A treatise of algebra, in three parts. Containing

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lines, and tiress istos mora. Thei intersections

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ursections Mith ae stra in sine can never e tam i mo, is , 7 The curves, hos equations are of tbre dimensions for the Ibiscorder of lines, orseois hisco curves and thei intersections With astrato sine in ne aer excred -Three. And, aster the fame manner, in curves are determine that elon to the heber orders, o in-fnity. . Some curves, is the were completet described, could ut a straight Iine in an infinite number of Potnisu ut these elon to nomo the videre Me have montiones thenare notgeometrical or algebraic curves, A the relation belwix their ordinates an abscisses cannot be expresseda a finite equatio involving onlyordinates an abscisses illi determine quanti

ties. . , .

1ἀ A the more os an equatio be me impossibi alWays in patrs, o the intersections

of the curve anxit ordinatelwmul vanisti in

. . .

os cynta di N. Is PM stili move on parallel o iiseis: the potnis os intersection ut beronis

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limit.

Whereas, in thes umes, se dimension aremen numbers, a the roms of thei equations may become ali impossibie, it sollows that the figure of the curve may be like a circle oris I

that

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conjugatum'

Ic in the quation, I be supposta, o, thenthe more os the equation by whic His dete

passe throtio a punctu m duplex in the curve 'Wheii is suppost iis, is one of the values

os x vanish, the curve, in that case, passes through A.' IDtW vanish, thenisister AE touches the curve in As oti in is apoctum As a punctum duplex is determined rom theequalit os imo roo is soci a punctis a triplex determined froin the equality of three roqia '

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the Zaxo ab hec Onae, an consequently Μandam hecome the greater.

Pinandi vanish and the curve there meets

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negative, , --ax ecomes m inary, and the two values os a Gome imaginary thatis, b ondi there Me no ordinates that meet the curve, an consequently on stat fide, the curve is limite in B.

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sio A TREA τε sa, Paxet III. have determined his locus is Miro the comsideration os ita equation. 6 14. et it e require to describe the linethat is the locus of this quation, b

Here, it is plain the ordinate inean meetuae curve in ne polat oesy, there Mini tone value os a correspondite to eata value os e.

Ista be supposed greater than e then, ill --πbecome negative, and the ordinaxe Williecomenegative

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figure fritie scas e have been consaqering agrem,it the figure of the hyperbola.

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os a vanisti cause, in that case, sequently, i A be ahen, b, the curve Willias throush D, and therea ch the ordia

nate.

willaecome imaginar , so that no par of the curve is found beron D.