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# An Introduction to Algebraical Geometry by Alfred Clement Jones

By Alfred Clement Jones

This scarce antiquarian e-book is a variety from Kessinger Publishings Legacy Reprint sequence. because of its age, it may well comprise imperfections equivalent to marks, notations, marginalia and mistaken pages. simply because we think this paintings is culturally very important, now we have made it on hand as a part of our dedication to retaining, protecting, and selling the worlds literature. Kessinger Publishing is where to discover thousands of infrequent and hard-to-find books with anything of curiosity for everybody!

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The polar coordinates of two points are (rlf 0^), through the pole bisecting the angle which they subtend their join in P. Find the polar coordinates of P. 26. , (r2 , tt 2) : the line at the pole Q from meets the origin form THE POINT a harmonic If the coordinates of series. Prove that /?. P, Q /*, Q 25 are ( 0), find those of OR internally and externally in the same ratio. 2 2 points whose coordinates are (aw 2am), (am~ divide P and Q are two and S is the point (a, 0). Prove (i) that PSQ arc collinear, is constant for all values of MI.

It is evident then that two conditions are necessary to fix a and further that in the cases above given these two conditions are sufficient: we shall see later that two conditions are straight line, not always sufficient. When one condition the line) Thus have if is we (e. g. a point on the line, or the direction of given, a relation between the constants can be found. >) lies on the straight line, we Aa + Bb + C = 0. THE EQUATION OF THE FIRST DEGREE 38 one of the independent terms of the other, and the equation of the line can be found in a form which involves only one unknown or It is then possible to find the value of ratios or constants in undetermined constant.

H r-f ic = 0, to find the equations of its three diagonals. If the Let ABA'B' be the quadrilateral. <-! r) AA = /r)~r [straight line through C'] [straight line through 6') = and represents CC'. tH Also the equation can be written (n and represents DB'. /' = [straight line through B} are the three diagonals of the quadrilateral. Examples II 1. What is the value of a if h. the three straight lines a- 4 y -4 3#-j2=:0, x i/-f3a=0 are concurrent? 2. Find the area of the triangle formed by the three straight X-5 = 0, y + 2x-l = 0, #-t/4 1 = 0.