The Principles of Analytical Geometry, Part 1 |
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Page 22
... referred to rectangular coor- dinates , and this is done by using the formulæ in Art . 12 . The general equation to the straight line referred to rect- angular axes is Ax + By + C = 0 , and by substituting for x and y their values in ...
... referred to rectangular coor- dinates , and this is done by using the formulæ in Art . 12 . The general equation to the straight line referred to rect- angular axes is Ax + By + C = 0 , and by substituting for x and y their values in ...
Page 23
27. The equation to a line passing through the origin and referred to rectangular coordinates , is ( Art . 18 , Cor . 2 ) y = mx . For y put p sin , and for x put p cose , and we have , for the same line referred to polar coordinates ...
27. The equation to a line passing through the origin and referred to rectangular coordinates , is ( Art . 18 , Cor . 2 ) y = mx . For y put p sin , and for x put p cose , and we have , for the same line referred to polar coordinates ...
Page 37
... referred to any axis , it is often important to know the position of that point , or what the equation to that locus becomes when referred to any other axis . The three follow- ing articles will enable us to determine in all cases the ...
... referred to any axis , it is often important to know the position of that point , or what the equation to that locus becomes when referred to any other axis . The three follow- ing articles will enable us to determine in all cases the ...
Page 38
... referred to the old axes , OM ' = X and PM ' = Y the coordinates of P when referred to the new axes . Then therefore Again , x = OM = OT- SM ' = OM ' cos 0 - PM ' sin 0 ; x = X cose- Y sin 0 . y = PM = M'T + PS therefore = OM ' sin0 + ...
... referred to the old axes , OM ' = X and PM ' = Y the coordinates of P when referred to the new axes . Then therefore Again , x = OM = OT- SM ' = OM ' cos 0 - PM ' sin 0 ; x = X cose- Y sin 0 . y = PM = M'T + PS therefore = OM ' sin0 + ...
Page 39
... referred to axes Ox and Oy , will give the equation to the locus referred to axes OX and OY . This proposition evidently includes the case of passing from oblique to rectangular coordinates or vice versâ . EXERCISES . 1. Transfer the ...
... referred to axes Ox and Oy , will give the equation to the locus referred to axes OX and OY . This proposition evidently includes the case of passing from oblique to rectangular coordinates or vice versâ . EXERCISES . 1. Transfer the ...
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The Principles of Analytical Geometry: Designed for the Use of Students Henry Parr Hamilton No preview available - 2016 |
Common terms and phrases
ANALYTICAL GEOMETRY angle POX axes being inclined axes being rectangular axis of x bisecting the angle centre Chapter chord of contact circle x² Conic Sections cosa+y cosw Crown 8vo cuts the circle denotes the distance diameter Differential Calculus equal equation becomes equation x² evidently ex recensione Find the coordinates Find the equation Find the length Find the locus fixed point x'y given circle given line Greek HYPERIDES initial line line cutting line joining line OX line represented line ST line whose equation lines are parallel middle points origin of coordinates P₁ perpendicular point of intersection points whose coordinates polar coordinates polar equation PQ² radical axis radius referred required equation Second Edition Shew siny Ox straight line passing substituting tangent Third Edition touching the circle triangle Trinity College University of Cambridge values x²²