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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 142, page id 845634801:0148
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=148
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
# Lines: 46 recognised, mean confidence 0.88
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# After the first blank line: the recognised lines in reading order, one per line.

DE E At E N D A FFON C
T E EO R FM A I.
ETA quad. - quad. F Blolidoin A, XguetT Z plano- plano, _ F quade.
cubus + Z plano- plano 4 in P quad., aquetur B Colido. solido. Inno-
relcat autem E ese D: A quad. I D in A, XquabitF ~ coliao = D quad. 2
IH B O R P. M A II.
er A quacr. - quadr. = B Colido in A, aquetur Z. plan O- planO, et F qua-
Ddrati- cubus = 1. Z. plano- plano + In F quad., xquetur B solido. Colido.
Innotelcat aurem P. eAC D: A quadr. = D in A, XquabiEUF ~ solido - L
quadr. =.
Constirutione aurem cum hujus cum ancecedentis equationis bene aenica: sune duo
latera, d quibus quadcaco. quadrarorum differentia, applicata ad aggregatum larerum.
Facie BColidum, id est Factum duplum ex rectangulo sub laceribus in dhifferenciam, adjun-
ctum differentia cubo.
Diserencia veco iplorum laterum eAt E. seu D. dCFEZ plano- planum, a quadraro dif
Eerentix lacerum plus rectangulo sub laceribus in iplum rectangulum. ec A est latuS
unum; hic majus; illic minus.
In serie vero quaruor continne proportionalium: AFD differentia exrremarum: B(0
lidum, differentia cuborum a singulis alcerne sumpeorum: Z. plano planum quod Hc ex
ucraris excremarum in differentiam cuborum a reliquis alterne lumprorum: ec sIC A pri
ma; hic major inter extremas; illicminOr.
Sint proporcionales continue 2. N C40. Y C200. 10. 18B Y 832N, aguetur 1680.
Igitur 1 O. + SN, aequabitur 20. es sit L_ 2.
Et SErOO = 83ER, aequerur 1680. Peitur 1O - BN, aequabitur 20, G fiL X N 10.
Noca antem est 8 disserentia inter 2 es 10. quoniam LC. = 672DN, aequatur 692 22 +. Pnub
sit LN 64. quantum est quadratum abs d.
T H E OR F M A TII.
E+ Blolidum in A = A guadr. - GuadC., EGLIatIE Z platO. pLANO; eC P qu2.
drati- cubus = Z plano plano 4 in P quadr., aequerur B solido- Colido.
Innorelcat aurem P. CNC D: D in A = A quad., x quabitur D quadi. 3
Consirurione aurem aequalicaris bene aenira: est B solidum quod sic sub 2eoreonto
quadracorum in aggregacum laterum, seu alicer, cubus agoregati duorum lacerum, mul-
raeus facto duplo absrectangulo sub laceribus, in aggregacum larerum: ex Z plano- pla
num factum abs quadrato sogregati laterum minus rectangulo, in ipsum rectanoulum
et AC F. Ceu D aggregarum iplorum lacerum, A majus iplorum minuere.
In lerie aurem quatuor continue proporrionalium: est B solidum aggresarum cubo.
cum a quatuor lingulis: Z. plano. planum quod tic sub urravis extremarum in aggrCGaEuNS
cuborum a reliquis: D degregaum excremarum: _C Ec A prima, vel quarta.
Sine proporrionales continue. 2. N C 40. V C200, 10. 1248 N = 1 O 0, aque
tur 2480. Ioitur IZN = L 9, aequabitur 20. 5 fit LN 2, vel 10. Noca autem est 12. agerCB
TuM 2 85 10
1C . 9920X, aquabuur 155,304 C fit L  144. quancum est quadrarum abs 12.
P R O B L F ML A II.
Dualicatem giradeato. Guaatal2Hecclub cubo, permedium cubica
radicem habeltis planam ad quadraticam deprimere.
Pr