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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
# Folio 42, page id 826603459:0488
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IDEDIOATIO
quatio ad regulam primam; Eproprer quadratum Cemistis cer-
mini absoluri, majus C’ubo coefticiencis termini medii, nempe
72X72 = 5184∞ 729 in D x 9x9., Hujus ancem aequa-
cionis, est radix unica possibilis affirmarira; nempe 7 = 8
deorlum (uclupea octensum eAt;) reliquae dux impossibiles.
Ouod argumento est rectam. c B non nili in uno puncto expo-
liEx curra Occurrere. Ouamris enim verum sic quod recta co B
occurrae etiam in B, curra AB, non camen illud ad praelens
negorium omnino spectar: quipec haec a quario non spectat cur-
ram aAB, sed curram aAa, uc lupra dictum eAt. Aeque idem in-
celligendum eric de puncto h, iilque omnibus quibus incerleca
tur BA cciam, ulera vercicem ex alcera parce Turlum continuaea.
Pari modo, E potira elet aequatio r3  27 r = L 154. nise
quod illic radix qua unica cst possibilis, eec negacira, 2de09:
Turlum lomenda: De conreniret haec aequacio rectae per R ductas
AnEmPC AK, Eire A C Curlum, DOnacur 5 =3.
acque hoc continsit quoties h, vel AC (tive lurtum sive deo
Orlum) major est quam 2  AF. HOC eA, quocies e vel cA
minus quam o, vel plus quam 4d: Ouippehillud, cric C, lu-
Pra F; Ehoc, eric intra e.
Denique; E Donacurxquatio ro = 27r = L 54. (ade093
B = = 2.) perinde cst ad veramris eegulam exisatur; (quia
quadracum semissis cermini absoluci, equarur cubo criencis
Coetticiencis, 27 X27 =-9 F 9X9 = 729.) Si ad certiam exj.
Bacur; Ccripeo circulo cujus radius 3 (= V 23 = V9,) inscri
bacur recta quae (Ic 6 (= 2+;) haec aurem cum (c diameter,
quippe 6 = 3 + 3) dirimet cicculum in duos Cemicir-
culos; utriulvis aurem Cemiperipherix crienei subcendic re-
cta radio aequalis; adeoque cum A = 3, cum F = 3; icem
L (n A + B) 6. HOC eAt, B r2 = 27r = FG4, (pOlICO
C, in _,) radix affirmacira t6 deorlum lumenda; de negatira
in 3, n 3. (lumendae Curlum,) quae propcer aequalicacem
Cuam coincidune, adeoquepro duabus currae incerlectionibus
indicane unum contactum, nempe a. Si vero (C 1 2 = 27r L
543 (POCItonempe Gin, P,) radicum maxima 6 eric ne-
eacira, Cursum Cumenda; _ dux minores 33 3, aftirmacirae, lu-
mendx deorlum, ec (propcer aequalitarem, adeoque coinci-
denciam) indicabune puncum concactus, a.
Cinventis aurem omnibus radicibus r; (i illis sxillarim aua
Feratur