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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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Hi, P 157OL LC0 M.
A ccla je dis, que si on commence par o, quelque nombre, qu’on mette pour le
Second terme, la Commme d’aurant de Tois le plus srand terme lera tous jours double
des quanricés données; car li pour a, b, c, d; on prend quelque nombres, qu’on
rondra, qui Poyent en progreclion Arichmecique depuis le rer terme o, cela Lucce.
dera tous jours en la melme Porte ainsy qu’il a elté cy derant demonltre.
EPISTOL A XIV.
D. Vicccomitis Bruneker ad D. Zoh. W allis.
DOsEACCCPEASD. Fermarii liceras, quas ad ce nuper cransnisi, quae Problema, pri-
dem propolicum, de Tolis Inceoris exponunt; rem aliquatenus expendens, qua-
dratos quos quarie intiniros (qui in dacum non quadracum ducti adscita unitate
quadcatos conticianc) in hujulmodi lectem video concidere. Nempe
24O: 245+ X53X53, 45 18 XCBC.
SIC 8XO: FX5+X5ZX533X5 262 X9C.
lIC 28X D: 4 X 33 =X 3334 X 33 71355 X (9C.
32 X : 3X 337X3337X331135 X896.
3XO: LX3 FX33X3 15 X 334 X19.
72XG): 2 X X3 FX +3 7X 13 195 X8C.
27X9: 5X5F FX5135X (6.
43XQ: LXF3 ZX F3 +2 X T3 185 X 20.
75X D: 3X5XZX5F3Z XCC.
5XG: 4 X Z7 LX 17 1BX L7393 X eC.
20x9: 2 X 17 +X 27 1BX F7323X(C.
8OxG: FX77 +X27 48X 27393X (76.
6x9: 2 X 9+X9 18Y983,X 9886+ ∞.
24 29: XX9 + x9 32953  93 06 Y _9C.
96x9: 5x97 24 (3c.
Oi Feactionis cujusque numeraior aequat denominatorem tuum dempro, denomi-
naLOTE proxime praecedente; Denominator rero numeratorem aequat cermini proxi
me praecedentis in impropriam tractionem reducti. Copnita rero serie quae ad nu-
merum aliquem non quacracum accinet, habetur inde series quae spectet istius non-
quadrari mulciplum per quemris quadracum; scilicer dividendo seriem inventam
per radicem quacraci mulciplicancis. Primores aurem duo termini cujusque lexiet
reperiendi sunc vi Canonis nostri geteralis ; Nempe, quories D q est aliquo.
ia pars numeri 4Q, (sire D aliquota pars 2 R,) habetur inteser quadratus rem
ablolvens. HToc est, (subslicuendo = = 0, aeleoque = = R, et Bropterea
D = G e N = - i N.) quories = i n = D est aliquota pars numeri  == 2R;
ve) (ductis urisque in cz) quocies a an e= est aliquota pars numeri 2AC. EO ica-
que jam redacta elt quaestio, ut reperiatur quactratus aliquis qui in datum non qua-
dracum ductus, ab alio aliquo quadraro ditterar aliquora parte dupli rectanguli sub
radicibus. Quod inductione commode insticura in reltixari poreric. Eac lunt qua
de hoc nesorio jam occurrunt,
Octot. 22, 2657.
a Colarissime
Amco tuo sdelssimo, atquo
observantissimo,
BROV Al. R F. A.