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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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806
DM et L L C LU HC
ductus extriberet 52282453927143347857, qui
unitace superat quadracum nuerI 7230660684.
Adeoque 5025068734834899736 (duplum rect.
anguli Cub racieibus 34748337,87230660684)
elEnumerus a primicus qua licus: nempe cujus qua-
dracus 25252316292322095858983939677172
869696 in 433 ductus, extibebic 10933879954
575467506040015854235852578368, qui uni-
cace deticit 2 quadraco numeri 10456490785428
6695753. Ouxlicus itaque quadracus locorum
talcem 38, (numerus latis ingenS,) Polt 15 P0.
Ticiones decegitur, operacione scilicet non nili ad
P concinuata.
Acque hic quidem tixistem pedem; nili quod
5 b f b = a = 347483377. unum acthue aue alterum, mancilta loco, HOcan.
dum relter; non quidem canquam huie negotio
necellarium, sed nocam Fortan non injucundum.
Et primo quidem, quamquam (uc modo dictum est) compendium jam proxime
cradicum de inveniendo a sive a Succencuriato, (Cujus nempe quactratus In n
ductus, unitare quadratm (uDereE,) ejusque ODC, a vero, (cujus quadracus in n
ductus, unitace a quadraro deticiat,) omnino verum sie uluique accommodum:
Ti camen illud placeat neplivere, adeoque opus incepcum cousque continuare do-
nec prodeat a verum; id tacile obrinebitur (line operolo caleulo) propter cal
dem eodem ordine recurrentes aequationes. Exempli gracia. In numero priclem
expotito n = 109 ubi invencis aequacionibus quae conveniune iplIS a, B, C, d, _c.
ulque ad my (ubi habetur 857525 = a, sive a Succecaneum,) exdem ipla aequa-
LTIONES OCCMEPHNE PFO M, n, 0, P, _C. qua priuS PrO 1 b, C, d, c. (li lalcem exci
PIaS X ec y duas ulcimas in quibus lilticur; quas iplas eciam, nili illic siltere pla-
euerie aequationes, iplis L e  contormes elle oporcebit.) Poceric itaque caleu-
Jus, d principio insticucus, ad eas aequaciories inveniendas, stacim siltere, quum
Primum ad iptum L vel m, (unde scilicer a, Cire a Succencuriacum, collisitur,)
verreniatur. Fet qui hoc auxilium placuerir adhibere, pocerit ille sine magno
dispendio etiam compendium jam proxime cradicum negligere.
Alcerum, quod icem nocacum velim, hoc elt; Nempe, uti tractenus tradidimus
Formam inveltioandi quadrari primi radicem, cujus ope quadracorum deinceps
omnium in intinicum radices, juxca seriem jamdudum cradicam, tacillimo nego-
rio extibeantur: Si tamen ee seriem illam neslisere placueric, porerunt de reli-
quorum illorum quadratorum radices eadem arte (led lonsiori parum opere)
obtineri, qua de illa prima, concinuaco seilicet
opere inchoaco donce ad quadrati secundi,
cercii, quarri, _c. racicem perveniatur. Sic,
verbi gracia, Rxpolico uc TuPEA, n =- F3. VBL
verveniatur ad aequarionem hanc, 4 ef f 3s
3e= 2 collesimus superius, poni posse
e = 2f; nempe li Donacur f= 2; (unde e
recrocedendo reliquorum ralores inveltisari
mus, adcoque de iptius a quae radix est qua
draci primi.) AC verO Si pOnamUS = L, erit
C = 2f; adcoque potico e== 2f. e, proceden-
dum erie donce limilis reCurret iIeruM aqua-
20; quod tiet ubi ad h, m, pervenicur, nempe
+Im + 3m = 312 = 2, ubi polito m = 1,
Crit 1 = = 2 m = 2: unde (vecrocedendo) na-
bebitur a = 233640 radix quacrati secundi.
Sin acthue ponamus, non m = L, Sed M = 1.
Cxit I = 2M: adeoque Dotco V = 2 M n pro-
cedendum crie donee recurrat similis aequario,
Puca 4r 5. f 35 = 3r - c; unde, POLIO S- 1
Cric r = 2, e a = 303264540. Sin ponamus
= I, Procedendum uc prius, ad radicem quar-
Verum
2
56694
44.2
385
=6 = 15032212
4C + d =- b = 66490233
26454C
ec
e de deinceps quintis dec. ad Abucum.
e
nC
Ma
11
11
1
11
0
el
lui
cet
p
lu