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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 378, page id 845634801:0384
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=384
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 100 lines, status machine
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V AR EORVM DE REBVS MIAT FE A A FFCTB
pri. Scd _ cirCUMFerenEiA BDC dupla CA Ad CIFCUIFETEDEIAI BEC. Rectus enim et
angulus BLIC, cujus amplicudinem detinivie circumtetentia BF. C, quadrans ideo rori
cixcumtetenrixe lui circuli, de similis circumferenta DGC. Dicoiraque lunula DBEC
rectilineu extriberi aequale. Subcendantur enim BC, DD, CD, Ac criangulum rectar.
gulum BBL. Er quoniam Similes (UNECITCU FerenEa BFD, DGC, BEC, lacetA BD, DC
non secabine circum ferenriam BF C. Circuli aulem, circulorumve similes sectores,
miliaque legmenta sune ue d diamerris quadeara. SeGmencum igitur F BC duplum ett a
scomenrum FBD seu CDC, e illud haecambo adauat. Ec vero criansulum BDC a
Ferr a lunIA SCGMENTA FBD, CDC, adlumirverO LESIENEuM FBC ca 2d aquans. Lui
Ix itaque DBEC exhibecur xquale rectilineum, criansulum videlicer rectangulum DBC
Ouodtacere oporrebat.
Non distimilimechodo quadeabirAnalysta lunulam conctaram excircum ferenciis duo
rum circlorum existentium in ratione uspra e quadcupla alicerve mulcipla, edoctus pr
7C
PROPOSTTTO TTI.
In circulo duas eircumte-
FENEIAS LIETC exISENECS I
ratione cripla, in qua eciam se
habeane rectarum, gux ipls
CircumFerentiis SUDEENdUINEUE
quadrata.
Exponacur criangulum rectansu
lum ABC, habens angulum ad C
rectum, angulum vero ad A erien.
rem recti. FA igitur quadratum ex
BC ad quadratum ex AC, uC unuI
ad eria. Produestur aurem BC in
D, Polica C D aequali excessui que
AB hyporenula crianguli praectat
AC balI, ec lumatur media prOPOF
tionalisinter BC, BD, _ SIcBZ. Sum-
Pro denique quovis centro de inter-
vallo aequance BC perpendiculum
expoluci crianguli, describarur circu.
lus, in cujus circumterencia in scet
baneur rectae FC, GH, II LipEB
aequales, de subrendatur FI. Est ie
tur circumferentia P L ad circumte
rentiam FC eripla. Dico Cimilicet
quadrarum ex subcena F. L ad 9u4
dracum exF C ese quoque rriplum.
Rgacurenim diaMeteE FMI.
Ouoniam circumferentia FG FL L
eripla est ad circumterenciam FC.
ideo est FC ad FI, Sicur quadratue
Cx FM ad quadrarum erip lum ex FMI
minus quadraro quadruplo ex FC
Id enim expolitum est in Analycicis
angularium sectionum Zecerice
Theorematis quarri. Fcideocum l
FC constructa ip(BZ aequalis, FM
vero dupla ipsius BC: est BZ ad F
(ICMI
oreltionem subrenlarum. Deinde opusrerexenei licebit per synthelin (urijam in racte
necripla e quadrupla cdo exemplum,) cuum invenrum ordinare.
Ceut
quadr.
Plum,
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