An Elementary Treatise On Analytic Geometry, Embracing Plane Geometry And An Introduction to Geometry of Three Dimensions
An Elementary Treatise On Analytic Geometry, Embracing Plane Geometry And An Introduction to Geometry of Three Dimensions
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Analytic Geometry, Embracing Plane Geometry And An Introduction to Geometry of Three Dimensions 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 Analytic Geometry, Embracing Plane Geometry And An Introduction to Geometry of Three Dimensions
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133 is «* + #» *y = — j— > which in the present example becomes l 2 4- l 2 1 Digitized by LiOOQ IC EXAMPLES.
211 3. Find the species and situation of the locus & _ 2xy + f — Sx + 16 = 0, and transform and construct a 2 — 4ac = 0; therefore the locus is a parabola.
The transformation is effected by Art. 146.
tan 20 = -— a —c = -co; .-. = 45°.
(1) Fig. 101.
Hence the new axis of x (Ox) is inclined to the old at an angle of 45°.
c' = i(l + l + Vi) = 2 [Art 143, (7)'] ; [here we take the minus valu...e of V& + (a — c) 2 because we squared — 2 to get ¥\ d' = $ (_ 8V2 + 0) = — 4V2 [Art 146, (2)'].
a' = f/g (8) = 4V2 [Art 146, (2)'].
Therefore, turning the axes OX and OY through 45°, (1) becomes fyt - Wtx + Wty + 16 = [Art. 146, (3)], or f — 2 V&z + 2 v% +8 = 0. (2) Now transform to parallel axes, OV and 0'y\ From (5) and (6) of Art. 146, we have y' = - V2, a/ = |V2, which in (4) of Art. 146 gives %
What to read after An Elementary Treatise On Analytic Geometry, Embracing Plane Geometry And An Introduction to Geometry of Three Dimensions?
You can find similar books in the "Read Also" column, or choose other free books by Edward a Edward Albert Bowser to read online
To quickly assess the difficulty of the text, read a short excerpt:
133 is «* + #» *y = — j— > which in the present example becomes l 2 4- l 2 1 Digitized by LiOOQ IC EXAMPLES.
211 3. Find the species and situation of the locus & _ 2xy + f — Sx + 16 = 0, and transform and construct a 2 — 4ac = 0; therefore the locus is a parabola.
The transformation is effected by Art. 146.
tan 20 = -— a —c = -co; .-. = 45°.
(1) Fig. 101.
Hence the new axis of x (Ox) is inclined to the old at an angle of 45°.
c' = i(l + l + Vi) = 2 [Art 143, (7)'] ; [here we take the minus valu...e of V& + (a — c) 2 because we squared — 2 to get ¥\ d' = $ (_ 8V2 + 0) = — 4V2 [Art 146, (2)'].
a' = f/g (8) = 4V2 [Art 146, (2)'].
Therefore, turning the axes OX and OY through 45°, (1) becomes fyt - Wtx + Wty + 16 = [Art. 146, (3)], or f — 2 V&z + 2 v% +8 = 0. (2) Now transform to parallel axes, OV and 0'y\ From (5) and (6) of Art. 146, we have y' = - V2, a/ = |V2, which in (4) of Art. 146 gives %
What to read after An Elementary Treatise On Analytic Geometry, Embracing Plane Geometry And An Introduction to Geometry of Three Dimensions?
You can find similar books in the "Read Also" column, or choose other free books by Edward a Edward Albert Bowser to read online
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