An Elementary Treatise On the Calculus With Illustrations From Geometry Mechan
An Elementary Treatise On the Calculus With Illustrations From Geometry Mechan
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On the Calculus With Illustrations From Geometry Mechan 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 the Calculus With Illustrations From Geometry Mechan
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To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after An Elementary Treatise On the Calculus With Illustrations From Geometry Mechan?
You can find similar books in the "Read Also" column, or choose other free books by George a George Alexander Gibson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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
15. With the same notation as in ex.
What to read after An Elementary Treatise On the Calculus With Illustrations From Geometry Mechan?
You can find similar books in the "Read Also" column, or choose other free books by George a George Alexander Gibson to read onlineMoreLess
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