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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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LCa210.
Similiter li ad eandem regulam exisatur aequario r3
Adeoque recta illa hure crreulo non lepibut.
Verum si ad eandem regulam exigat aequatio, 13 = 27 r = = +54: res Ra-
eim ad impossibile dereniet: Ouippe 3) 27 (9 ==Rq, adeoque v0=
AIque 0) 154 (173 = C. AC circulo cujus Radius elt 3, non pocerit inseribi
Tubcenta 273, cum haec sit duobus radiis, hoc et diametro, mmajor.
+ 206; om.
mino idem obtinget. GuipDe 9) 296 (325 = C, major ellet quam duplum R =3.
29
5) 27 (0 = R4.
subtensae impossibiles.
Ouid altem: num aequationes has (ee ejusmodi mille alias) omnino impolli.
Biles dicemus. Nullo modo. Haber etenim illa racicem r = + 7: haec, radicem
r = =8; Ormodo oltentum elt, easdem ad Regulam primam exisendo.
FF quidem aequationes omnes hujusce Formae, quae ad regulam primam exami
natae radicem realem habene (vel actirmatiram, vel falcem negatiram,) illa ad
hanc regulam li exisancur, ad impossibile nos deducunt; (hoc est, illa omnes in
quibus quadratum semillis quancicaris absoluia, majus est cubo crientis coefticien
eis termini medii:) Contra vero quae videbaneur illic impossibiles, (nempe ubi
quadratum semissis quanticaris absoluex minus est cubo erientis coetheientis, ra
dices hie habebune reales. Nec ulla interim aeguatio utrobique extribebie tadices
reales, nili illa Pola ubi quadracum lemittis termini absoluri, aequatur cubo crien-
eis coesticientis. Oualis clF 13
illic 9XOXO =
27 r = = 54; IICM r3 = T2Y = = = 76. (quipDe
27; hic 4 X 4 24 = 64 = 8X 8.) alixque similes.
Cujus quidem ratio est, quia coetticiens medii cermini in prima resula LuPBOnITuE
3 Ai. (iriplum rectansuli duarum quancitatum A, F;) in secunda vero, (nOn
3 Ain Led 3 R4 hoc elt) A9 F A. F F. 9 (nam, in circulo, 3Rg = Fg = A9
F A1. F F. G quodnos alibi demonstrarimus, elque cognitu non inucils:) adeo.
que quocies concinsit aequales inricem esté A, L, (quodrunc erenit quando di-
etum Ouadratum dicto Cubo aquatur, nec alias unquam,) perinde erit sive dica-
cur coetticiens 3 A, Sire A g. L A: L F 9; adeoqne perinde erit ad utram CXISa-
cur reculam aequatio illa; Secus aurem, ubi nOn aquantUE. Atque haec quidem
ucut disna tine quae tulius explicentur; non camen id crit hujusloci; cum videam
me jam Cacis ne dicam nimium) prolixum ce.
Ac quortum, inquies, cendun haec omnia. Num uc Analycicen Fallacem olten.
dam: (ut quae nec catus impoltibiles deregat, ex polsibiles interim canquam impol-
sibiles perhibeat.) Ntullomodo: Sed, caure tractandam; ne nos ipsos decipiamus
dum ea quali inde cradira repuremus quae non sunt; es pro determinatis habea.
mus qux Analysis in ambisuo relinquit, ee indeterminata.
Aequid, inquies, de Aiquatione nostra dicendum est . aur quomodo solvenda
Tunt ilta crarnoparn .
Dicam breri. Nempe rexanda adhuc est aegnatio illa, quae nos rexavic tracte.
nus; uc tandem quid cerri prodat. Ouippe LIIe ONInO NOn PaTO PatituX A.
quacio Analytiea, acque Prorens Hlomerieus, (OdyfL. 5.)
ripcor cercos vnemeris
Adavaros TIpcotC soios es TE datel ans
Oru cu mumeris lic, veriaisan nec plane tidem tallat; Tuas camen tabet in sidiuas,
=nogor deiolo pieorros,
5)296 (323 =C.
9) 254 179=C.
Traons Berdia dist.
Formidabiles astuutias,
Onodta 301O ZECSY7OS
nec nisi lcus lalidem prella verum latebicur. Comprimendus uaque elt LLOles,
 prenlandus torcius, ne clabatus.