Mathematical Problems and Examples, Arranged According to Subjects, from the Senate-House Examination Papers, 1821 to 1836 InclusiveW.P. Grant, 1836 - 335 σελίδες |
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Σελίδα 65
... axes of the curve of the second order , the equation of which is Ay2 + Вxy + Cx2 + Dy + Ex + F = 0 . 31. x , y and X , Y are the coordinates of a point referred to two systems of rectangular coordinates having a common origin and ...
... axes of the curve of the second order , the equation of which is Ay2 + Вxy + Cx2 + Dy + Ex + F = 0 . 31. x , y and X , Y are the coordinates of a point referred to two systems of rectangular coordinates having a common origin and ...
Σελίδα 66
... axes of x and y , and the cosine of the angle which it makes with a given straight line passing through the origin . 44. If an odd number of equidistant ordinates be drawn in a curve , the area between the extreme ordinates may be found ...
... axes of x and y , and the cosine of the angle which it makes with a given straight line passing through the origin . 44. If an odd number of equidistant ordinates be drawn in a curve , the area between the extreme ordinates may be found ...
Σελίδα 67
... axes to another having the same origin . Transform the equation xy = c2 , where the axes are inclined to each other at a given angle , to one where the axes bisect the angles made by the former . 49. Define a cycloid and investigate its ...
... axes to another having the same origin . Transform the equation xy = c2 , where the axes are inclined to each other at a given angle , to one where the axes bisect the angles made by the former . 49. Define a cycloid and investigate its ...
Σελίδα 69
... Required the proportion of the axes of the ellipse , so that it may cut the parabola at right angles . & also 4 ^ _ ? ky + x ^ _ Ny + 4 x + 4 о 1826 18. Having given two conjugate diameters of an ellipse CONIC SECTIONS . 69.
... Required the proportion of the axes of the ellipse , so that it may cut the parabola at right angles . & also 4 ^ _ ? ky + x ^ _ Ny + 4 x + 4 о 1826 18. Having given two conjugate diameters of an ellipse CONIC SECTIONS . 69.
Σελίδα 70
... axes . 19. The abscissa and double ordinate of a common parabola are a and b , and the diameters of its circumscribed and in- scribed circles D and d ; prove that D + d = a + b . 20. Three straight lines revolve about three given points ...
... axes . 19. The abscissa and double ordinate of a common parabola are a and b , and the diameters of its circumscribed and in- scribed circles D and d ; prove that D + d = a + b . 20. Three straight lines revolve about three given points ...
Συχνά εμφανιζόμενοι όροι και φράσεις
acted altitude angular apply attraction axes axis body centre of force centre of gravity chord circle coefficients cone conic section coordinates curvature cycloid cylinder density described determine diameter direction distance drawn earth eccentricity ecliptic ellipse equal equilibrium Explain Find the equation fixed fluid focus force varying geometrical given angle given point given velocity horizontal plane hyperbola inclined Integrate intersection Investigate latitude latus rectum length lens locus logarithmic longitude meridian moon moon's motion Newton nodes orbit oscillation parabola parallel particle passing perpendicular plane triangle position pressure projected Prop prove quantity ratio rays refraction revolving right angles right ascension roots shew sides sin² sine solid of revolution specific gravity sphere spherical reflector spherical triangle spheroid square straight line string surface tangent Trace the curve true anomaly varies inversely vertex vertical weight
Δημοφιλή αποσπάσματα
Σελίδα 3 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 280 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Σελίδα 126 - If two straight lines meeting one another, be parallel to two straight lines which also meet one another, but are not in the same plane with the first two : the plane which passes through the first two is parallel to the plane passing through the others.
Σελίδα 2 - IN right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar and similarly described figures upon the sides containing the right angle...
Σελίδα 2 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Σελίδα 255 - If a body be projected from a given point in a given direction with a given velocity...
Σελίδα 4 - If a solid angle be contained by three plane angles, any two of them are greater than the third.
Σελίδα 157 - To find the magnitude, direction, and point of application of the resultant of any number of parallel forces acting on a rigid body in one plane.
Σελίδα 7 - A and B can do a piece of work in m days, B and C in n days, and C and A in p days. In what time can each alone jjerform the work ? 39.
Σελίδα 314 - ... varies inversely as the square of the distance of the particle from the centre.