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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 137, page id 845634801:0143
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=143
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 recognised, mean confidence 0.85
# 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.

divi
patio.
iea Ut
5di
ad. 3
1ad.
qu
2nO.
ciit
n
Oune
50
A O V A Y EO N V M.
Clibus- F F quad. cubo, aatur B in A quad. quad. - Z plano. Colido F F quad. - cub0.
Vreaque pars applicerur ad A. F. C. illic Oricur F quad. quad. = A in F. cubum F A quad.
in E quad. = A cubO in E. F A quad. quad. Ouod SiB in A quad. quad. = B in P quad.
Ea quoque commodam divitionem recipiet ab A L F, orieturenim, B in a cubum
Bin A quad. in P. F B in F quad. in A - B in E cubum. AdXGUICTUFErSO, _L CAPFOPECF
uc aequaliras rire ordinetur, F quad. cubus F B in P. quad. quad. Ctaruicor Z. plano. Solido
A = Bin D in A quad. =D quad. In A quad. + B in A cubum + D in A cubum - A
L H E O R E M A LV.
C+B in A quad. quad. = Aquad. cubo, aequetur Z plano- Colido, & F quad.
cubus + B in F quad. quad., aequetur Z plano- (olido. P aurem innOte-
ICaLCACD: B in D quad. + D cubo in A =B in D = D quad. in A quacl. L BF D in A cuDUM
A quad. quad, aquabicur B in D cubum f D quad. quadrato.
2TOO =L OC, aqueTUT 1O0OO. TPIEUr LIOO -= 1OC, aquabitur 10000. C fit LN 5.
Ouare 400N = 809 + 16C - 100, aequabieur 2000. x ista LN. est radixprimum quaesita,
ex sit 1C
Vurpatur quoque anastrophe contraria interdum ria, ut quum in xqua-
tionc ambioua, continsicunam radicum dari e duabus pluributre, de qui-
bus aequatio porest explicari: repetuntur anactrophes restisia ad aslequen.
dum radicem correlate, rariaque Auune inde _ Ordinantur FheOrCMata,
qualia lunein cubis.
T H E OR E M A V.
Acubus =Bplano in A, aquetur Z Colido, _ rursus B p lan. in F = F
cubo, aequetur Z Coldo. Innorelcat aurem F esse D: A quad. - D in A,
requabitur Bplano D quadrato.
Ouoniam enim A cabus =B plano in A, aquatur Z Colido. EC rurtus B planum in D
D cubo, aequatur Z Colido. Ergo A cubus =B plano in A, ~quabitur B plano in D -
DcubO, _Eper niccatheEn A cubuS. + D cubo, aequabimr B plano in A F B plano in D.
Vecaque parsaequarionis dividicor per A. F D, Ec Aquad. F D quad: - D in A, aqualc
B plano.
Oua aequatione secundum arrem concepta, A quad. -D in A, equacur B plano D
quad. Vrest ordinatum.
Si1C- 8 N, aequetur 7.
Teitur 8N = rC, aequabitur 7. es quoniam LN pocest esse r.
1O = 1 N, aequabitur7. unde radix primum quaesita fit ~ 22 + =
Y A E O R E N A VI.
S=BI Aquad. = A cubo, aquetur Z. Colido, _rursuS B in F quad. = F.
cubo, equetuE Z WMO. Innotelcatautem P CNCD: A quad. - F B- D in A,
Duomam enim B in Aquad. F A cubo, aquatur Z. Colido, de rursus B in D quad. -D
DCubus F A cubO, XGuABHHT BLI Bgund. = A quad. veraque pars aequarionis dividi-
COr per D L A, SED quad. F A Guact. - Din A, aquale B in D - a. qua aequatione secun-
Aum arceM concepta, A quad. F B- D in A, aequabirur B in D-- D quad. Vi est ordinacum.
S190 F 1C, aquecur 8. 1enr 9O = 1C, aequabieur 8. ex quoniam 1N potest esse 1. 12 +
Ouibus
Quad.3 aguetur alteri parri
aequale, de F innorescar eNe D. Landem isicur, D quad. - quad. - D cubo in A ] D quad.
in A quad. -D in A cubo. f. A quad. quad, ae quarur B in A cubum = B in A quad. in D f
B in D quad. in A - B in D cubum, ec omnia ordinando, B in D quad. in A. , D cubo in
quad. - quad., aeguacur B in D cubum. = D quad. quad.
lraque Facta est anastrophe, Mucpetabatur. FlInC OrdinatuE
aquabseur, B in D= D quadrato.
cubo, aguacur L 1014O.
ErBoB in A quad. 7. A cubo, X quaBIeuE B H D quad. -D cubo,  per merathelin
BX, aquacur B. unde ractur primum quaesica sir v 24 - 4.