The Principles of Analytical Geometry: Designed for the Use of StudentsJ. Deighton & Sons, 1826 - 326 sider |
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Resultater 1-5 af 19
Side 11
... infinite number of solutions . For example , if it be required to divide a given straight line into two such parts , that the rectangle contained by the whole line and one of the parts , shall be equal to the square of the other part ...
... infinite number of solutions . For example , if it be required to divide a given straight line into two such parts , that the rectangle contained by the whole line and one of the parts , shall be equal to the square of the other part ...
Side 52
... analytical solution of the proposed equa- tion . 1 Since the equation admits an unlimited number of solutions , the points P , furnished by each solution , will also be infinite in number ; the assemblage of these points will form.
... analytical solution of the proposed equa- tion . 1 Since the equation admits an unlimited number of solutions , the points P , furnished by each solution , will also be infinite in number ; the assemblage of these points will form.
Side 80
... infinite , a vanishes , and therefore the locus of P is a semi - circle . 2m According as APB is acute or obtuse , m will be positive or negative , and the centre will be situated above or below AB . The locus of P will therefore be an ...
... infinite , a vanishes , and therefore the locus of P is a semi - circle . 2m According as APB is acute or obtuse , m will be positive or negative , and the centre will be situated above or below AB . The locus of P will therefore be an ...
Side 103
... infinite branch ZAz . If r be supposed negative , it may in like manner be shewn , that to the left there is an infinite branch Z'V % . The hyperbola therefore consists of two infinite branches , symmetrically situated on opposite sides ...
... infinite branch ZAz . If r be supposed negative , it may in like manner be shewn , that to the left there is an infinite branch Z'V % . The hyperbola therefore consists of two infinite branches , symmetrically situated on opposite sides ...
Side 107
... infinite distance , and will separate those diameters which meet , from those which can never meet , the curve . The lines CZ , Cz are called asymptotes , and are defined by b the equation y = ± -x . 104. COR . When the abscissa is ...
... infinite distance , and will separate those diameters which meet , from those which can never meet , the curve . The lines CZ , Cz are called asymptotes , and are defined by b the equation y = ± -x . 104. COR . When the abscissa is ...
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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.