By Alfred Clement Jones

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**Read or Download An Introduction to Algebraical Geometry PDF**

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**Additional resources for An Introduction to Algebraical Geometry**

**Example text**

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.