The Principles of Analytical Geometry: Designed for the Use of StudentsJ. Deighton & Sons, 1826 - 326 sider |
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Resultater 1-5 af 72
Side 16
... Whence is derived the following construction . = From B as a centre , with radius = m , describe a circle cutting the hypotenuse in P , and make PM , or PN = 1⁄2 / m : then MNP is the line required . If it were proposed to draw a ...
... Whence is derived the following construction . = From B as a centre , with radius = m , describe a circle cutting the hypotenuse in P , and make PM , or PN = 1⁄2 / m : then MNP is the line required . If it were proposed to draw a ...
Side 18
... whence if a straight line be drawn parallel to the base , and terminated by the other side , it may be of given length . Let ABC , fig . 6. , be the triangle , and supposing the problem resolved , let M be the required point , and MN ...
... whence if a straight line be drawn parallel to the base , and terminated by the other side , it may be of given length . Let ABC , fig . 6. , be the triangle , and supposing the problem resolved , let M be the required point , and MN ...
Side 19
... Whence it appears that ( x ) is a fourth proportional to b , c - m , and c . The point M may therefore be determined by the follow- ing construction : In BA take BQ = m , through Q draw QM parallel to BC , meeting AC in M ; then M is ...
... Whence it appears that ( x ) is a fourth proportional to b , c - m , and c . The point M may therefore be determined by the follow- ing construction : In BA take BQ = m , through Q draw QM parallel to BC , meeting AC in M ; then M is ...
Side 24
... in T ' , then rd AT ' = r + r therefore , AT or AT ' is a fourth proportional to AB , AP and AP BQ : whence is deduced the following simple con- struction . Draw any radius whatever Am , and Bn parallel to 24 ANALYTICAL GEOMETRY .
... in T ' , then rd AT ' = r + r therefore , AT or AT ' is a fourth proportional to AB , AP and AP BQ : whence is deduced the following simple con- struction . Draw any radius whatever Am , and Bn parallel to 24 ANALYTICAL GEOMETRY .
Side 31
... whence r = which is imaginary ; therefore , no point situated to the right of B , can satisfy the conditions . This indeed is evident from merely inspecting the equation AB . BP " = AP " 2 , for since AB and BP " are each less than AP ...
... whence r = which is imaginary ; therefore , no point situated to the right of B , can satisfy the conditions . This indeed is evident from merely inspecting the equation AB . BP " = AP " 2 , for since AB and BP " are each less than AP ...
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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.