Plane And Solid Analytic Geometry
Plane And Solid Analytic Geometry
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INEQUALITIES 1. Extension of the Method for the Determination of Loci.
If we look back over the locus problems which we have thus far solved, we find that there is invariably but a siiigle essen- tial condition governing the motion of the point tracing the locus. For example, the sum or the difference of two dis- tances or of their squares is required to be constant ; or the slope of one line is given as proportional to that of another. This single condition it is comparatively simple to expres...s analytically and thus to determine the locus.
In a great many problems, however, the motion is governed by not just one, but by two or more essential conditions, in- terdependent on one another. An example of such a problem 't is the following : A triangle ~ has a lixed base AB and its vertex F moves on an indefinite straight line L, parallel to the base. Tind the locus of the point of intersection P of the altitudes.
Here the motion of P is • governed by tico essential conditions ; first, by the motion of V, and secondly, by the fact that P is the point of intersection of the altitudes.
What to read after Plane And Solid Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by William F William Fogg Osgood to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
INEQUALITIES 1. Extension of the Method for the Determination of Loci.
If we look back over the locus problems which we have thus far solved, we find that there is invariably but a siiigle essen- tial condition governing the motion of the point tracing the locus. For example, the sum or the difference of two dis- tances or of their squares is required to be constant ; or the slope of one line is given as proportional to that of another. This single condition it is comparatively simple to expres...s analytically and thus to determine the locus.
In a great many problems, however, the motion is governed by not just one, but by two or more essential conditions, in- terdependent on one another. An example of such a problem 't is the following : A triangle ~ has a lixed base AB and its vertex F moves on an indefinite straight line L, parallel to the base. Tind the locus of the point of intersection P of the altitudes.
Here the motion of P is • governed by tico essential conditions ; first, by the motion of V, and secondly, by the fact that P is the point of intersection of the altitudes.
What to read after Plane And Solid Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by William F William Fogg Osgood to read onlineMoreLess
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