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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 95, page id 845634801:0111
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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 0.89
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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A. QV, A FF O N V M
AdtciatuE vero quacato- quadeatum, tam liib quadrato quam latere:
aguaro attecti quadrati, a quo deducta guadraro-quadratica est, cam pal-
Ca ch tuorum quibus Constat lingularium homogeneorum distributionem.
ut quadratica porestassuna cum dicli dati plani comparationis, rel ejusdem
Produetione, Feceric Palcemunam aequationis, planum vero (i b lacere, una
cumapotome dati plani comparationis, vel eodem producto, parrem alie-
ram; alque adco utrage parte ducta quadeatice, omnia Fuerine ordinata
Adticiatur denique quadrato-quadeatum sub cubo: aequatio adFect
quadrati, a quo deducta quadrato- quadeatica cAt, cam luorum quibus con-
NaESInSCLALLCIH HO.HOSCCOrum PaCa est dictriburionem, uc quadraci sym
bolumta cum plano lub lacere, Feceric partem unam xequationis, dacum
vero plasum compardechis alteram es utraque parce ducta quadratice.
LIEEFDLCEALIONCI CONGEUAME aCCCPCTINE, uE homogenca tam (IB laTCrC
quam Guadraco, acque deleo omnia tuerineordinata.
Charum esto _ Postreum, cubicas omnes affectiones per climacticum
irreoularem adcentum, e guladraticis posse deduci, verum in illis ad primx-
vasnon patere re ductionis vam, nili per aequationes porestatum eque. alta-
rum daftectarum: xequatlonum tamen inde concticutarum spectata pro-
Sed _incer anomalas plamaricas, dignxe speciali nOta Tunt ex quae perti-
nent adhomogenca aftectionum, que de PorestatibuS HCTANEUIE: CPCANTuE
illa lud primaera origine a puri quadrari aeguatione, insticuro pla(IMALC PCF
addicionem relsubductionem: nam quum 2d plasina adsumitur coefticiens
quaelBecmajorradice propolita, sire ea adfrmetur per lypothelin, sive
negete, semper inciditur in aequationem plani sub lacere nesati de quadra-
uoriescunque poreltas negatur de aftectonis homogeneo, radicem
porestatis esse ancipicem: quoniam ex ancipice illa quadrarica religua
omnes AuunE de ACMCintuE, Calva radicis primaera amphibolia.
C A P V X IX.
Deductiva quadratorum affectorum a puris.
Vae omnia ut tianc cridentiora, Theorematum aliguot, ad plasimata
de quibus s pertinentium, jam sequirur FarFa80.
E A E O R E M A 1
EF A quad. Xquetur = planO. A F BCAOF. E quad. = B in F 2 ae quabi-
Ouoniamenim A quad. proponirur equale Z plano, est aurem A F B radici F. aqua
liS, CrBOF =B XquABHEMI A. Leaque quadracum absF. =B aequabitur Z planO: quadra
cum aurem illud constac lngularibus planis. E. quad. =Bin F. 2 Y B quad. Ouare omni-
bustris oldinati L Guall. = B in F 2, aequabicur Z. plano - B quad. ut estenunciatum.
T H E OR E M a II.
A quad. XqueTT L planO. A = BCAOF. F quad. i Bin P 2 Xquabi-
Duoniam enim A quad. aequatur Z plano, est aurem A = B radiei L. aqualis, er eo L
FB aquabituE A. LEaque quadearum abSF. + B aquabicur Z plaNO: GURdEALI AULCM
iAud constacingularibus plaS. F quad. + BINE. 2 F B quad. Ouare omnibus BeHCOr-
dinaris LGuad. F B in L.2, a quabitur Z. plano- B quad. ur est enunciarum.
THBO.
Priccasmaxime jurac.
10. Vnde Porilina.
TuE Z plano =B quad.
tuTZ planO = B quad.