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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 269, page id 845634801:0275
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=275
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
# Lines: 55 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# 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.

exeneiae
mecta
m, vel
23jo1e
um ME
um.
nedi
diattl
reg
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st
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Aae
C6,
inu54
EpCOP
Peet
DSFVDO-HTE SOE A BYM.
PrOPONAnEUE quaMOTrECtX CAC in continua proportione, ex quarum extremis compo-
sica elt Z, ex mediis X. Oporret distinguere medias _ exrremas. Ac vero dato circulo
Kcinscripea, Cec a diamerro ica secare inscripram, ur segmenra in (CxipEX HMLM COIKMA
PEOPOTEIORE InFEK MUTUa LL SMCMCA Mametri. Ouare cenro A, incerrallo AB Xe quali a-
26
EA lecer circulum in F, C. BC vero in II. ErBOpeF Ca quae oltenla sunc, es uc FLL 20
DROTOSTETO XVITI.
Data differentia mediaru, e differentia extremarum in serie proxo-
IEa qUatuOF rectatum continue proportionalium, invenire continuepro.
Portionales. Oportet aurem difterentiam extremarum majorem esse cri-
PEOPOHANEUE QUAEHIOEReCTR
esse in continua proportione.
quarum exrremae differane per
L, medix per X. Oportet in-
venire sre medias, sive extre-
mas. AEvero ad angulum quem-
cumque inscriprae d diamerri,
exhibere licet mutua carum le-
omenea in conrinua proporcio.
nC. Triavouli aurem rectangu
li, cujus hyporenusa est equalis
differenrixe extremarum, per-
pendiculum differentia media-
rum, balis subrenditur angulo
aequali ei qui Ac in sectione
diamerri de inscriprae. Ouare
constieuatur eriangulum rectan-
gulum ABC cujus hypOrenLa
ABCC dimidia Z aequalis, per-
pendiculum vero BC dimidia
CK 2
X X qu a-
BC ipli X. Ouare factum est quot oporcuic.
midiae Z deseribacur circulus, cuiinceribatur BC aequalis daca. X. EC agacur diameres
CAD. Ex in junCta BD de COnEinUatA, POnAtUT AF composica ex AB, BC aqualis. et
AIB, ita HIB adHIC, _ ita FI C ad HG. Est aurem FG aequalis ip (Z ex constructione, de
ela differentia melliarum.