This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1886 Excerpt: ...in this line we take points P, Pu at the same distance OP = p from O; then P is the point (p, Jir) or (--p, fir) or (--p, --fir), Pi is the point (p, or--p, %tt) or ( p, --fir), etc. Fig. 41.. Fig. 42. 92. To find the polar equation of the circle. (i.) Let the pole O be at the centre. Then, if r denote the radius, the ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1886 Excerpt: ...in this line we take points P, Pu at the same distance OP = p from O; then P is the point (p, Jir) or (--p, fir) or (--p, --fir), Pi is the point (p, or--p, %tt) or ( p, --fir), etc. Fig. 41.. Fig. 42. 92. To find the polar equation of the circle. (i.) Let the pole O be at the centre. Then, if r denote the radius, the polar equation is simply p = r. (ii.) Let the pole 0 be on the circumference (Fig. 41), and let the diameter OB make an angle a with the initial line OA. Let P be any point (r, ff) of the circle. Join BP. Then OP = OB cos BOP, or p = 2 r cos (6--a), 23 If OB is taken as the initial line, the equation becomes p = 2rcos6. 24 (iii.) Let the pole O be anywhere, and the centre the point (k, a). Then in the triangle OPC (Fig. 42) OP2-20PXOCX cos POC+ OC2-CP2 = 0, or P2--2 Pk cos (6--a) + k2--r2 = O, 25 the most general form of the polar equation of a circle. Ex. 25. 1. Find the distances from the point P in Fig. 38 to the two axes. 2. Prove that the equation of a straight line, referred to oblique axes in terms of its intercepts, is identical in form with 7, p. 39. 3. If the straight line P0P3 (Fig. 39) bisects the second and fourth quadrants, what are the polar co-ordinates of the points P2 and P3? Give more than one set of values in each case. 4. Construct the following points (on paper, take a = 1 in.): (a') (a, l) (a'-l) Hi (-a'-l)-Sa, (4a, tan1!), (4a-tan-If) Note. The expression tan-1-in higher Mathematics means "the. 4 3 angle whose tangent is-5. If pu denote the two values of p in equation 25, p. 109, prove that pl and p, = k2--r2. What theorem of Elementary Geometry is expressed by this equation (i.) when the pole is outside the circle? (ii.) when the pole is inside the circle? 6. Through a fixed point Pin a circle a chord AB is d...
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Add this copy of Elements of Analytic Geometry, to cart. $19.95, good condition, Sold by THE OREGON ROOM rated 4.0 out of 5 stars, ships from Phoenix, OR, UNITED STATES, published by Ginn & Company.
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Good. 1898 Edition, Ginn & Co., brown covers with black lettering on cover & spine that reads fine, light wear, top corners bumped, text contains markings-mostly in light pencil, sound binding.
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