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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 242, page id 845634801:0248
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# Lines: 53 recognised, mean confidence 0.89
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V P P L E NE F N X V M
DROPOSTFTO III.
aucem exterior primae lic proportionalis uet palemeleeccuta
ee partem interiorem ejuldem: crit quoque pars exterior lecunda PlOPOi-
tionalis inter partem exteriorem primae ex partem interiorem ejuldem.
Sub A cenrro descriprum circulum, secene duxe linex rectae ab eodem B puncto ex
era circulum sumpro, eductae. Vna in punctis C, D; alcera in punctis F, P; unde parres
exteriores secancium
sInEBC, BE; incerio.
TeS C D, E F: Citaurem
BF proporrionalis in-
ter BC, CD. DicoBC
FOre quOquE PFOPOE
cionalem inter BF, P F.
Ouoniam enim ab c0-
dem B pancco cireu-
Iam SecanEBCD, BEF:
ideo csturBF ad BC.
ica BD ad BF. L.X hy-
Pocheli aurem eAt CD
ad BE, uEBF ad BC.
Ouare est CD ad
BE, Sicur BD ad BF,
ex per lubductionem
eAt C D ad BL, BCHL
BC ad F. F: COHI-
guenter ur C D ad BC, ita est BF. ad BC, d ira B C ad F. F: Ieaque BC proporriona
lis estinter BF, B F. Ouod crat ostendendum.
PROPOSY FTO IV
Si dux linex rectae a puncto exera circulum eductae iplum sccent, quo
aucem sic lub partibus exterioribus eductarum, ae quale sic ei quod AE sub
InECTIOTIbUS: EXICLIOTES PAFLCS PCTUTaTIM LUIIPEX, CrUMECONtinuCpid
pPortionales intEI ParteS InTeTIOTCS.
Sub A cenro deleriprum circulum, secene dux linex re ctae ab eodem B puncto exte
circulum sumpro, eductxe. Vnaquidem in punctis C, D; alcera in punctis E, F: une
parres exteriores lecantium (unEBC, B F; interiores C D, L F: quod aucem Aic sub BC
BE, aequale sicei quod sc sub DC, E F. DicO inter D C. P. F esse continue proporcc
pales BC, BE, eas adsumendo permurarim; ur videlicer interiorem partem primX Le
cancis lequatur pars excerior secantis se cunde; vel incerioreim secundae pars exteriorpes
mae: nempe cAen D C ad B F, ita B F adB C, e ita B C adF F.
Ouoniam enim id quod Hc tub CD, E F, aequale es ex hypothesi ei quod Ec sub BC
BE: ideo eAur C D ad BE, ita B C ad F. F; per synaerelin, ut C D ad BF, ita B D adt B
Sed exratione constructionis estBF. ad BC, sicur BD ad BF. Ergo CAtuL C D ad BLV
ita BE ad BC, e ira consequenter BC ad E. F. Ouod crac demonstrandum.
P R O P OS F F F O V.
Daris duabus lineisrectis, inrenire incer casdem duas medias Continue
proportionales.
Sine darae dux linea reCXZ, X. Oporcexinvenire inter Z. e X duus medias conci
nue proportionales. SicZ. major, Lminor.
LCl
Si dux linex rectae a puncto exera circulum eductae ipsum secent, pars
C
iX