By Alfred Clement Jones
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Extra info for An Introduction to Algebraical Geometry
And hence prove 38. + CA* = 3 (AG* + <7 2 -f CG 2 ). 39. The sum of the squares on the diagonals of any quadrilateral is double the sum of the squares on the lines joining the middle points of the opposite sides. The diagonals of a trapezium are drawn and the mid-points of the show analytically that there is a point common parallel sides are joined to these straight lines which divides each of them in the same ratio. ) in the points 41. A variable line cuts any two lines intersecting at 40.
And l- (a, b) a, b). ( What 23. >, the origin ? Write down an equation 24. moves lines so that the difference of its is by the coordinates of a point which distances from two intersecting straight satisfied constant. ) : if they are inclined at 30 trace the graph of 25. 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.
Hence the sides of the triangle represented by cir \ c A'B'C' are the straight lines whose equations are same way is an + z Now = 0, bv -f z 0, av -f 2? = 0. e. - through the point A'. - through the point A. Hence A and A' both lie on bv cw = But (bv + z) = : then the equation of the straight line AA'. In exactly the same way ctv-au Q represents the straight line and an-bv the straight line CC'. this is - BB r , THE EQUATION OF THE FIRST DEGREE 54 Hence the equations of the three straight vertices, via.
An Introduction to Algebraical Geometry by Alfred Clement Jones