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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 356, page id 845634801:0362
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V AR TORYME DE RE BYS NIA FE FM APFCL.
cumfereMiae dari circuli sub A cenerO _CKCIIE CML a GUDKMI. LX demonstraris ab Archi
356
mede propolitionexVI ec.
PROPOSTTTO II.
Invenire quadratum dato circulo dfae.
Ac per primam Archimedis eo niuns uererios erians l eclangulum cujus alcicude
vis prianeur est aequalis ei quoc pran vale in dimidium alcicudinis. Ouod igicur Ho
Cx CeIPEKIIEETO, E LeMTOTAIIEEO CMLMLCM Xequale circulo. Ouare incer Cemidiam
erum circuli. ∞ lineam rectam aequalem semi- circumterencix sumatur media proporcio.
nalis, a qua eftormerur quadrarum. Frir igicur illud circulo aequale.
xoualis elt Berimerro cMc Bats se.camcto, CCuo CHaGuale. Area aurem cuju
P R OPOS FFZO TTI.
illa recta semidiameter invenietat Crculi. Describaruricaque ex postulato circulus. L.1 8
IV
Inscriptas circulo lineas rect.
ita producere, ut producte lin
aequales circumferentiis, quibus
in lexipex subcenduntur.
Circulo sub A cenrro deseripco: it
scribancur primum diameter BL
praecerea quaeliber rectae BC, BF. Op0
Tet rectasBC, BD, BE ita producere, U
producta sne aequales ipsis circumte
renriisBC, BD, BE. FangaEcirculum
rectaFBC, polica FB aequali duploro
tius circumferentix circuli, e delcriba
cur Helix cujus principium (IC B, princ
pium vero convertonis recta BF. EFII
helicem incidane continuatx FB qui
demin C, in (criptX verOBC, BD, BF in
FI, L, K. Cnde AaE BIaequalis Cemi- cit
cumferentiae, et BC aqualis cori circun
Ferentiae circuli. FFHIEL incer B e C
verlus punctum F. Dico lmilicer BCH.
BEK esse equales circum ferenciis BLC
BL F. Er quorquo livex in Ccribenu
cidem circulo e Porrigentur ad hel.
cem. Dico porrectas _ in helicem iII
cidentes fore equales ipsis circumteret
eiis inera quas describuntur. Ecenim et
nacura d definitione heliccn Archime
dearum, est ur circum Ferencia BLD 2C
rix BD. Fr8 lecta b eltaequalis elteumterenrix BL. C. Vigee aurem in reliquisea
potice
Invenire circulum dato quadrato xqualem.
aequalis, ad lacus dari quadrari, ita lematatueter expoluci ad aliam rectam. Fric igicur da
Exponatur circulus quiliber, e is quacETUE. FEEax vElatus quadrati circulo e
PROPOSTTIO
descriprus daro quadrato eric aequalis.
circumterentiam BL. C, ira recta BI ad LCclaM BF. Sed recta BL est aqualis circum tetet
demonttrario.
OpOrE
duma
leced
icer
pieeur
5
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