A Mathematical Treatise: Containing a System of Conic-Sections, With the Doctrine of Fluxions and Fluents, Applied to Various Subjects, Viz.; To the ... Radii of Evolution, Refraction, Reflection - Softcover

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Excerpt from A Mathematical Treatise: Containing a System of Conic-Sections, With the Doctrine of Fluxions and Fluents, Applied to Various Subjects, Viz.; To the Finding the Maximums and Minimums of Quantities, Radii of Evolution, Refraction, Reflection

In order to this, I confider a Curve-line to be generated by the motion of a point, urged by two powers acting in two difi'erent Directions, the one parallel to the Abfcifl'es and the other parallel to the Ordinates. I prove from thence, that if this point (when arrived at a given place) did continue to move with the velocity it has there, it would proceed in a right line touching the Curve in that place: From whence I conclude that the Direc'tion of the point in the faid place, is in the Tangent: So that the three Direétions being known in each place, the proportion between the velocities of the urging powers is likewife known.

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