The Principles of Analytical Geometry: Designed for the Use of Students |
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Page iii
... secondary object , it must be left to others to decide ; his principal end , however , will have been attained , if his Work shall ... SECOND ORDER On Surfaces of the second Order in general On Surfaces which have a Centre On the Ellipsoid.
... secondary object , it must be left to others to decide ; his principal end , however , will have been attained , if his Work shall ... SECOND ORDER On Surfaces of the second Order in general On Surfaces which have a Centre On the Ellipsoid.
Page vi
... SECOND ORDER . CHAP . I. II . On Lines of the second Order in general ........ 91 On the Ellipse and Hyperbola ..... 98 III . On the Properties of Tangents to the Ellipse and Hyperbola 109 IV . On the Properties of Conjugate Diameters ...
... SECOND ORDER . CHAP . I. II . On Lines of the second Order in general ........ 91 On the Ellipse and Hyperbola ..... 98 III . On the Properties of Tangents to the Ellipse and Hyperbola 109 IV . On the Properties of Conjugate Diameters ...
Page viii
... SECOND ORDER . CHAP . I. On Surfaces of the second Order in general II . On Surfaces which have a Centre .... III . On the Ellipsoid .... IV . On the Hyperboloid of one Sheet .... V. On the Hyperboloid of two Sheets VI . On Surfaces ...
... SECOND ORDER . CHAP . I. On Surfaces of the second Order in general II . On Surfaces which have a Centre .... III . On the Ellipsoid .... IV . On the Hyperboloid of one Sheet .... V. On the Hyperboloid of two Sheets VI . On Surfaces ...
Page 29
... order , therefore , to obtain the solution in the case in which the point falls without the circle , as at P ' , we ... second root of the original equation . The negative root , therefore , expresses the value of CP ' . m - 2 - √ ( a2 ...
... order , therefore , to obtain the solution in the case in which the point falls without the circle , as at P ' , we ... second root of the original equation . The negative root , therefore , expresses the value of CP ' . m - 2 - √ ( a2 ...
Page 39
... order to obtain the second , we must extend the hypothesis from which equation ( 1 ) was derived . In that equation we supposed the point P to be situated above AB , but as it may equally be situated below AB , cos P ' will , in this ...
... order to obtain the second , we must extend the hypothesis from which equation ( 1 ) was derived . In that equation we supposed the point P to be situated above AB , but as it may equally be situated below AB , cos P ' will , in this ...
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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
a²² abscissa Algebra ANALYTICAL GEOMETRY assumed asymptotes axes are rectangular bisect centre CHAP chords co-ordinate planes coefficients conjugate diameters constructed cos² denote directrix distance draw ellipse and hyperbola equal equation becomes equation required equation sought find the equation formulas given line given point Hence hyperboloid imaginary inclination indeterminate equation infinite latus rectum Let y=0 locus major axis manner meet the curve negative ordinate origin parabola parallelepiped perpendicular dropped plane of xy point of intersection points of contact polar equation positive principal diameters principal vertex PROB PROP quadratic equation radius rectangular axes right angles roots second order shewn sides sin x sin² square straight line substitution supposed surface system of conjugate tangent triangle unknown quantity values whence
Popular passages
Page 7 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 1 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Page 244 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 116 - Fig. 83,84. conjugate diameters is equal to the sum of the squares of the...
Page 66 - The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.
Page 115 - ... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Page 14 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 68 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Page 79 - If two chords intersect in a circle, the difference of their squares is equal to the difference of the squares of the difference of the segments.
Page 253 - It will be demonstrated art. 452, that every section of a sphere made by a plane is a circle.