The Principles of Analytical Geometry, Part 1 |
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Page 1
... drawn parallel to OX : for suppose that PM is three times the unit of measure and PN four times : X N P 0 M N then ... draw the lines NP , MP parallel respectively to OX and OY ; their intersection determines the point P. 2. Instead of ...
... drawn parallel to OX : for suppose that PM is three times the unit of measure and PN four times : X N P 0 M N then ... draw the lines NP , MP parallel respectively to OX and OY ; their intersection determines the point P. 2. Instead of ...
Page 3
... drawn parallel to OX through P , meeting QN in T , we have P MN PQ2 = PT + TQ - 2PT.TQ cos PTQ , - - T or PQ2 = ( x , − x ̧ ) 2 + ( Y2 − y1 ) 2 − 2 ( x − x ̧ ) ( y , —y1 ) cos PTQ . - But the angle PTQ is evidently the supplement of ...
... drawn parallel to OX through P , meeting QN in T , we have P MN PQ2 = PT + TQ - 2PT.TQ cos PTQ , - - T or PQ2 = ( x , − x ̧ ) 2 + ( Y2 − y1 ) 2 − 2 ( x − x ̧ ) ( y , —y1 ) cos PTQ . - But the angle PTQ is evidently the supplement of ...
Page 4
... drawn through it is called the initial or prime line . The length OP , which is called the radius vector , is usually denoted by p , and the angle POX , which it makes with the initial line , by 0 . 10. A point is then determined if we ...
... drawn through it is called the initial or prime line . The length OP , which is called the radius vector , is usually denoted by p , and the angle POX , which it makes with the initial line , by 0 . 10. A point is then determined if we ...
Page 6
... drawn from the pole O bisecting the angle POQ , and meeting the line joining PQ in the point M. Shew that the coordinates of M are 2p'p " cos§ ( 0 ′′ — 0 ′ ) , and 0 = § ( 0 ′ + 0 ′′ ) . p ' + p " 9 ( 7 ) CHAPTER II . THE STRAIGHT LINE ...
... drawn from the pole O bisecting the angle POQ , and meeting the line joining PQ in the point M. Shew that the coordinates of M are 2p'p " cos§ ( 0 ′′ — 0 ′ ) , and 0 = § ( 0 ′ + 0 ′′ ) . p ' + p " 9 ( 7 ) CHAPTER II . THE STRAIGHT LINE ...
Page 9
... draw PM parallel to OY meeting OX in M. Then PM is the y of the point P , and OM is the x of it . It is also evident that wherever P be taken on the line ST , the triangles PMS and TOS are similar ; therefore PM : MS :: TO : OS , or ...
... draw PM parallel to OY meeting OX in M. Then PM is the y of the point P , and OM is the x of it . It is also evident that wherever P be taken on the line ST , the triangles PMS and TOS are similar ; therefore PM : MS :: TO : OS , or ...
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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