# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0391
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0391?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 385, page id 845634801:0391
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=391
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000391.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 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.
# 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.

nterenia
D. de
letinica
extribe
115ADC
B
eruneib,
DaB
ne
ircut
dempe
CM
38
RESFORSDRDM. EFDER VITI.
lum BDC. Ouare criangulum BAV _ GUAIE CHTHAnguIODAC, SeV BAF. Spacium ita-
que mistilineum illud DBC, aequale est lectori DAC ex trianoulo BA L. CIITODIGUC M-
dacur sectio BF. Spacium isicur mistilincum illud DBC addicum sectioni BF, aequale est
lectoribus BAF, CAD. Ouod erat octendendum.
PR OPOSFFLOVTTI.
Si ab UnaGUAqLC exTremitatum diametri, Cumantur in candem partem
circuli circum ferenciae aguales; ab altera aurem carundem exrremitatum,
incribantur linex rectae ad cerminos sumptarum aequalium circumteren-
tiarum: spacium circuli quod inter rectasin eriptas interjacet, ae quale est
lectori ab eadem circumterentia, qua spacium iplum, comprehenlo.
Reperatyr aucecedens diaoramma. Dico spacium circuli E B D comprehensum à rC
ctis F.B, BD e circumterentia FD, esle aequale sectori E. AD. A lemicirculo enim BF. C.
anteratur spacium BD C comprchentum a rectis BD, BC d circumferentia D C, ip (2
etiam dematur sectio BE: Superesitaque spacium EBD comprehensum d rectis EB, BD
de circumterentia E D. Ab eodem aurem semicirculo auteranEUE seCEOrES CAD, BAF
qui quidem praedictomistilineo BD C spacio, una cum sectione BE sune aequales. Super-
CsLIGITE SECtOFEAD. ErgOlectOrI E. AD aequale eA spacium E. BD comprehentum a re-
Atis E. B, BD e circum ferentia FD. Ouod ecar ostendendum.
PEOPOSFFTO IZ.
CUM aD eOdCI pUInCtO CIFCUIFCFENFIX IINSCFIBUNET CHCMO ErCS LInCX
rectae, quarum media latus est retrasoni, secans bitariam angulum ab in-
Ccripris exrremis Factum. Itaque delcripra sune duo criangularia spacia.
Quorum bales sune circumterentix xquales, latus aurem in(eripti LCETAGO-
ni crus ucrique commune. Dimidiam differentiam duorum illorum spa-
ciorum criangularium, figurx cum miltilinex, cum rectilinex, adae quarc.
Suib A centro, intervallo quocun-
que AB describatur circulus, in quo
Cumatur B C circumferentia FerraGO
ni, et a puncto C lumantur verin-
que circumferentix aquales CD, CF
circumferentia cecrasoni iminores,
ee subrendantur BD, BF. SunE ita-
que descripra duo spacia triangularia
DBC, CBE, quorum bales DC, CF
Cune circumferentixe aequales. larus
aurem cerraconi BC crus est eistrian.
sulis mistilineis commune. Ttagne
oporrer dimidiam differentiam duo
rum illorum spaciorum eriangula.
cium, Egurxe cum miltilinex cum se-
ciam abscindane BD, BE in F, C. Dico in primis disterenciam dimidiam inter spacium
BC _ spacium CBF, aquari criangulo mistilinco CGF, Ccu CDF. Deleriptus
enim circulus sub Bcenero, incerrallo B C duplus tic ad circulum sub ACenErO, incer-
allo AB delcriprum. Leaque sector F B C ad illum percinens circulum, aequalis est le
tori D A E ad hunc perrinenri; qui quidem sector D A F. xqualis octensus est spacio
histilinco DBE. Ouare Si ab his aequalibus commune verinque auferarur spaciummi-
lincum BD C C, relinquerurrriansulutr. mistilineum C. D F eriangulo mistilineo CCF.
equale. Estaurem FBC sector dimidiusrorius lectoris FBC, id est spacii mixcilinei DBF.
inaequa
Ccilined daaequare.
Sub cenero B, interrallo BC de
Ccribatur circulus, cujus circumferen.