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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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Y OL
U M
Ohde collie
= 17 403 432
26
389
54988
2575
TC
167863
34. 7246C
TT60T6875123
563850903159
e = 1807569584602
4 C = a = 66664 274.35249
a = 2 b + c = 25F40424455100.
Videmus ilaque numerum an radicem quadcari quatiri, notis falcem e4 serixtum,
adeoque s quadratum iplum nocis salcem 27 Seribendum, (numerum facis valtum,)
policionibus nonnisi 22. investixatum. Ouam inreltigationem lacis pro rei na-
cura compendiolam esse vix erie qui difticebitur.
Verum aliud adtue superest compendium, quo non raro etiam hujus laboris
pars quasi dimidia abscindicur. Ope scilicet regulae jamdudum traciex; nempe,
si differentia numeri expositi, in quadratum aliquem ducti, ab alio quovis qua-
draio, sit aliquota pars dupti rectansuli sub quadratorum illorum radicitus; quo-
tiens divisione emereens, erit radix quadrati quaesili. Quod cum continsere ne-
ceste luc, quocies ea ditserencia elt vel F, vel 2; siquando reperiatur quadratus
qui in datum non quacratum ductus, rel alium quadratum unitate aut binario su-
peret, vel etiam binario deticiat, exinde collisi quadratum quasirum cerrum cst.
Hhoc aurem incer operandum, praelercum in longioribus numeris, ubi compendio
maxime opus elt, lapissime occurret.
Exempli GraLA, expOSicO (ut modo) n = +3: quia pOLIIO +, ∞2 L Y = 16a
- 8 a b + b, habetur aequatio, 3b +5 = 4b0 = 302 adeoque 2c = b = c; A
ab initio poticum Fuisser 13 a = F, Prodiitet 3b - + = 430 + 303 adeoque
26 = b; unde exit c = L. b = 2. a == 5. Cujus quadrats in (3 ductus unitate
superabit quadrarum numeri 18, adeoquc 180 (= 2X5 X 18) eAt veruS numerUS a
quaelicus, cujus nempe quadratus in 13 ductus, unicate minor exir quadrato nu-
meri 649.
Eodem modo; expOTito n = 109, ubi operando uE Spra (POTito 209 a f L
= +00 a = 20ab FB) perveniatur ad 16kl + 5 V = 9k - F, ad eoque 3I = P
=2I manitestum li ab initio POnCrCTI 109 a =- T, prodicurum tirisC 16 k l 1. 5 p2
= 0p f2, adeoque k = 2 I unde habetur l = L, _ (retrocedendo) a = 851525
cujus nempe quactratus in 23 ductus unitare superet quactratum, unde candem,
dicto modo, colligerur qualicus a = 25+4042.4455 200 cujus quacratus in 12
ductus unitate a quacrato deficiet. Adeoque qui ad y prius procellerat calculus
Pocerie ad L cerminari.
Sic expolito numero non quadrato 433; potito 433 a f + = 44 7 a - 42 ab. + B
operatione ut praeleribicur peracta prodibii aequatio 8 0 f. T = 38 op f 0 p. 2d
eoque 5 p = 0 = 4 P; Ergo, si poluistem ab inicio 433 a = L, prodiittet 8 0
X = 38 op. f 9 p, adeoque 5 p = 0. et PrOpterCa p = 1, 0 = 5, ec. unde
prodiret a =347483377, cujus nempe quadracus 120744697291324. 129 in 433
11iii3
ductus