Elements of Analytic Geometry
Elements of Analytic Geometry
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In our eReader you can find the full English version of the book. Read Elements of Analytic Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elements of Analytic Geometry
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10. Show that the perpendiculars erected at the middle points of the sides of the triangle of Ex. 13, Art. 35, meet in a point.
Examples on the intersection of curves are reserved until the student is familiar with the equations of the curves ; but he will observe that the process is the same, whatever the degree of the equations or the system of reference : to find the intersec- tions of any lines, combine their equations.
37. Lines through the intersection of loci.
Let (1 ) Ax + By + C = 0, (...2) A'x + B'y + C = 0, be the equations of any two straight lines, aud 7i any arbitrary con- stant ; tlieu is (3) Ax + By + C + k {A'x -j- B'y + C') = the equation of a straight line through their intersection. For the values of x and y which satisfy (1) aud (2), evidently satisfy (3) also, hence (3) passes through the poiut of intersection of (1) and (2). Moreover (3) is of the first degree, hence the equation of a straight line.
Note. This reasoning is entirely independent of the form and the degree of the equations.
What to read after Elements of Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Hardy Arthur Sherburne to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
10. Show that the perpendiculars erected at the middle points of the sides of the triangle of Ex. 13, Art. 35, meet in a point.
Examples on the intersection of curves are reserved until the student is familiar with the equations of the curves ; but he will observe that the process is the same, whatever the degree of the equations or the system of reference : to find the intersec- tions of any lines, combine their equations.
37. Lines through the intersection of loci.
Let (1 ) Ax + By + C = 0, (...2) A'x + B'y + C = 0, be the equations of any two straight lines, aud 7i any arbitrary con- stant ; tlieu is (3) Ax + By + C + k {A'x -j- B'y + C') = the equation of a straight line through their intersection. For the values of x and y which satisfy (1) aud (2), evidently satisfy (3) also, hence (3) passes through the poiut of intersection of (1) and (2). Moreover (3) is of the first degree, hence the equation of a straight line.
Note. This reasoning is entirely independent of the form and the degree of the equations.
What to read after Elements of Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Hardy Arthur Sherburne to read onlineMoreLess
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