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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 301, page id 845634801:0307
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1ales.
EXHIM
al
A D A N GY L A R ES SECTFOHES.
Inratione minoris majoritre inequalitaris ex Theorematis), 6. d 9 lacistieri potelt:
aein majoris inaqualitatis ratione ex Theoremaris s e S hujusmodi deducitur
Consectarium.
Duoniam cademrecta circulo inscripea non diameter, duabus circu-
lexcuciis siubcenditur, quarum una minor est semicir cumterentia circuli, al-
Cera major, xqualicasincer subrenlam minori majorire e subtentam (eg
mencominoris, pertinebit ad subrensam quoque simili segmenco majoris,
Lad sibrenlas denique reliquis circum ferenciis quae xe que. mulriplices, M2-
lorem minorem. re in circulationibus componunt.
Neque enim obsacillud quod Theoremare 8uo animadverlum est, quum segmenrum
lemicirculo majus in parres aequales distribuitur, sive diamerer in sectiones incidat, live
cus, non enim muratur adtectionum ad perpendiculares pertinencium qualitas, aue
numerocum ab ordine praescripro series: in secunda Siquidem illius Theoremaris Agura
cec ex subcenta AE concludacue summa lubcenlarum CB, BI, post ramen ex ditterentia
mecae lummae ee subcenta CB priusconctula, id est ex subrenta BI, concludicurrandem
Atterenria subrenlarum ab A puncto eductarum, quae in lectiones ipsi l puncto urrinque
Proximas, incidumr: quae igirur illic mutara sune, hac operatione deinceps resitueHeuE.
dc in balium proscestione, quum segmenta aequalia semiperipheriam excedune, (WE
Bentum eA Theoremate quinco.) invercicur ordo homoseneorum sub gradu, de EC
poerestio incerdum qualis Theoremare nono est expolica. E quae ex duplici analogilimo
bcen ae urriusque minimae in ucraque semiperipheria, ad difterentias sibi ureinque proxi
Marum, mulaca ettinde eolundem homoxeneorum sub eradu qualicas, analogismis in.
elme did 2d agocegatum bi uerinque proximarum resticuatur: quod quide ex prae-
alipeo quinri Theoremachs proscellum Facienti, Laris constabic: acque hincpaceleit con-
d sectiones iaque datorum angulorum deducuntur ex Theoremaris lexcO et nonO
Toblemacia, ad ulum quoltes opus expostulatpatata, quaeque in infinicum pro racione
DR OBL E A A Y FO N I.
Datum angulum in tres partes aequales secare.
Colco Xradio, seu lemidiamerro circuli, B subren Ca angulisublecandi, F. subrenta
8menri
Aquactarum in E cet, minus E cubo, aequetur Z quadrato in B. d Aer F. duplex:
Subcehla circumtetentix reliquae ad incegrum circulum suberipla.
iquidem ul lupra octensum cA, aequalitas inter subceulam minorimajorive lesmento
lubrensam sexmienco minoris, perciner quoque ad lubrentam limilisesmenco majoris.
P R OBEF I A F F O N TI.
Darum angulum in quinque partes aequales dividere.
quacltaco. quadratum in F. 5 - X quadrato in E cub. 5 F F. quadrato cubo, Xque-
30
lectarii veritas
aata exrendiposunt. exemplum proponatur.
Subrensa circumferentiae suberipla
liEdem quae prius luppoliris.
dEX quadraco. quactaco in B.
LchecE eriplex:
Subcensa circumferentix subquincupla.
Subrenta circumterenria tenes  e scum circulum subquincupla
Babeenla Ceuterencix compolix ex circumterentia lubquintupla, de dupla
ubqututuplacocusclrculi.
Quod