# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0232
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0232?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 226, page id 845634801:0232
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=232
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000232.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 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.

DE N Y A E R O5
226
Si veronon puds ctionarus punctis conster coefficiens, se d ramen eoloct p
rumpae, ur dubitationipossir ese locus quanta eligenda radix vel parabola: ideone du
vilio Frustra sie, et de noro opusinchoare necese habeat delusus Analysta. TUnC, UE AtEO
maois omnia procedant, tam coessicientes, quam resolvendae magnirudines ad idem
magniendinis genus reducentur. Fc ex earum ita re ductarum summasquandoguidem pet
necarionem adfectio es) radix elicietur consenranea, ee rerinebitur.
Casus teriius.
Ouod adfectio fuerie per adErmarionem mixtim de negationem à potestate: LHCCta
quidem sub coetlcientibus ad Ermaris homogenea, una cum porestare lateris educendi
crune ablarira maonicudini resolvendae: AF contra effecta sub coethcientibus negatS
erumt addicira. Ieaque ad educendum latus lingulare primum, locus erir permixrim an
recedencibus quoque praecepris.
Casus quarius.
Ae quando porestas abhomogenea sub oradu avellirur, aruIa ea FeILTUIE POTCHA.
lateris lingularis primi, e restitura deminuirur ab homogenea de qua negarur, vel 10
mogeneam minuit. Semper aurem inchoandum est opus à divisione, cum de minorera
dice quaeritur, de resticuta porestas ab homogenea sub gradu deminuieur. C um vero quxe
rirur de majore, reducitur coëtticiens ad idem magnicudinis genus, et ex excessu elici
cur radix porestaris arulsae restiruroria, secundum ea quae in epidigmatis adnorara (UnE.
Praeceptum terrium.
De dirilorum constitutione, ordine, d litu, post cductionem lateris
lingularis primi.
Terria cura esto, ur post eductionem primilareris sinoularis, et emendaram consiua
Cabductione expolicam relolurionimaonieudinem, diridenres scansorix in (uo collocen.
cur siu _ ordine, tam superius quam inferius. Ac inferius quidem collocentur mulciple
ces lacerum elicirorum gradus parodici, ipsimet qui diriderent in analy (ipura porella
FiS, UE Pore
In analyE quadrari, duplum laceris elicicis
In analoh cubi, Prima. dividens seanforia magnieudo, eriplum laceris eliciri. Secunda
criplum quadearum ejusdem.
In analys C quadrato. quadrati, Prima, quadrux lum lateris eliciri. Secunda, sexruplun
quadrarum ejusdem. Ferria, quadruplus cubus ejusdem.
In analy li quadeaco. cubis Prima, quincuplum laceris eliciri. Secunda, decuplum qua
drarum ejuldem. Ferria, decuxlus cubusejuldem. Ouarra, quinruplum quadrato. qua
dracum ejuldem.
Inanaly (i cubo. cubi, Prima, sexruplum laceris eliciri. Secunda, de cuguineup lum qui
dracum ejuldem. Terria, visecuplus cubus ejuldem. Ouarta, decuquineuplum quadta
r0. quadrarum ejuldem. Ouinta, sexruplus quadearo. cubus ejusdem. Ec ira deinceps.
Ecoccupemmulciplices gradus illi, sedes sibi delignatas inter puncta singularium 
restarum, ur porelarerales, ledem laterum. Ouadrata, se dem quadratorum. Cubi, le dem
cuborum, _C.
Spertu aucem ipsae coefticientes magnicudines incet VACMLES AOICHDAHEUE, aL
circo moreantur idenridem in cccdencta puncta sibi addicta. Frpraererca, secundu
dividencibus reliquis se des incermediae, incer puncta iplis subgradualibus ad dicta.
Nempe, S coetticiens sub- quadrarica est, Duoniam in relolurione quadraci dividens
duplum laceris ettet, cedlu coetticiens it duplum lareris eliciri, et cHCCtA VOCeTUEN
gnirudo expleltonIs; a C MMAChHDUSCHO: L Plano porine coetticientem c resion
fixura numeralisincermedix, quam delienara quadratiea puncta superius reliquerum
Sicoelliciens sub. cubica est, Ouoniam in relolurione cubi dividens prima magnst
do, estrriplum lacus primum. Secundas laceris primi criplum quadrarum, ideo lunco qua
que