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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
# Folio 420, page id 851708439:0444
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A L C F B _ A.
Cap. LICit HI.
20
Duo autem calis repettatur nus (unde alii derirentur) plures ostendi metho.
dos, locis cicaris. Sed, quam praetero, acque hie ML LAtAaISHIA PLOPOL LL LIIIIH
bus inguisitionibus imitandum, cs ea D. Vice Comiris Bronneker; quam Cumma-
nim exhibeo (prouc eam ab illo acceperam) ad Finem Fpist. 27. et tuliuis expono,
Epist. 19.
Mechodus ea, calis clt.
Esto, verbi gratia, propositus non quadratus n = 13, _C quacratuIS quaeltuIS aa.
Ergonaa F F = F3 a a F T, est numerus quadratus integer: Cujus Radix, ma-
nitelto, major est quam 3 an sed minor quam 4 a. F. Ho 3 a = v.
Tum cA 23aa F + =9aa + 6 ab + bb.
HIOc est 4aa F L - 6ab = bb
Ergo
Elto
Hoc ct 206+406 + F = 3bb
2D = a = b
a = b + 6. FrSO
4bb + 8bc + 406 + L = 6b
Sad. + 6aC+ 566+ 1 = 4dd. F 4aC sut)
260 f26d F 466 f + = 3c5+
30c  1 = 4c d = 3 a d
2dc = 3ec = X = 4 d d
a
2e0 + 2Cf + 3eC = L = 4 ee
ec + F = 6cf + 4ff
+2 45
3655 + 2258 + 88 + 1 = 36f5 +C
88
ErgO
sh = 88 + 5= 465 105b + 4Bb)
358 + c=25b + 4 hB
s
E
3hB + 6b1 + 397 1 = 2. BB. F 263 + 4. 11)
461 + 355 + 2 = 3bb
Et similicer procedendum erit pro quovis alio propotico numero non. quadrato.
Si Mechodi deseriprio haec videatur nimis brevis quam ut tacile incelligatur; sic
plenius explicetur.
Duoniam n = 23 esL RUETUIS PTOPOLtIS non. quadratus, qui in a a (quadracum.
quaelicm) mulciplicatus, atumpro 2, taciat, nd d F l- L5l d F L HUIMCrIIM
quadracum in incegris: Manitectum est (primo incuitu) quod quadracus hic mi-
nOr.