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The Analyst.
37
XXIV. For the fuller illuſtration of this Point, I ſhall conſider it in another light, and proceeding in finite Quantities to the Concluſion, I ſhall only then make uſe
of one Infiniteſimal. Suppoſe the ſtraight Line MQ cuts the Curve AT in the Points R and S. Suppoſe LR a Tangent at the Point R, AN the Abſciſſe, NR and OS Ordinates. Let AN be produced to O, and RP be drawn parallel to NO. Suppofe AN = x, NR = y, NO = v, PS = z, the ſubſecant MN = S, Let the Equation y = xx expreſs the nature of the Curve: and ſuppoſing y and x increaſed by their finite Increments, we get y + z = xx + 2xv + vv: whence the former
D 3
Equa-