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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)
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 O M M E R C L U M
nisi unum seiplum extribicurum Cuscixit, (Je demande un autre ec. 85il re-
spnd qu’en entiers, il n’y a que le seul nombre 243, je vous promets de le desa-
buser en luy en exhibant un autre;) hujulmodi aucem unum nos extribuimus il
teorum, nempe iptum F.
Cux plures non extribeam, Lacto el, non quod ckiltimem alium nullum elle, lea
quia nec ipse plures poltular, nec exo rem ipsam cat Cn judico (nam cut b0-
nOd) ut Tolicica rideatur nICaaCOHC AIBMa; HCCMM IIL de Ie HCFOEI LC TOTA TUnI
Anelia cum Gallia Celtica  Beleica, (quos simul omnes nominatim prorocat,)
SC TOcOS ConvertanL. NOM c Maso moen e u  late recu)
quam li ego pari ostentatione, extribicis duobus numeris quadracis, (16 ∞ 25,)
qui omnibus lui parcibus aliquocis addici Catlem ea ma (10114
= 25 + 5 f 2,) iltiusmodi duos alios quadratos extribendos, pere-
rem. Cui Colvendo accingar se, si velic, Fermatius; vel, s malic, neglisat: non
enim eso inquilicionem hanc canci puco, uc vel illum exinde periiorem elle juct.
cavero li tolveries vel secus li minus.
Daro quovis numero non quadrato dantur infiniti quadrati, qui in datam nu-
merum ducti, adseita unitate conficiant quadratum. Pxemplum: datur 3
numerus non quadratus, ille ductus in quadratum 2, adscita unitate consicit 4
qui est quadratus; item idem 3 ductus in quadratum 26, adscira unitate, facit
4, qui est quadratus: 8 10c0 = 8 26, possunt alii insinici quactrati idem prae
stances inveniri. Sed Canonem seneralem, dato quovis numero non quadrato, in
quirimus.
Flujulinodi Canonem hume adhibuit D. Vicccomes Brouneker, demonstratione
sua tirmacum. Sic N, numerus dacus quilibet, (quactrats, rel non. quadraLS;
integer vel Fractus.)
O alius quilibet quactratus, (interer aut Fractus,) cujus radix R.
D =- Q0 N; duorum , N, dilterencia, Puta O = N, vel N - 9. CanON.
Est
d9
conticiet NX
5) numerus quacracus, qui in N ductus, adseica unitate,
F F. =
a2B. + D9, numerum quadruum Num 2C+ Dy
+QN + Q4 = 2ON + N9 99 + 2ON F N9 O F N C F N
29 = 2ON F N9 99 = 2ON + N9 On N Qn N
Alium icem de meo libuit adjicere; qui quoad modum procestus, sic paulo actue
s; quond rem iptam, idem cum eo qui pracellic; demonttrucione pariler
Frmatum.
Sit N. NVumerus datus quilibet.
Canon. EIC
ciet NX
Ma
A, Duilibet ad arbitrium assumptus. Per quem
Q Duadratus quilibet dividatur; licque
M, Divisionis istius quotiens. A) O (M.
P, Numerus quilibet.
D, Disserencia duorum  A IPN.
AR
numerus quacratus, qui in N ductus, adseita unitace, conti.
MAN + D4
Ma
numerum quactracum. Nat
nan +DC
Alterum Problema sie expesitum est.
16P
19= =M A N + F419.
N9
e
10P9 4 = 2Bl AH + P94G
26Pq NQF EM AN +. P9NG
Mq
26P9 214
A + PY
A n PF
+22
Florum
qu
nem
quiai
nolI
qua
1l
1
e