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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 302, page id 845634801:0308
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PHE OR E M A F A
Ouodpohtremum, rudioribus ee in AnalyrietsiBImus Forrassis exercisatis exemplo, lic
oltendilse cuerie opera. prerium.
Sit drculus cujus diamerer AB, sectus in Ceomenta HIIa Qualia, quorum majus B AC.
circulum.
Scementi itaq; BC C quincuplum,
aequale erir bis circumterentix lub-
cendenri quaruor angulos rectos i
ve circularioni circa R punctum,
et praeterea iph circumferenrix BC
e quinquies sumprum segmeneun
BC, illud compolicum metietur: se
peratur quinquies, SInEqUE lCSICHE
BGC, CAD, DBE, EAF, FBC. erit
itaque segmentum BD, quod relin.
quicur ex incegro circulo linde aute-
racur BC C bis, duplum ipsius C
reliqui ex semicirculo, ablaco inde
seGMENEO BGC. erBO d FC aquale
ipliBD (quum rectae BC, CD ipl1.
CD, DE SnE xquales,) duplum quo
que eririphus C’A, ac proinde de FA
criplum iphusC A.
Fademqueratione, quoniam rectae CB, CD ipsis quoque ED, F P Cunr aquales, erunt
seomenca BD, DE aequalia, et scomencum BF quadcuplum ipsius C A: Similicer Lunca
sCGMENEA GF, E. C aequalia, ac proinde de C A quincuplum segmenci C A erir igitur eriau
gulum rectangulum AC B anguli simpli, BAD dupli, BAE cripli, BAF quadrupli, B65
quincupli.
Positaigicur semidiametro prima continue proporcionalium, e ipsa CB secunda, eaque serie con
sinuara: erit ex sexto Theoremate recta CB aequalis sexta, minus quarta quinguies; plus secunat
quinquies.
Innocis, sit CKL. CBL N. erit + DC -5C F 5N, aequaleipsi BB.
PR OBE E M A FFOV TTI.
Datum angulum in septem partes aequales dispescere.
Suppoliris quae supra.
Xcubo. cubus in F7 - Z quadraro. quadraro in F. cub. 14 F X quadrato in F qud
drato. cubum 7- F. quadraro. quadraco. cubo, aequetur Z cubo. cuboin B.
Fit E quadruplex
2. Subcenla peripherix sub. sepruplae.
2. Subrensa Cub. sepcuplae peripherix reliquae ad inceorum circulum.
3. Subrenta peripherix composicx ex lub seprupla et dupla sub. seprupta EOFI
circuli.
4. Subcenla peripherix compotica ex subseprupla ec quadcupla sub. seprupla 1o
eius circuli.
Ouod er Sc quoque declarabitur. Sic circulus cujus diameter AB, in quo subcendacus
recta C. B, e Crperipherix CB pars seprima BK, cui ad datur peripheria RD, equalis du
pla seprimae paeri corius circumterentix, de ducantur BD, D A. Dicoangulum DBA
sexcuplum, aequalem esse quaruorrectis, e praecerea circumterentix ADC. dc proinc
ex TheOremare 6 aqualicarem inter rectasBC, BK explicabilem quoque esse de termi
nisBD, BC
Fianeaquales BD, DF, EI, IG, GE, FLI, H C, et quoniam circum ferenria DB sepries
SumpCas
minus BFIC; _ heminoris segmenri subquincux lum BFI, cui addacur legmencum HCC,
aquale dupla quintae parri quaruor rectorum, neque enim compolicum excedec lemi
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