A treatise of algebra, in three parts. Containing

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. I. The equation of the sper Ola,hen iis ordinates PWare parasse to an asymptote does no come unde the generat quation os last articla CF and Lae the vi mputes

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hesides, bilino both of them, the locus os huequation mali' ait hyperbola, ne of hoseaomptotes thalli parallel to ror a accordingas it is a sextat is antistini qua-

inias the coeficient oi x is a fratre, quia, oris than thesiua re os hal the comessicient os a rithe locus hal be an si se parabola, or diger- bola. 4 27, 9, 3. Iri Oh cas thereiore the ludis os the qua tion is si orie unis emon.

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Maa. Thes may aliae demonstrate more direm sto the consideratio of the generiaequatio of the lines of the seconcorde in

Meti For it is obvious that, is , 5. Pari II. the semia tris of that Mnera equation may beextermurared by assuminia a F - , will be transsirines into

ψhicli, by transposing the Iast term is, Let

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o negative. That is, accordinias, is perier, qua in or les than But a the coelii cient oss; rom hicli it appears that thelocus is an Alus, parabola, o hyperbesa, ac cordinias the coemcient of x is greater, quatio, o than me quare of halsili coefficient

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Henee likewise, fili ter x he wanting, and the term v not antire, then the term

6 34. Theclines of the econcorder have omemnera properties hich may be demonstrates sto the consideration of the genera equison representing them. The generat quationis Deti is exterminating the seconestem an be transserinta into the equation, From,hicli, have, Iis' 4e ob here the two values os mare almus eques, and have contrar signs se that se line DF, n, whicli the abscisses are taken, must bilech theordinates, an consequently is a diameter of the coni section. A , a this has been demonstrate generalty in an siluationi thelines PM, it sollam stat is an paralleis, as

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, o b draK meetinia coni section there is a lin DF,hic can bisec est these parallela ista consequently is an tWo paralleis,Mm, Mm, are bisecte in G and the line Grtha bisect these two, ill hi sed ali the therlines parallel to them, terminate by the curve. Whicli is a genera properi os an ille conic

There is one case hic must be excepted, When mi parallel tot an asymptote, hecause in that caleri meet With the conte section onlytione poliat.

yas In the genera equatio Asini, i mu

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' Let the wo Oint C and Si sion, and the straight lineo in the sanae plane. et the

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give angies FCO, SH, revolveramut thepoinis C an Mas potes, and et the intersectio of the sides CF, Κ, e carried along the strato line AP, and the intersectio a thesides CO, H, wil describe a line of the jecond

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cordinit, at has Men alaeady monstrared. 6 37. A the anoesico, SH revolve, ut the potes C andra, i the angle QS hecomes eques in the supplement of theseiive angies is seu right ones then in angi CP must vanisti, iliat is in lines Coeandriremust be- come parallel and the intersectionis must mort an infinite distance. An the lines Coand SHiecome, in that case, parallata one os In orderito det tineas his may be, describaon CS amare os a circle stat can have inscribedincit an angi equa to the supplement os the