# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0421
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0421?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 415, page id 845634801:0421
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=421
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000421.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.90
# 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.

R ESPONSORVM. LTBEK VTII.
L I FE R.
Daca Cumma vel disferentia duarum peripheriarum, quarum sinus datam habeanEra-
rionem, dantur lingulares peripherix.
E Enimvero si veraque peripheria proponisur minor quadrance, vel utraque major,
Eric,
Ve adereparum similium sinuum ad differenciam eorundem, ita prosinus dimidiae summae periphe-
riarum ad prosinum dimidia differenciae carundem, Vel ita prosinus complementi dimidia disserensia pe-
ripheriarum ad prosinum complementi dimidiae summa.
2 Duod siuna eperipheriis proponatur minor quadrante, altera major,
Ve aderexarum sinuum ad differenciam eorundem, ica prosinus dimidiae disferenciae peripheriarum
ad prosinum dimidia summa. Vel ita prosinus complemensi dimidiae summe au prosinum complemensi
dimidiae differentia.
D A F L S E B F F M 1.
Taearouni.
Dara summa vel disterenria duarum peripheriarum, quarum prosinus datam habeane
rationem, daneur Cingula.
F Enimvero si urraque peripheria proponatur minor quadrante, vel urraque major,
LEIE,
Ve adereearum similium prosinuum ad differentiam eorundem, ita sinus summa peripheriarum ad
sinum differenciae, Vel ita transsinuosa complemensi differentiae ad eranssinuosam complementi summa.
2 Ouodsi una e peripheriis proponatur minor quadrante, altera major,
Vtadereearum similium prosinuum ad differenciam eorundem, ita surus differentia peripheriarum
ad sinum adgregati, Vel ita transsinuosa complementi summa ad transsinuosam complemenei diffe-
rentia.
TEA O HP0Z cip8.
E +Z H P OXE LP ON Z X O A L A.
Canonis Mathematici Fyposyposis.
X angulis latera, vel ex laceribus angulos ec mixtim in criangulis ram planis quam
Iptraericis adsequi summa gloria Machemarici est. Sic enim exlum _ cerFaS dE maria
Felici ex admirando calculo mensurar. lraque ad eum sinem paratur Canon Machemari
cus, quo extribencur lacerderioneuli plani rectanguli, aectimata in numeris serie erina in ha-
bicudinc anguli acuri ad rectum quacunque. Deinde docetars obliquangulorum ad rc-
ctanoula, et Sphaericorum ad plana, reductionem.
Lacerarrianguli plam rectanguli vocaneur, LIyporenula, Perpendiculum, Balis.
Fiypocenula dicirurlatus subrensum angulo recto, reliquis Famoliori.
Perpendiculum unum elaceribus circa rectum. Basis alterum.
E duobus angulis acuris clanguli plani rectanguli, unus acurinomen rerinet, alcer di-
cicur reliquus e recto. Is aurem angulus acucusincellisitur, cui lacus perpendiculi voce
desionatum subrenditur, Leliquus erecto, cui balis. Fr rice verla, latus ei angulo qui
acuri voce primus exaudicur subcentum, Perpendiculum denominatur. Larus subcentum
Anontus reCtUS datuE ex se de constiruicur parcium xe, qualium eora cireum Ferentia
circuli, qua quarUOF E SImAEUT FECtOTUM, ad SUMITE ZIT CLX: Unaquae que pars curtus sub-
Ansuli
ce
EFIE
ExIE,
Teliquo e recto. B2(15.
diridirue in LX sclpula.