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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 427, page id 851708439:0451
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CaP. ACIX.
L C.
C AL P. XCIX.
Fadem porro continuata.
Ropolitio Capitis praecedentis haec eAt; P. rposito quovis numero non quadrato
(in inteeris,) uEn; sunt (in inteeris) quadrati numero infiniti, ut a a:
qui si mulcipticentur per expositum non quadratum, e productus auecatur
Onitate; fiet numerus quadratus: Puta n a a = T = IV. PheOrema PrOPONICUE
demonstrandum; et Problema (quomodo reperiantur illi Ouadrati pro, expolico
quoris Non. quacrato) solvendum.
Id aurem huc ulque consideratum est Capire praecedente. Nimirum,
Hoc, saltem in numeris tractis, univertaliter rerum esse, (tales quadratos haberi
Polle,) quicunque sic numerus propotitus, Guadracis aut Non quadrarus; Inre.
ser aut Fractus: Nec opus esse ut limitetur ad Non- quadratoS
In Inccoris aucom (prout Problema post expoticum est) id fieri non polse; Hist
Dro expolico Non quacrato.
Ouo calu autem Onus aliquis Ouacratus ralis haberi poller; rales innumeros, leu
numero intinicos, haberi polle: _, Quomodo reperiantur.
Tiem; Suxpolico quod in Inceoris unus hujusmodi Ouadratus sc possibilis; Me.
chodus ostenditur, Dua certo possit talis inveniri; et, consequenter, tales innu-
meri, certo ordine.
Id aurem ultra considerandum reltat; Num praeseripta Methodus talem semper
sic exhibitura; an tieri poltic (pront in quarenda maxima communi mentura mas-
nicudinum incommensurabilium fieri necesse est) uc aliquando excursura SIEIM
intinitum.
Hloc ego primum, analyrica inreltigatione, inquiram, humtieri posic: de post,
Tyncherice, demonstrabo, sic _le.
IN V F S F FG A FFO.
LELI3CILCIISI
Sisic n a a.= L, ( PrOUE SuxpOnituT) Ouadratus in Incesris: cum (radix ejus)
Y: naa = 2: exic numerus Inceger. Idemque major quam a V nn Sed MinOF quam
avn. F. Nam quadracus prioris estnaa; posteriorisna a f F +
4naa
Ex quoniam numeri a, n, sunc (per constructionem) Incegri: exic (disteren.
ria limitum d 2av 1
aset sriti
E consequentes, V: n a a = T: erit Intesex proxime major quam (Surdus)
2aNN
Esto m numerus Inteser proxime major quam Vn;
hujusque ad illum complementum p. = m = V n = +
Adeogue ipsius a Vn complementum ad am exie
ap = am = a V V.
Estos numerus inteser proxime major quam (Surdus)
2V n.
Ec quoniam ax (complemencum surdi ad am) po-
cest elte major quam L; (quamris enim p sit minor
quam x, potest ap eodem major elle;) Fso 2 inte.
Ser proxime minor quam a p. Dui iaque; ab eo demptus, relinquer ipsius a V n
complemencum ad I(inceorum co proxime majorem) ap 2 = Y arn zarn
Ponamus r - Adeoque-=
2aYn = ap - 2. Lb4t 1b= 1. 
TAh 2
deoque