An Elementary Treatise On Analytical Geometry
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On 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 An Elementary Treatise On Analytical Geometry
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To quickly assess the difficulty of the text, read a short excerpt:
y — y" = a {x — x") ; it is required to determine a.
For this purpose, let the tangent be regarded as a secant, and let us determine the co-ordinates of the points of inter- section. These co-ordinates must satisfy the three preceding equations, since the points to which they belong are common to the line and circle. Combining these equations, by sub- tracting the second from the first, we have y^ — y"^ -\' ^^ - — ^"^ — 0, or {y — y") {y + y") + {x -^ x") {x + x") = o.
Putting for y, its value ...y" + « (a; — x") drawn from the equation of the Hne, we get \2ay" + «2 (^ __ ^//) _|_ ^ + x"\ (x — x") = o.
This equation will give the two values of a; corresponding to the two points of intersection. The co-ordinates of one point are obtained by putting s — x" = 0, which, gives X =^ a;", and y — y" ; and those of the second point are made known by the equation 2aij" ■\- a" {x — x") ■\- x ■\- x" = o, when a is given.
If now we suppose the points of intersection to approach each other, the secant line will become a tangent, when those points coincide ; but this supposition makes X = x"y and y = y" ; Chap.
What to read after An Elementary Treatise On Analytical Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Francis H Smith to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
y — y" = a {x — x") ; it is required to determine a.
For this purpose, let the tangent be regarded as a secant, and let us determine the co-ordinates of the points of inter- section. These co-ordinates must satisfy the three preceding equations, since the points to which they belong are common to the line and circle. Combining these equations, by sub- tracting the second from the first, we have y^ — y"^ -\' ^^ - — ^"^ — 0, or {y — y") {y + y") + {x -^ x") {x + x") = o.
Putting for y, its value ...y" + « (a; — x") drawn from the equation of the Hne, we get \2ay" + «2 (^ __ ^//) _|_ ^ + x"\ (x — x") = o.
This equation will give the two values of a; corresponding to the two points of intersection. The co-ordinates of one point are obtained by putting s — x" = 0, which, gives X =^ a;", and y — y" ; and those of the second point are made known by the equation 2aij" ■\- a" {x — x") ■\- x ■\- x" = o, when a is given.
If now we suppose the points of intersection to approach each other, the secant line will become a tangent, when those points coincide ; but this supposition makes X = x"y and y = y" ; Chap.
What to read after An Elementary Treatise On Analytical Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Francis H Smith to read onlineMoreLess
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