# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 173, page id 845634801:0179
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=179
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.87
# 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.

1111
imtI
si inde
sextip.
5
ADEECTA
ES
A
TIM RESDLTETONE.
Vincrosam retoruconem Peceltacum purarum imitatus
CUL
PE
ime letotllo adtectarum porestatum, peaelertim
poceltaces adtectae decenter praeparaix Fuerine
Tunc autem decenter pexeparari incellignneur, cur
cissime fuerint adfectionibus obruex, iilque omnino
adtrmatis, autnegatisomnino, ita tamen utpocestas ad
Ermaca lic, non eriam ab homogenca rethomogeneis ora
du insigniris avellatur, ac denique mixeim ica negatis e adfIrmatIS, VENON
insic ambiguitas.
AdFectx enim hujulmodi porestates, ut tandem cornicum oculi con-
ATZHEUIES COMPOHUNEUE; e FelOlruntur ad purarum instar, habica dunta-
Xac datarum insuper magnicudinum, qua cum delignato oradu FaCiUHE
adsicientem homoseneam, e suberaduales dicuneur, ea qua decet rd
TiOnC.
Incellisuntur videlicet componi adfectae porestares à duobus quoque
laceribus, immiscentibus se subsradualibus magnicudimibus, una vel plu-
ribus, e in eadem relolruntur contraria compolitionis ria, obserrato co-
Ecticientium lubsradualium, licur porestatis, e parodicorum graduum.
congruente stu, ordinc, Lege, _ prosrenu.
Racionemque compolitionis, e de ca in artis etiam srmicudinem con-
cipienda Theoremata, uc in porestaribus puris, cdocet _ prxmonstrat in-
spectio e arans panaivors operis per Logisticen speciolam effecti, e eradi-
cum secundum cam mulciplicationis PEX CCPEUM.
Et lacerum ex relolutione orcorum adgresatum estradix poteltatis pro-
Politx adFcax.
Plane impossibilicacem in resolutionibus non inducir nonvra Bsa: 2E diffi-
cultarem parie ee anxiecatem, lub elatioribus praesertim parodicis ora-
dibuS.
Sciendum aurem est adfectione sub elatiore gradu quamcumque pore-
Carem posse liberari.
AdFectairem quadrato. quadrara ad quadrata per medium cuborum a
ractice plana reduci.
Ex Poreltares a radice plana, rel ulcerius climactica ad porectares a ra-
dice simplici rerocari.
Ac cum de homosenea lib geadunegatur porestas, radix est anceps.
Dux etiam amphibolia inest aliquando in porectatibus, quae adfectio
dibus partim negatis ex parcim adtirmatis obrolruntur, quando coesticien-
les sub cractu clatiore homogeneas nesatas, coefsiciencibus adtrmatas
Prxpollent.
Omnis icaque dubicacio primum collenda est, ne sic divinationi locus
Pocius quam arci. Neque enim de ambiguisars certa satuitur.
Eaecerum, urin puris, sic etiam in adfectis exisimusnumeros proponi in-
eoros e limmetros, non etiam tractos e alymmetros.
DF
Mti