An Elementary Treatise On the Calculus With Illustrations From Geometry Mechan

George a George Alexander Gibson

The book An Elementary Treatise On the Calculus With Illustrations From Geometry Mechan was written by author George a George Alexander Gibson Here you can read free online of An Elementary Treatise On the Calculus With Illustrations From Geometry Mechan book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is An Elementary Treatise On the Calculus With Illustrations From Geometry Mechan a good or bad book?

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Show that whatever be the value of m, the straight line y = mx +, / { (a + bm?)/ab } touches the conic ax"- + by 2 = 1.
10. A straight line moves so that (i) the product, (ii) the sum, of the squares of the perpendiculars drawn to it from two fixed points (c, 0), ( c, 0) is constant ; show that in each case the envelope is a central conic.
11. Show that the envelope of the circles described on the central radii of an ellipse as diameters is 12. The envelope of the ellipses (x - a) 2 /a 2 + (y -... /3) 2 //; 2 = 1 when the parameters a, /3 are connected by the equation is the ellipse A' 2 /a 2 + ?/ 2 /& 2 = 4. State the problem in geometrical language.
13. Show that the envelope of the family of straight lines ax sec a by cosec a = a 2 b- is the curve 14. If in Fig. 82 OZ=p, show that the equations of the tangent and normal at P are d'f) x sin > y cos (f> =p (i) ; x cos +y sin (/> = |3hr (ii), and show, from (ii), that ZP = Consider the curve as the envelope of its tangents.
15. With the same notation as in ex.

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