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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 65, page id 845634801:0081
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=81
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 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.

rimia
CCHH
BF
Secundo calu, Primum sic.
Secundum.
 midenr
Indecertium.
t in
2
quadra
quad
+D quadrace
in
M.
excectusbalis primi supra pelpelce.
lum lecundi.
N. compolica ex perpendiculo primi ec base secundi.
Apparec aucem primo calui cum demum locum cAte, cum D in N praestacipA B in M.
Secundo vero cum B in N praestat ip(D in M.
Z E F E YF CY M V.
Inremrenumero duo quactrata, aqualia duobus datis quadratis, UIF guX
Scorum alcerum consistatinera limites praestitutos.
Sine data B quadeatum, D g. Oporret alia duo quadrata iis aequalia constiruere, quo-
rum alcerum praecter quidem Pplano, sed cedac G plano.
Incelligatur Z9. aliudre planum equale Bg. F D9. Ergo Z rarionalis, ircationalis-
ve elt hypotenulatrianguli rectanguli, cujus larera circa rectum sunc B de D. Duari-
ricur aurem aliud crianculum rectangulum, cujus hyporenula quoque scZ, unum re-
ro e laceribus circa rectum (urpore ba(I5) sEmajor N, sed minox quam S. Fo igitur
reducicurres. Ve
Invenienda sine numero duorriangula rectangula similia, daras habentes B dt D hy-
Porenulas, ee diducti ab iis cerriieriangulibalis, compolira ex perpendiculo primi et
bale secundi, consistarinera limires pexetinitos.
Teaque 29. =- Ng. XqueTUE M9. LC L9. = Sg. aguerur R9.
Si igitur N Racuarur basis cerrii diducendi crianguli in duobus similibus criangulis
datas habentibus hyporenulas, etie per primum calum ancecedencis Z eretici ratio ditte-
renix basis de hyporenula ad perpendiculum, ur Z9. = = D in N, + B in M ad B in
N, + D in M, sCu DE X ad  a.   m . v . qui limes eAt primus.
EE R S Aatuarue basis ejus cerrii crianguli, erir ob eandem expolicam caulam rario
difterencia balis es hyporenulae ad perpendiculum, uc Z9. =- D in S, + B in R ad
3 in S, + D in R, seu vE X ad Z .  o . t  un. Cui times eA secundus.
Potta