By William F. Osgood
The thing of an straightforward university path in Analytic Geometry is twofold: it really is to acquaint the scholar with new and engaging and critical geometrical fabric, and to supply him with strong instruments for the learn, not just of geometry and natural arithmetic, yet in no much less degree of physics within the broadest experience of the time period, together with engineering. to achieve this item, the geometrical fabric could be awarded within the easiest and such a lot concrete shape, with emphasis at the geometrical content material, and illustrated, each time attainable, by means of its relation to physics. This precept has been saw through the e-book. hence, in treating the ellipse, the equipment really utilized in the drafting room for drawing an ellipse from the knowledge quite often met in descriptive geometry are given a number one position. the concept that the tangent makes equivalent angles with the focal radii is proved routinely: a rope which passes via a pulley has its ends tied on the foci and is drawn taut via a line fixed to the pulley. in addition, the that means of foci in optics and acoustics is cleariy set forth. A achieve, there's a bankruptcy at the deformations of an elastic airplane lower than pressure, with symptoms as to the third-dimensional case (pure pressure, etc.). The equipment of analytic geometry, even of their least difficult kinds, make critical calls for at the scholars skill to understand the reasoning of upper arithmetic. for that reason, in offering them for the 1st time, simply algebraic problems, similar to are attributable to literal coefficients and lengthy formal computations, will be avoided.
(Typographical mistakes above are as a result of OCR software program and do not take place within the book.)
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