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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 118r, page id 00068196:0233
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aralogismus bi jac Gregorii cum Circulum
e
algebraice quadrari posse negat, in eo
consisti
ostendit haberi quadraturam Circuli
Exipseos
per vel b
perbolae, aut sectoris un se
libolae
a c d sint polygona inscripta eidam sectori facta
visectione continua, et hrchordarum, et b,d, 5, etcpolygona
eade repondentia eidem go polygona circumscripta, ulti.
n term quae secies tan convergens tandem terminatur in circulum,
ultimum in ultimo ergo et co coincidunt ubi inscriptum
et circumscriptum seu Z etco coincidunt. His positis ostendit,
si quantitas habeatur eodem modo composita ex a et b, quo ex C et d
Datum iti terminationem seriei. seu Z veloco sit enim quantitas
illa Su sint aaeguatio quam ingrediantur a, b, s. in qua si C
vel y a et N eodem modo, ubi monendo Z=eo habebitur retatio
inter , ut N adeoque habebitur Z quaeritu. ostendit autem
non dam cum autem sit C= Vab
imul
= 2ab: a + Vab. ostendit
(tolerabiliter) non daritquantitate compositam exte vab et ac
afat
ut ex a, et b Nerum hinc non sequitur quantitatea
ime
algebraicam vel etiam ratio nalem darii, edde
modo compositam ex a et b; quo ex duo duoeu
alteris; quod ut demonstrem dico revera quantitarem
unitatem esse quantitatem eodem modo compositam
quod si etsi modus componendi o non sit alsebrareus
Nam Z Z: C0 = 1 Ergo X: y similiter 1. porro
C:co eodem modo componitur ex c: d, quo X: y ex a: b
ergo 1 eodem modo conitu componitur ex a: b, quo ex c.d
quod era demous ruud effiiendum Dat
eatur emo quantitas cognitas cognita
eodem modo composita ex a et b
quo ex c et d
Quod erat faci inveniendum