This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1874 edition. Excerpt: ...y2 = 4px at the point fa, i/, ) of the carve. An equation of the first degree is frequently called a linear equation. For (Art. 90), _ = z--(6.) represents a right line through two points P2 and P3. If these points are upon the parabola, the equations of condition which must hold are y32 = 4px3, and ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1874 edition. Excerpt: ...y2 = 4px at the point fa, i/, ) of the carve. An equation of the first degree is frequently called a linear equation. For (Art. 90), _ = z--(6.) represents a right line through two points P2 and P3. If these points are upon the parabola, the equations of condition which must hold are y32 = 4px3, and y22=4px2. Subtracting, But Pi =p + Xi;.'. sin2 T =;.. =, Pi sin2 T a form of the linear equation of the parabola of some importance; in which pi is the radius vector of Pu and T the angle between the tangent at Pi and the axis of x. Also since--= tan r; yi & sin T m..'.--=;.. 2 p cos T--y, sin T = 0. 2/! Cost' yl 255. Examples.--Construct the tangents represented by the following equations, with the parabolas to which they are tangent, finding the equations of the parabolas, when yi = 4 (1.) y =- ( +?) Ans.if = 82x. (2.) y = x + S. Ans.f = 8x. (3.) Find the equation of the tangent to the parabola y1 = 16x, when Xi-9. Am. 3y--2x--18. Proposition 3.f 256. Theorem.--The equation V y = mx---also represents a line tangent to the parabola y1 = 4px; in 2p t which m =--= tan 257. Schol. 1.--The locus of the foot of the perpendicular from the focus upon the tangent line is the tangent at the vertex. For, the equation of the tangent may be written my--m2x =p, and the perpendicular to it through the focus, (p, 0), is (Art. 128) my + x =p. Subtract, .. (1 + m1) x = 0.. x = 0, which is the equation of the tangent at the vertex. This enables us to construct a parabola approximately by drawing successive tangents, as in the figure. 258. Schol. 2--The locus of the intersections of tangents perpendicular to each other is the directrix. represents some tangent; in which equation let us replace m by (Art, 123), y = mp represents a second tangent...
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Add this copy of A Treatise on the Principles and Applications of to cart. $16.27, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2023 by Legare Street Press.
Add this copy of A Treatise on the Principles and Applications of to cart. $26.62, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2023 by Legare Street Press.
Add this copy of A Treatise on the Principles and Applications of to cart. $27.44, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2023 by Legare Street Press.
Add this copy of A Treatise on the Principles and Applications of to cart. $39.79, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2023 by Legare Street Press.
