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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 54, page id 845634801:0070
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=70
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.92
# 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.

E Y F CY H
Enim vero quadratum differentiae cuborum; plus rectaneuli sub lateribus qua
druplo cubo: aequatur quadrato adcrecati cuborum.
tam enim ordinarum es, quadracum aderepari cuborum minus quadrato disferen.
rix: xquari quadruplo cubo rectanguli. Velola Fuerir opusancirheli.
Sit differentia Cuborum 316. Rectangulum sub lateribus 21. AdgregatuM CubOruM L N, 2C
aquatur 136900.
Duplusideo Cubus major Y 136900. = 316.
Duplus miner Y 136900-316.
Z E F E ZTC Y M XVI.
Daco adoregato cuborum, d rectangulo sub laceribus: inveniuntur la
Eera. FnimVerO,
Quadratum aderecari cuborum, minus quadruplo cubo rectaneuli sub lateri-
bus: aequatur quadrato differentiae cuborum.
VerarsUS ex proxime reperira ordinatione licerinferre perantithe (n.
Sic aderegarum cuborum 370. Vectangulum sub lateribus 21. Disferencia cuborum L N, 1. Q
aequarur 99256.
Z E F E Y TCV M XVTI.
Data disferentia laterum, d difterentia cuborum: inrenire lacera.
Sic data B, differentia larerum. Ditterencia vero cuborum, D Colidum. Oporrer in
venire lacera.
Summa laterum esto F, ergO F. = B erir duplum laterismajoris, _ E. = B erir du
plum lacerisminoris. Differencia aurem cuborum illorum, est; B in F quadrarum 6,
 B cubo 2. aequalis consequenter D Colido8. Ouare D sol. a: D cubO. XQuaTUT F. QuadeaTO.
Dari aucem quadrari dacur lacus, ex data differentia lacerum e eorumdem summa, dan-
curlarera.
Dara isicur difterentia larerum, de difterentia cuborum: invenieur summa lacerum.
Enimvero,
Differentia cuborum quadrupla, minus cubo differentiae laterum, si adplicetur
ad triplum differentiae laterum: oritur quadralum aderesati laterum.
Sit B6, D solidum 504. summa laterum LN, 1 Q aquatur 100.
ZE YE F T CVM ZVTTL
Daca summa lacerum de summa cuborum distinguere latera.
Sic daca B, summa laterum, D Colidum vero, summa cuborum. Oporret distingue
relacera. Differentia laterum, cAto F. ErgO B F P. cs duplum laceris majoris, B =L
duplum laceris minoris. Summa icaque cuborum, est; B cubus2, +. B in E quadracum b,
aequalis consequenter D Colido 3. Ouare D Co. 1. -= B CABD XquATUE F. quadratO.
Dari aurem quadeari datur lacus, ee data summa lacerum ec differentia corundem: dan-
cur latera.
Dara isirur sunima larerum dt summa cuborum: dantur latera. F nimvero,
Summa cuborum quadrupla minus cubo summae laterum; si adplicetur ad tri-
plum summa laterum: orietur quadratum differentiae laterum.
Sit B 10, D solidum 370. E LN,
29 aquatur 16.
Z E YE Y LCV M XIX
Data differentia lacerum, et differentia cuborum: invenire latera.
Sic daca B differentia laterum, de darum quoque D Colidum, differencia cuborum.
Oporcetinrenire latera. Rectangulum sub laceribusecto A planum. Er rero adparet et
Benela