Elements of Analytical Geometry
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In our eReader you can find the full English version of the book. Read Elements of Analytical 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 Analytical Geometry
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To quickly assess the difficulty of the text, read a short excerpt:
For we have CO = OR = CA V% = a V2.
124. If the values * Art. (105), be substituted in equation (1) of the same article, giving to r 8, first the negative and then the positive sign, we ob- tain the two equations y 8 ^ J(2o* - x*) (1), y 8 = ^ (2ax + x*) (2), which are the equations of the ellipse and hyperbola referred to the axis and principal vertex A. See figures of Arts. (106), (107).
125. Let a?', y', and x", y", be the co-ordinates of any two points of the ellipse. These co-ordinates, wh...en substituted for x and y in equation (c), must satisfy it, Art. (23), and . Give the two equations of condition a y 4. JV 2 = a 2 i 2, ay 2 or y' = -(a 8 - *') ...... (1), y" 2 = -(a* - a 8 a 8 Dividing the first by the second, member by member, we have INDETERMINATE (iKOMETRY. 147 y-- a * x'* _ (a -f- x')(a x') whence, we deduce the proportion y' : y" 3 : : (a + x')(a x') : (a -f x")(a - x").
But a + tf = AP, a z' = PB, a + a:" = AP, Therefore a x" = PT>.
N 2" 11 MP 8 : M'P 2 : : AP x PB : AP' x P'B ; that is, the squares of the ordinates of any two points of the ellipse are to each other as the rectangles of the segments into which they divide the transverse axis.
What to read after Elements of Analytical Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Albert E Church to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
For we have CO = OR = CA V% = a V2.
124. If the values * Art. (105), be substituted in equation (1) of the same article, giving to r 8, first the negative and then the positive sign, we ob- tain the two equations y 8 ^ J(2o* - x*) (1), y 8 = ^ (2ax + x*) (2), which are the equations of the ellipse and hyperbola referred to the axis and principal vertex A. See figures of Arts. (106), (107).
125. Let a?', y', and x", y", be the co-ordinates of any two points of the ellipse. These co-ordinates, wh...en substituted for x and y in equation (c), must satisfy it, Art. (23), and . Give the two equations of condition a y 4. JV 2 = a 2 i 2, ay 2 or y' = -(a 8 - *') ...... (1), y" 2 = -(a* - a 8 a 8 Dividing the first by the second, member by member, we have INDETERMINATE (iKOMETRY. 147 y-- a * x'* _ (a -f- x')(a x') whence, we deduce the proportion y' : y" 3 : : (a + x')(a x') : (a -f x")(a - x").
But a + tf = AP, a z' = PB, a + a:" = AP, Therefore a x" = PT>.
N 2" 11 MP 8 : M'P 2 : : AP x PB : AP' x P'B ; that is, the squares of the ordinates of any two points of the ellipse are to each other as the rectangles of the segments into which they divide the transverse axis.
What to read after Elements of Analytical Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Albert E Church to read onlineMoreLess
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