An Elementary Treatise On Coordinate Geometry of Three Dimensions
An Elementary Treatise On Coordinate 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 Coordinate 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 Coordinate Geometry of Three Dimensions
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To quickly assess the difficulty of the text, read a short excerpt:
- = 0.
Ex. 3. The conicoids ■2z^ - 2>/z - 5zx - Gx>/ + z = 0, 4z^ - 6>/z - \Ozx + Ixj/ + 2z = have four common generators.
(y = 0, z = ; 2 = 0, x=0 ; x=0, ^i/-2z = l ; ?/ = 0, 5. R-22 = l. ) Ex. 4. The conicoids z^ + di/z + 6zx - Zxy - 1 2? = 0, 4j2 - 2?/2 - Azx + 2. Iv/ + 82 = have two conimon generators and touch at all points of these generators.
Ex. 5. Prove that the intersection of tlie coniccnds 22 + 22-. Y + 2=0, y'^-'2ij-x-\=^ is a quartic curve whose equations may be written . V=A*-2, ...v/ = A2+l, 2 = A-1.
Ex. 6. Find the points of intersection of the plane A" -9;/- 42 = and the quartic curve which is common to the parabolic cylinders 22 + 102-y + 26 = 0, /-2j/-, r + 2 = U. Am. Two coincident at (17, 5, -7) ; (2, 2, -4) ; (82, 10, -2). Ex. 7. Prove that the conicoids 3x'2 + 42- - 4//2 - zx - 2xy - 2x + 22 = 0, ^. 2 _ yi _ 8^2 + 7^2 + 1 22.^ - 1 1 xy - 2x + 22 = touch one another at all points of the common generator x=y = z, and that their other common generators lie in the planes 2{x-yf + \Z{x-y){y-z) + \2{y-zf = 0.
What to read after An Elementary Treatise On Coordinate Geometry of Three Dimensions?
You can find similar books in the "Read Also" column, or choose other free books by Robert J T Bell to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
- = 0.
Ex. 3. The conicoids ■2z^ - 2>/z - 5zx - Gx>/ + z = 0, 4z^ - 6>/z - \Ozx + Ixj/ + 2z = have four common generators.
(y = 0, z = ; 2 = 0, x=0 ; x=0, ^i/-2z = l ; ?/ = 0, 5. R-22 = l. ) Ex. 4. The conicoids z^ + di/z + 6zx - Zxy - 1 2? = 0, 4j2 - 2?/2 - Azx + 2. Iv/ + 82 = have two conimon generators and touch at all points of these generators.
Ex. 5. Prove that the intersection of tlie coniccnds 22 + 22-. Y + 2=0, y'^-'2ij-x-\=^ is a quartic curve whose equations may be written . V=A*-2, ...v/ = A2+l, 2 = A-1.
Ex. 6. Find the points of intersection of the plane A" -9;/- 42 = and the quartic curve which is common to the parabolic cylinders 22 + 102-y + 26 = 0, /-2j/-, r + 2 = U. Am. Two coincident at (17, 5, -7) ; (2, 2, -4) ; (82, 10, -2). Ex. 7. Prove that the conicoids 3x'2 + 42- - 4//2 - zx - 2xy - 2x + 22 = 0, ^. 2 _ yi _ 8^2 + 7^2 + 1 22.^ - 1 1 xy - 2x + 22 = touch one another at all points of the common generator x=y = z, and that their other common generators lie in the planes 2{x-yf + \Z{x-y){y-z) + \2{y-zf = 0.
What to read after An Elementary Treatise On Coordinate Geometry of Three Dimensions?
You can find similar books in the "Read Also" column, or choose other free books by Robert J T Bell to read onlineMoreLess
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