The principles of analytical geometry |
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Page i
... Inclination of Straight Lines to the Axes , Page 196 200 and to one another .... 205 IV . On the Plane situated in Space .. 209 V. On Problems relating to the Straight Line and Plane 215 VI . On the Inclination of Planes to the Co ...
... Inclination of Straight Lines to the Axes , Page 196 200 and to one another .... 205 IV . On the Plane situated in Space .. 209 V. On Problems relating to the Straight Line and Plane 215 VI . On the Inclination of Planes to the Co ...
Page vii
... Inclination of Straight Lines to the Axes , and to one another ... IV . On the Plane situated in Space .. V. On Problems relating to the Straight Line and Plane 205 209 ... 215 VI . On the Inclination of Planes to the Co - ordinate ...
... Inclination of Straight Lines to the Axes , and to one another ... IV . On the Plane situated in Space .. V. On Problems relating to the Straight Line and Plane 205 209 ... 215 VI . On the Inclination of Planes to the Co - ordinate ...
Page 19
... Inclination of Straight Lines to the Axes , Page 196 200 and to one another .. 205 IV . On the Plane situated in Space ... 209 V. On Problems relating to the Straight Line and Plane 215 ..... VI . On the Inclination of Planes to the Co ...
... Inclination of Straight Lines to the Axes , Page 196 200 and to one another .. 205 IV . On the Plane situated in Space ... 209 V. On Problems relating to the Straight Line and Plane 215 ..... VI . On the Inclination of Planes to the Co ...
Page 22
... inclination of either side to the base exceeds a right angle . 24. COR . In an acute - angled triangle , three squares may be inscribed ; one upon each side . Of these three squares , to de- termine which is the greatest and which the ...
... inclination of either side to the base exceeds a right angle . 24. COR . In an acute - angled triangle , three squares may be inscribed ; one upon each side . Of these three squares , to de- termine which is the greatest and which the ...
Page 32
... inclination , to draw a straight line , such that the part PQ , intercepted by these lines , may be of given length ( m ) . Supposing the problem resolved , draw PM , making the angle APM = ACQ , and meeting AC in the point M ; and draw ...
... inclination , to draw a straight line , such that the part PQ , intercepted by these lines , may be of given length ( m ) . Supposing the problem resolved , draw PM , making the angle APM = ACQ , and meeting AC in the point M ; and draw ...
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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
a²+b² a²b² abscissa Algebra ANALYTICAL GEOMETRY assumed asymptotes axes are rectangular bisect centre chords circle co-ordinate planes coefficients conical surface conjugate diameters constructed cubic equation denote diametral planes directrix distance drawn parallel ellipse and hyperbola equal equation becomes equation required equation sought equilateral hyperbola find the equation Geometry given line given point Hence hyperboloid imaginary inclination infinite latus rectum Let the equations Let y=0 locus major axis manner meet the curve negative ordinate origin parabola parallelepiped plane of xy point of intersection polar equation positive principal diameters PROB PROP quadratic equation rectangular axes right angles roots secant second order shewn sin² squares straight line supposed surface surface of revolution system of conjugate triangle vertex whence x²²
Popular passages
Page 62 - the hyperbola, the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the principal diameters
Page vii - To bisect a given triangle by a straight line drawn from a given point in one of its sides. Let
Page 80 - The rectangle contained by the focal distances of any point, is equal to the square of the semi-diameter conjugate to that which passes through the
Page ii - the first is to the third as the difference between the first and second is to
Page 144 - parallelepiped, the square of the diagonal is equal to the sum of the squares of the three edges.
Page 181 - that every section of a sphere, made by a plane, is a circle.
Page 19 - To find the area of a triangle, in terms of the co-ordinates of its angular points;
Page 2 - sides, and the line drawn from the vertex to the middle of the base, to find the