# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0101
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0101?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 85, page id 845634801:0101
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=101
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000101.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 68 lines, status machine
# Lines: 68 recognised, mean confidence 0.81
# 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.

a
eis
ex
D
let
1
1I
e
Ost
et
UM
201
112
1Cs
DU.
eAt
ex
2E4
te
AE QV A YY O N V M.
differentia vel summa laterum, vel suorum oraduum, una cum dato sub iis
aut corumgradibus paribus vel disparibus facto, alcerutrum ex lateribus.
Ad aequationes denique mulcipliciter affectarum, affectionem aftectio-
ni adjunget sub direrlis laterum parodicis oradibus.
Auc eriamnon se adirer uni quaestionum Formulae, sed se lub Z erecicis
exercebie sub quocunque efficto rel propolito chemate.
Dux Geometrico operi aptaturus, recordabitur latera ad exeremas li-
neas rectas in serie continue proportionalium referri, Facta vero lub laceri-
busauc laterum paribus rel disparibus eradibus ad aliquarum e mediis po-
Cectates.
Ec quum incidet in aequarionem Mechanico suo henc obriam, de illa
conder Theoremalimile, cujuscunque aequalicatis Syctaticum de Exese-
cicumr.
AEquationem xequationi similemresularirer dicimus, quum uerobigue
Par eAporectas, leu xeque alta, iplaque affecta afticientre, lub pari gradu de
cademaffectionis nOLa.
SuodHatue peam praeterea requiritur speciale ec condiconariums
similicudo anomala est.
C A P Y F TTI
Constum d aequationum quadraricarum ex Zetericis.
Llectorum lane, qua ddae quantur, quadratorum constiturio, ex Z etc-
EiCIS digNOSCITIE PEOBC: CunE aurem aequationum hujulinodi eres IpC-
Cies: Ka Ta Parirn, A’no Pari, A DiBON O
Lebusitaque Lbrematis de carum consticutione Analycta ita PoterIE
ratiocinai.
T H B O R E M A 1.
R A F A B A Y IK 1I5.
FA quad. F B in A, Xquel Z quad: sunteres proportionales radices.
quacum media est L, atterencia vero exrremarum B; de AC A MIMOL CX
Data mediaerium proporcionalium linearum rectarum, ex differentia inter
Oca enim in lineis rectis locum habene comparariones, ealdem ad radices qualeon-
que, mplices, planas, solidalre, auculcerioris ordinishomogenas, polseaprari, diste-
Sil igicur daca Z media crium proporrionalium, B diferentia exFremarum, et 0.
PorreacTrenice minoreMexEremam.
E.AO illa A. major isICUE Cric A + B. dueatur minor in majorem; Ac A quad. + D
In A. Er vero quando sunc proportionales, quod tcsub extremis aequacur medix qua-
draco igitur A quad. - = B in H, aequale eAt Z quad. Id aurem iplum est quod ordiacur.
L= 10. N. aequatut 14 4. E)t V 144. media incer extremas disferentes per 10. es sit L N minor
T E E OR E M A IL.
ATIODAFTKHS.
A quad. = BIn AL, LGLETIE Z. QUAd: LIINEErES PFOPOrEIONaleS, QuLALUI
media estZ, dureLCACd verO exEremarum eAt B; dE HL A MajOT CXETCMA.
FX 2C.
trema.
Ex Zecericol placet.
extteus, ideiremitarem extremam.
ruic Campanus in libro de proporcione.
excrema ex seris ercum proporionalium. 8. 12. 18.