A treatise of algebra, in three parts. Containing

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so that will determine to yo mand G the co-essicient m eing supposed nom, sincerit is unit, or a divisor os ille comesent of the hishinterm os the equation Oninyo are to Observe, that i the iri term mx of the quadrati divisor is negative, then, in orde to obtain an arithmetiςa progression, o are noto subtrin, ut ad the divisors - - - - ',

these una an disserences Letis e bat term in an progressio that ryes rom be

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the divisors ound in his manner ill succeed, i the proposed quatio has a quadratic divisor. . , 69. suppose, sor exam e the biquadra-6-- x' sa - λαπι is proposed, whicli has no simple divisori then to discoveris it has an quadratic divisoriobe petation lathus:

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hocio

is ino,

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os the proposed equation the two last of hieliare impossibie. The divisors hicli the therarithmetica progression give, do mi suc-

7 iter the fame manne a Rule may bessi vere se finding the cubi divisere, orthos of higher dimensions os an proposed

equation.

Where theirst differences are nothhemselves in arithroetica progression a in the last cale, ut the disserences oscit terius, o the secon dir- serenoes, are ii arithmeticas p*gression the

common

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common disseriace Minian whence, is known. The quantityis is ound in the columnis thesecond differences, and iis alWays tote assumet

seme diviser of the la ter of the proposed equation, as in is of the messicient of the fies term Wheiace est the coessicients of a diviserm P - nx' s, Missi hicli tria is tolemade, a b determined. Is it is a diviser os four dimensions that is required by proceedinii like manner, o Willobtain a series of differences hos secon dif- serenoes are in arithmetica progression. Ditis a diviso os sive dimensions that is requires,

gression hos third differences illie in arithmetica progression an is observire these progressions, o ma discove reses for de termining the messicients of the divisor rei.

The seundation of these Rules eing that, is

an arithmetica progression e, e, assumed the fir differences of their quare mill e in arithmetica progresson, iliose differences belaietae is dari MIsa -- c. Whos common disserenoe is ete And the secon differences of thei cubes, and the third differences of their ourthiOWer arelikeKis in arithmetical progression ascis asilydemonstrared.

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vering the divisors,hEn there are two letters, is ali the term have theriam dimensionc sor,

7 et Besides ille method hi theria explainedfor finding the divisors of lower dimension thalma divide the proposed quation, there are othera that destrue tot considered. The mlowincis applicabie in quations os est serta, though,etiverit oni sora se of sour dimensions.

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In this operationes is unnecessu to many diviseri that emetas the quare motissine iast ter of the proposed equatioii V And, i the proposed quation is iterat, yo needoni try thole divisors of the last term that are

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quadratic divises requiressi comes This divisor nausi e trie When cita. Dat the fame time the forme expression not servin in stat case. B this formula, divisera may bedound wliose second term may be irratio LHo the divisere of higher equations may beseund when the have any ma be understo fio What has Messeid of those of seu dimen-

solis.