# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 317, page id 845634801:0323
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.88
# 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.

Accell
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M. P
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cubol
1B
E S P O N S Y M.
L Y X E R
Si Fuerinc eriangula rectanoula quorcunque, et horum se cundi angulus
acurus sc duplus ad acutum primi, cerri eriplus, quarri quadruplus, quinci
quincuxlus, _ eo continuonaturaliprosreltu, primi aurem trianguliper-
Pen diculum sacuatur prima proporrionalium, balis ejuldem secunda, ca-
Que lcries continuetur.
In secundo, crir balis ad perpendiculum, uccertia, minusprima ad se-
cundam bis.
Interrio, ut quarta, minus secunda ter, ad certiam cer, minus prima.
LAquaEEO, uE quinta minuscertia sexies, plus prima, ad QuAFEAI QLLaFCF,
minus secunda quater.
Inquinto, u lexta,minus quarta decies, plus le cunda quinquies, ad quin-
cam quinquies, minustertia decies, plus prima.
Insexto, ut septima, minus quinta quindecies, plus terria quindecies,
munus prima, ad sextam sexies, minus quarta ricies, plus secunda lexies.
In seprimo, ut octara, minus lexta vicies lemel, plus quarta tricies quin-
Guies, minus sccunda sepries, ad seprimam sepries, minus quinta trictes
quinquies, plusterria vicies lemel, minus prima.
Etica in infinitum, distributis suc cessire in duas partes proporcionalibus,
Ccundum carum seriem, urrobique primum adtumatis deinde negatis, s
lumpeis mulciplicibus, uc ordo gradtuum in arciticiola geneli porestatum,
quibus ex addicuntur, exigit.
T H E O R E M A IV.
Si Fuerinceriangula rectangula aequalishrporenula, quorum primian-
Culus acurus sir in submulcipla ratione ad an sulos acuros tucCCdentiUM OF-
are criangulorum, ad acurum videlicet secundisic subduplus, cerriisuberi-
elus, quarri subquadruplus, ex eo continuo ordine: construatur aurem se-
Res lincarum recarum continuc proporcionalium, quarum prima litX qua-
aS lemitiyporenulae, secunda bali criansuliprimi, incer succedentes conci-
hlc proportionales ex succedentum criansulorum bales, hac erie xqua-
litas.
Fertia continue proportionalium, minus prima bis, erie aqualis bali
criangulisecundi
Duarta, minus secundater, bali triansulicertii.
Duinta, minus certia quater, plus prima bis, bali crianguli quarri.
Bexta, minus quarta quinquies, plus lecunda quinquies, balitriansuli
Quinei
Seprima, minus quinca lexies, plus certianories, minus primabis, bali
criangulisexci
Octara, minus sexta lepties, plus quarta quarerdecies, minus secunda
epries, bali crianguli seprimi.
Nona, minus seprima octies; plus quinca vicies, minus certia sedecies,
Plusprima bis, Bau trianguli octavi.
Occima, minus octara novies, plus sexravicies septies, minus quarta tri-
cies, plus secundanories, bali criansulinoni.
Ec ita in infinitum, ucper loca proporcionalium imparia nora adfectio
TICCE.