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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 444, page id 845634801:0450
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=450
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# Lines: 41 recognised, mean confidence 0.89
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444 NLVN LAE EN ADY ER. N OVA CFCL, SEV, ANTIHEAEKPZ.
Secundum.
Si Fuerinceres magnicudines inaequales, quarum media sumpea vicelies
de quater, et ad dica minima sexies sumpexe, ean dem magnicudinem com-
Donat quam minima sumpra vicelies e quater, et addica maximae lexies
sumpexe: differentia inter quadruplum medix ee criplum minimae exie
maxima aequalis.
Sic enimminima B, media D, maxima A. Ergo ex hyporhesi B6, pluSD 24. X9u2
bitur A6 pluS B 24. Elrrinque auFeratuE B 24. Isitur D24 minus B 18 xquabitur A
Ex omnibus per sex dirilis, D 4 minus B3 aequabicur A. Ouodipsum est quod enuit
CiaEUE.
AN ATTOAETKYON OESDPHMA.
Sune rres inaquales figurx planae de inter se commensurabiles; mini-
ma, legmentum hexasoni; media, quadrans criansuli hexagoni; maximan
complementum securiclae hexagoni.
Pormir inaequalitas, de inaequalicaris gradus demonstrari; at symmetriam alymmetrian
venemo demonstraveric, quin criangulum hexagoni aliud. ve rectilineum circulo p
mum compatavetit. Fa vero comparatio adhuc neseicur, cize Pisuris est, iy eo decorys.
vasst netra.
X E Y A O H O P F Z It A.
Teaque qualium quadrans crianguli hexagoni erit parcium quinque, la
lium scomentum ese quatuor necesse eAt.
25 dorod AEI5.
Sicenim tegmentum hexagoni B, quadeans crianguli hexagoni D, complemencum le
curiclae 2. Ouoniam igitur eres sune inaequalesmagnicudines, acque harum B minima,
media, Z maxima, et se habent incer se ve numerus ad numerum. P.Ao D parcium quila
que, calium B exierrium aur quaruor, de nihil praeterea. Sic aurem, (ed tieri posIE, P.a
cium irium; exprimo igicur de secundo Lemmate erie J. undecim. Iraque complemet
cum constabir duobus legmenris ee dodeanre segmenri. ScnluS aUteM FEPUBNAT. QUa
re CM B quaTUOF.
Elenchus aoomozisias.
Posia D magnicudine parcium quinque, porest ostendi D major elle parcibus cribus.
An vero ideo B eric quatuor, concesto etiam co, quod nescicur, habere le B ad ,
numerum ad numerum: Omnino ea conclulio asyllogistica est. Ouid enim (i B stacuu
cur quacuor parcium cum aliqua racionali tcactiuncula. An quaruorcum Cemiste se non
habere ad quiuque, vrnumerum ad numerum, hoc est, ur 9 ad 10, alius quam anoz
Sinos n cirecoperenros negiveric: Sane polira D parrium 11, fic B paulo major 9; L
ropaulominor 17. Secundum limires Acchimedaos. Ex tis aurem duobus id daet
dimanarum reliqua mesexprur naru rd eubador r8 ninas iu ras r Srpecr dm aveias oa
uate.
HEeas YS AVLo CAEH ES.