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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 272, page id 845634801:0278
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=278
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 32 lines, status machine
# Lines: 32 recognised, mean confidence 0.87
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

ESF V DO. M F SOL A B Y M.
Tacadirua.
in proposica serie quatuor conrinue proporcionalium. sit data disferencia mediarum 6, extrema
rum r9. et oporteat invenire concinue proporcionales. Duo sunt isicur similia triansula FCH C
in quorum primo dacur dupla C. E. nempe disferentia mediarum 6, es dupla F. H 7. differentia Mtet
T9 e dupiam 6. Ouare fir dupla C H V 13. Intriangulo vero C C. F datur duplum lateris = 6G
plusporest disserentia extremarum differentia mediarum, seu adgregarum extremarum aderesa
mediarum. Fiet igiturHE H C V 13 ad FC N 325, id estuc V 2 ad V 25 seu 2 ad 5, i a C L
CC30, e ita CH7 ad FC 35. Est igicur z0 summa mediarum. cui addica disserentia ca
facit 36 duplam majorem mediarum, rel ablata 24, duplam minorem mediarum. SE que est 3.
summa extremarum, cui addita differentia earum 19, facit 54, duplam majorem extremariim
ablaca 16, duplam minorem. Acque adeo series proporsionalium quaesita est A F 27, LCt
ED 12, E B8.
legmentaunius in continua proportione inter mutua segmenta diameti
leomenta dus epaa PFoPotione intermutua lesmem
ca diamec hOn ctuL.
PROPOSFFTO ZXI
St dux inscripex circulo ina quales parallelae diamerrum secene, e lin
CAculi enim cujus A centrum, diametrum BC secent in D, E, inseriprae parallela ina
quales F C, HII, ec seomenta FD. D C sinr conrinue proporcionalia incer BD. DC. 
Co leomenra HLE, E. lnon Fore conrinue proporrionalia inter BF, F. C. Moat 
FD. D C sunc in concinua proporrione et. DC, 1deo cum lecabitur perpendic
laTICeK FC Per Farecta LL occurrenre ipli C B in H. Esic K B ipsI F C aequalis. Ipla ali
rem R F lecer HL LM L, L Per GaBatUTG Mip A F L. paralleta, SeCAnS FI Fin VI. FrIE 3
TUTL. M iphI LC aqualis. Sed _HL, MI erunc aGuateS. P’eF H veto asatu ip (1 L
parallela HIO. Mleleu, led hitieri poltir, seomenta HIF, F. I Cunc in concinua propou
neinter BE, L. C, erit O B aequalis ip l FI I. Erat aurem K B aequalis ip( FC seu L. 2
Ouarc K ericaequalis compolicae e duabus H L, M I, id eAt duplx HI L. Fs aucem
DH AlHL, itA F. K ad EL. Ouare F K erie dupla F. L. Hoc aurem est ab lurdum. 1
OpOrtel EK quae compolica eAprima, Secunda, ec rerita Cc majorem cripta L. L. 10
Plcudo. melolabi expolitio.
Nrarun cis F aduvaror est methodus demonstrandibene MathCMAEI