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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 109, page id 851708439:0133
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CaP. LLLII.
IL L C F B R A.
(vropter nullam hic subincellectam ciptram) locum capestet Vnitatum. Adeoque
membrorum luis locis politorum aggresatum 3249 cltradicis 75 Guadratum.
Similiter; pro ejuldem Cubo. Cum (C Ac =
SX 5 X 5 = +25, hoc elt, 50X5OX5O = F25000. Sc.
des ipsis AC = F25, erit LOCUS QULARHIS. EF A gF =
SX5X7 = F75, (hOC est, 5OX5OX 7= 17500,) adeo
que 3 A gF = 525 (hoc cst 52500,) Sedem capesser
Loco tertio. Similiterque AF 9 = 5X7X7 = 245
hoc est5OX 7X7 = 2450.) Adeoque 3 AF9 = 73
Joco secundo; Ft F C = 7X 7 X7 (proprer nullam hic
Tubincellectam ciphram) iplo Onitatum loco. Omni-
ningue sc politorum summa 185293, est radicis 57 Cubus.
Et pariter in aliis poceltatibus.
Hoc iaque in omnibus obserrandum erit, inter sedes Diasonalium (ut A g.
Eq pro quadrato; AC, P. C, pro Cubo; et sic in exteris;) cor reliquenda sunt lo-
ea intermedia, quot sune intermedia in quaque porestare Proportionalia membra,
leu complementa; qua haec intermedia loca capeltant. Hloc elt, in Guadrato,
unus locus intermedius; in Cubo, duo; in Biquadrato, tres; et sic deinceps.
Quodque de Radice ex noris binis dictum est; pariter intellivendum de radice ex
tribus, pluribulre; gradatim procedendo; ut tieri solet in exirahendis Radticibus;
quo haec pocistimum spectant.
Verbi gratia. Pro Radieis 5r209 Ouadrato: Posito primum 5 == A, erit Ag =
25; sed cum sequentibus octo locis racuis;
proxter Tubince llectas ciphras bis quatuor. P0.
Ticoque 7 ==F, 2 A P = 70; Sed cum sequen-
tibus locis racuis septem; propter Cubintet
lectas in A = 5, ciptras quatuOT, e eres in
E = 7. EEFG = 7X7 = 40; Sed cum leX
locis racuis, propter lubintellectas ciphras bis
eres. Dux complent quadratum radicis s
uc prius 3249. Hloc est (propter sex loca ra-
Cua) 3249000000, quadratum radicis 57000.
Deinde; Polito a =57 (cum tribus locis
vacuis) Peu 57... cujus inrentum est qua-
dratum A9 =- 3249. . . ... Sumpioque F = 2
(cum duobus racuis Locis;) FFIt Z A F=
51 71 2] 0) 0) Radix.
25
. .).-
AC
lao.:.l.. l EgF Cnomon.
82 40
22(8
.. 1.. 1 Ag
l.. 12 A F
.. F qSCnomOn.
32 71 841. . 1.. 1
327T6400).. I AG
20296]0. (2 A F
(8T) Fgs Cinomon.
228 cum quinque locis vacuis, (propter sub. 32 72, 86 95 81) Ouadeacum.
intellectas ciphras in 57, tres; d in 2, du-
25:) seu 228... .. EFE g = 2+2 = 4, cum quacuor locis racuis (propter fub.
incellectas eiphras bis duas.) Dux complent quadratum 327184 radicis 572; seu
327284... . Tadicis 572..
Tum propter sequencem ciphram o in radice; nihil hinc mucatum est, praeter
addicas in quadrato duas ciphras 00.
Denique, Polico 5720. =A, cujus quadratum jam inventum cst, Ag =
32758400 (Led cum duobus locis racuis, proprer unum racuum in radice:) Tum-
Pcoque E = 9. Erit Z AP = 102960. (cum uno lOCO vacuO, Propter Ciphiram
in A Tubincellectam:) EtF. G = BF, in unicacum loco; (proprex nullam hic sub.
incellectam Ciphram.) Oua complent 3272 86 96 81, Quactratum radicis 57 209.
Ec similicer in aliis. Nempe, promotio unius loei in Radice, tacie promocio.
nem duorum in quadrato. Singulaque membra tunt uno loco promoriora quam
proxime praecedentia, propter una pauciores Ciptras subince llectas.
Similiter; proejuldem radicis Cubo. Nimirum, Cumpro primum A = 5, (hOC
elt, 50000, proprer lequentia loca quatuor;) Cubus ejus est AC = +25, (cum lo-
eis racuis +2, nempe ter cocidem quoc subincellisuntur in radice ciphra: Seu 50000
X50OOOY50OOO = T25 O00OODDDODOD.) SUMPIOque F. = 7 (hoc est 7000)
Cubus hujus est 7 x 7 X7 = 343 (cum 9 locis vacuis.) Trem 3 AgF = 525 (cum
locis vacuis EF, propter bis quauor subincellectas Ciphras in A A, _ treS In F.)
Et 3 AE 9 = 735 (cum locis racuis L0, PTOPter quacuor Ciphras suhintellectas in
a, et bio ieo in LF.) Dux omnias complemt 185193 (cum 9 locis VaCLIS) prO Cu.
BAF.9
735. CGMOmOn.
343
93
Lunus
bo radicis57.