntoproportionales comnu l. 2. 4. 8.
rursus 192 - 5 C, aequabitur 216. e fit LN6.
29Q + 5 C, aquabicur 216. 8 fit LN 3. FB
P H E O R E M A V.
CF A cubo. cubus F B in A quadrato cubum, eguetur Z Colido. solido,
D_ rurluS E cubo- cubus =Bin E quadrato cubum, xguetur Z Colido
Colido: lunc lex continue proportionales, quarum alterne lumpearum dit-
Ferentia est B. Fic aurem Z Colido. solidum, ductu urriulris extreme in qua-
drato. cubum differentie reliquarum alterne lumpearum, ex dum intessioi-
cur prima minor inter extremas, tir A differentia alterne lumpea quinque
primarum, e P differentia quinque postremarum.
Sunto continue proportionales, 1. 2. 4. 8. 16. 32. TCC - L 2TOC, aquatUr
515; 632. ex fit INII. EtrursuS LCC -2r O C, aquabitur 5153632. 8 fit 1N 22.
C A PV F ZZ
Equalicarum inversarum consticuriva.
Inversarum denique systatica sunt hac.
ET E O R F M A I
SFB planum in A = A cubo, aucta L. LoldO, LTurtuS L CUIbUS =BPId
noin l, aeqlu L. loldo: sunc rres proporcionales, a quibus quadr aca
alECF-