A treatise of algebra, in three parts. Containing

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these

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PM must then e measu redis a scale hereth parameter, o 2AB, is unit. Or, Di bemore convenient, the parameter a be suppostato express o Ioo, or an other number,

here the parameter i IO, Oo, Sc. o that other number.

6 o. hen the circle meet the parabola in one potntini besides the vertex the equatio has only one real root, and the the two imaginary. Thus, i the equatio has in or D salison hea messide os B ac does, the circle canmeet the parabola in Wo minis onin hereos is one and there re the equatio must have tW imaginas Oolsa a Me dentonstrate else-Where. Is the circle ouc the a Mia, thenino roots of the equation are equat.1tas also obvious, that the equatio must necessarily have Me rea mota ecause, since thecircle meet the parabola in the vel lexin, it mustmeet it in on otherioint, at leas , esides A. y Instead os maliing the circle pas throughthe vertex A, ou nia supposiecit totas throughsem other ivei potnt in the parabola, and that intersectioniseinisium, the quadratis fouod sor determining the intersections in Y a . VM reduce tora cinci t

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comes

here e in them terminas a contrar sign ovilia it has in the third, andida contrar inito vilia it has in the ourth.

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structio the mora os a complete cubic equationina be seundi an parabola whaisbeveri 6 49. It is eas in se fio 8 43. - to

coniti uelit the root of a hi quadratica an parabola aster the secon term is ahen Way.

But the root of aliquadrati may be determine is an petu abolaoni me cannot belli ordinate on the axis, ut may be qualto the perpendicular on a line parallel to the axis, meeting the parabola in F CD in H, and PM in L. Deet FG be an ordinate to the axis in G, and the rest remaining a besore, lat FL ' PLαy, the

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vit ita is a complete uadratic equation Aiati comparing with it in equison

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iis locus an elli Then is substitutin sin

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deduce his construction.