The Principles of Analytical Geometry: Designed for the Use of StudentsJ. Deighton & Sons, 1826 - 326 sider |
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Resultater 1-5 af 9
Side 143
... principal vertex , and the line AX the axis , of the parabola . The principal parameter is sometimes called the latus rectum . 159. COR . There is only one focus in the axis of the parabola . For the focus being that point at which the ...
... principal vertex , and the line AX the axis , of the parabola . The principal parameter is sometimes called the latus rectum . 159. COR . There is only one focus in the axis of the parabola . For the focus being that point at which the ...
Side 150
... principal vertex , is y2 = mx + nx2 ; therefore , extracting the square root , y = ± n } x { 1 + = ± n $ x { 1 + 1 / 2 m -- n 1 m = ± { x + x + 2 ' n • m - n - 118 ] 8 - • m 100 8 · • m n 1 X • which is of the same form with that of the ...
... principal vertex , is y2 = mx + nx2 ; therefore , extracting the square root , y = ± n } x { 1 + = ± n $ x { 1 + 1 / 2 m -- n 1 m = ± { x + x + 2 ' n • m - n - 118 ] 8 - • m 100 8 · • m n 1 X • which is of the same form with that of the ...
Side 156
... principal diameter , then in the ellipse , y = hyperbola , y2 circle , y be a2 2 ( a2 - x2 ) b2 = ( x2 - a2 ) a - x2 2 = 2 equilateral hyperbola , y2 = x2 — a2 --- ( 2 ) Let the curve be referred to the principal ... vertex , then in the ...
... principal diameter , then in the ellipse , y = hyperbola , y2 circle , y be a2 2 ( a2 - x2 ) b2 = ( x2 - a2 ) a - x2 2 = 2 equilateral hyperbola , y2 = x2 — a2 --- ( 2 ) Let the curve be referred to the principal ... vertex , then in the ...
Side 164
... principal diameter AX , such that drawing any chord whatever PMP , and joining AP , Ap , the angle PAP so formed may ... vertex A draw two chords AP , Ap , at right angles to one another , and join Pp cutting AX in M : the aim of the ...
... principal diameter AX , such that drawing any chord whatever PMP , and joining AP , Ap , the angle PAP so formed may ... vertex A draw two chords AP , Ap , at right angles to one another , and join Pp cutting AX in M : the aim of the ...
Side 167
... principal diameter , and the tangent at its vertex . The abscissas of the points of intersection will be found PROPERTIES OF THE THREE CURVES . 167.
... principal diameter , and the tangent at its vertex . The abscissas of the points of intersection will be found PROPERTIES OF THE THREE CURVES . 167.
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The Principles of Analytical Geometry: Designed for the Use of Students Henry Parr Hamilton Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
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
Populære passager
Side 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.
Side 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.
Side 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.
Side 116 - Fig. 83,84. conjugate diameters is equal to the sum of the squares of the...
Side 66 - The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.
Side 115 - ... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Side 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...
Side 68 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Side 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.
Side 253 - It will be demonstrated art. 452, that every section of a sphere made by a plane is a circle.