# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 260, page id 845634801:0266
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=266
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.84
# 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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# After the first blank line: the recognised lines in reading order, one per line.

SE Y DO - NI E SOL A B V M
sancur GI, BL; spraese CI secet AB in K. Rectangulum igitur est circulo inscriptum
GCDI. Icaque aequales m H, ElL, acque adeo aequales AK, EB. Sel il, C.D lC
260
EL aequalia.
tir aequalis. Abs L. B verorelecerur L. N ipu L. D aequalis. Iraque reliqua NB reliquae L.C
Ac aequalis.
culo AB, CD sesC lECAMEINF, ideDCH AC Ad L. C, SICUTF. D ad E.B. e componendo et
ME COMPOSITA Ex AE, AM SCU FD Ad EN COMPOSITaM ExEB, BN SEUFC, SICUFFD ad
EB. Ouarc est F. C ad FD, ACUT F. D ad E. B. EFprOindE CFIE VEAE. ad FC, ita F. C ad F. D,
_ ita F. D ad FB. Ouod crar ostendendum.
PeorosstIo ILI
Si fuerint quatuor linex rectae continue proportionales: CFIEuECOmPON.
ca c cribusprimis ad compolitam e cribus postremis, ita se cunda ad cerriam.
Sint quaruor linex rectae continue proportionales A, B, C, D. Dicoesse, uc compottu
ex A, B, C ad composiram ex B, C, D ita Bad C. Est enim B ad C, SiCuF A adB, X l
cur C ad D. quare componendo est B ad C, sicur compolica ex A, C. ad compolicam e
BD. Errurlis componendo est B ad C, sicur compolica ex A, B, C ad compolicam 
B, C, D. Ouod erar demonstrandum.
Continua proportione inter lesmenta diametri: qux per exeremum inlct
Pexe ducitur, ipsiperpendicularis, occurret diameero in puncto quo contu
nuata est diamerer per interrallum inscriptae.
Circuli diamerrum AB secer in lCrIpTa CD In E, _ GINESCBIMENTA AF, FC, FD, LBH
conrinua proporrione, hoc CM, sITUE AE ad E C, ita F C ad F. D, _ iTa FD ad F. B. ExCtlC
eancur in aequalia legmenea permulal,  , LDesmenta aequalia Cune, et C L,
Producaneur FB, ID se que mucuo secent in L. Frianoula igitur rectangulA LDE,
FCK aequalium lunc larerum, ee aHoulorum. IEague L. B HC F A xqualis, 1d CH C D ex H1Y
porhe(i. ABS FA igIEuT reSCCCTE FM IPI C L aGuaIIS. Ilaque Tegua M Teliquae L
Ouoniant sBitur parallelX suNEFC, DL, aeque adeo triangula FCE, LDE CCUFCR
sune similia, erie FF ad FL, SICUTE. C ad FV. EI LBaMCeHdo erit MF. difterencia into
FM, FE ad EN diFFeTCMITAI IIeL LIV, CL, LICUE LC ad FD. Sed d quia in(cripEX CII
lROPOSTFTO IY
St diametrum circuli ita SCCeF in (CripEa ML LCZLACMLA LHCLAEX GINEH
cur aurem ad C perpendicularis ips CD, occurrens dimerro BA ContinuaEx in F. DIC
conmualtem a ipsi inscrixEX CD este dua. Caa C C POP
21
Lopot
pioporiis
pplearur
de duc
Pirer
DdentS
osie
drect