A treatise of algebra, in three parts. Containing

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ber, theb A the lacus of the quation avem infinite ares Wingonis me sese of A For, is, ecome infinite, hether positive ornegative, ac illis postive, an have illesime sign in euher cases an as econnes infinitet greater than the ther term ba: i, it sollam that in insinues aliam os rates have the sanieram in these cases ,

conI equently the tW iii finite arcs of the curvo

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is acquiredo

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therctore the curve minali si in the tuo a jacent angles QE and Qe, and have M and Axis ita tuo asymptores. 348. et the equatio givente. - κ

then stati ΡΜ and eques, and aieon disserent sides of the abscisse ΑΡ. Is

x, b, then the trio values sis vanisti, cause

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resolve imo a pia rari Mid impis equation, and

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iine

In genera the curves of the superior or-ders include ali the curves of the inferior ordem; and whateve is demonstrate generali of any one order, is also true os the inserior ordere. 'So, sor Xample, an genera propert D theconic sections holds triae of tino traight lines ac vellis of a coni section Particulari that the rectangies of the segments of parallels unde by them, Mitte alwaycto one anotheri a give ratio ' The genera properties of the lines of the thir orde are true of three

straight lines, oeso any one strato line and aconi stoion. And, a the ynera properties of the igher eser of lines descend also toti se os the inferior ordos, A thesi is scarce any

propert of the inferior Orders, ut has an na- log to some propert of the igher orderi ofvi hicli it is ut a particular case or instance.

Andinence, the properties of the inserior orderstea in the discoor of these of the siserior

sto.' have mewedio to iudge os thes ure os a locus fio the consideratio os iis equation. And when a locus icto be described examy, si every value os, o must by the resolutionis equations accordinito the Rules

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the locus. But there re geometrica eos mons bywhicli the mois of equations cante determinedmore commodioust for this purpose And, as by these constructions we describe the loci os theequations se reciprocatly When Atare destri es, the are sese in determining the mota sequationsa both which shallie explainta in thesislowing bapter Then me hali grue an a munt of the in genera an simple mediola o describing these in by the mechanical motion o angies an lines, hose intersections trace the curve; or os constructing them is findin geometricatly an number of their poluta.