# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 321, page id 845634801:0327
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=327
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 65 lines, status machine
# Lines: 65 recognised, mean confidence 0.84
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

entiae aqu
50c
1
X.
ust
bas eiret
e
ibin
ol
R E S P O N 5 V M.
n ebba eL
releriam
43729, 635, 533,296
100,000,000,000,000
153,208, 888,623,795
100,000,000,000,000
T E E OR E M A FFON II.
Xquadr. - quadr. in F. 5 = X quadr. in F. cub. 5 - + E quadr.. cubo, aequarur X
quad. - quad. in B. F.F sic rriplex. J. Sinus duplus anguli subquintupli. ij. Sinus du-
pus differentia inter anculum subguintuplum ex quintam parrem duorum re-
orum. iti. Sinus duplus anguli composiri exangulo sub. quintuplo, es quinta par.
e quaruor rectorum. N eque enim compositus ille rectum excedit.
+-
SC.  +OC, aquetur 1. Ononiam posito r simu TotO, fit L Sinus duplus aneuli partium XXX.
eo 2N est sinus duplus aneuli parcium VI. vel sinus duplus an eulI ParEIUM XXX. Vet eriam sinus du-
Plus anguli parrium LXXPIII.
Pricigicur 2 N radix trinomia 2 - v 3 - radise binomia ? 3. + V 3 
set
Veleriam radix erinomia Z = N 28 = radicebinomia 23 - v 33.
N = 5C + 1OC, aquetur 18, aen. oub. 615, 13r.. Ouoniam posito X sinu toto, darum homogeneum
ropositae aequalicaris fit sinus duplus anguli parerum XX. Ideo L N est sinuo duplus aneuli parsium LV.
60, 00c
Vel sinus duplus anguli partium XXXII.
Vel eriam sinus duplus anguli parcium LXXVI.
Pritigieur LN
Te
ret eriam
13,951, 294 748, 825
100,000,000,000,000
105, 983, 852,846,6 4+
100,000,000,000,000
194, 059, 145, 255, 209
100,000,000,000,000
THEOR EM ATTON TII.
X cubo. cubus in E7 = X quad. quad. in F cnb. 74 - + X quadr. in F. quadr.-
Lub. 7 = F. quad. quad. cubo, aquabitur X cubo- cubo in B. Et fit F. quadruplex.
dinus duplus angul subsepcuxli. ii. sinus duplus differeniia inter angulum sub-
cuplum es seprimam parcem duorum rectorum. ii. Sinus duplusaneuli compo-
 ex subsexcuplo ex seprima parse quaruor rectorum. iiii. Sinus duplus aneuli
ompositi ex differencia praedicta es sexsima quoque parce quatuor rectorum.
14C. + 7 OC = + OQ C, aquetur r. Ouoniam posito Sinueoro, fit L sinus duplus angu
Parcium XX X. Ideo 1 N est sinus duplus aneuli parcium 1V, cum duabus sexermis parcis unius. Vet
Mnus dupius aeuli parcium J. Al, Cam iribus sexrimis. rel sinus dupius aneuli parcium LV. cum quin-
 seprimis. Vel denique angult partium L. XXII, una sum sex septimis pariis uniuls.
Asi 7 N = 14 C + 7OC - , ODC. aquecur 2. Ouoniam 2 est sinus duplus aneuli recti, fit 1N
seprimis.
anculi parcium XU, cum sex sepcimis. Pe sinus dupus anBuII ParEIU LXLY, cum duabus
44504 18680
10000000DO Lacus tessera decagoni
8019377358
10000000000. Recta cujus quadraum quadrato lateris hepraeoni ad-
unctum, aequatur quadrato diametri.
simus dup
Erit ixitur 1P
Vel eriam