Mathematical Problems and Examples, Arranged According to Subjects, from the Senate-House Examination Papers, 1821 to 1836 InclusiveW.P. Grant, 1836 - 335 sider |
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Side xiv
... constantly call- ing upon him to get up problems of a useless yet extremely difficult kind in the lower branches , we run the risk of encumbering his memory without invigorating his mind , and stopping him short in his course long ...
... constantly call- ing upon him to get up problems of a useless yet extremely difficult kind in the lower branches , we run the risk of encumbering his memory without invigorating his mind , and stopping him short in his course long ...
Side 11
... constant ratio ; and find that ratio . - 75. Shew that the number of permutations of m things taken n together is equal to m ( m1 ) .... ( m − r + 1 ) times the number of permutations of mr things taken n - r together . 76. In how many ...
... constant ratio ; and find that ratio . - 75. Shew that the number of permutations of m things taken n together is equal to m ( m1 ) .... ( m − r + 1 ) times the number of permutations of mr things taken n - r together . 76. In how many ...
Side 63
... constant ; if the curve has a centre , determine its position . 13. What are the lines traced by the vertex and the focus 1827 of a parabola rolling on another equal to it , the vertices coin- ciding in one position ? 14. Explain the ...
... constant ; if the curve has a centre , determine its position . 13. What are the lines traced by the vertex and the focus 1827 of a parabola rolling on another equal to it , the vertices coin- ciding in one position ? 14. Explain the ...
Side 65
... constant . 29. Two straight lines , which are always tangents to a given parabola , are so inclined to the axis of x that the sum of the cotangents of the angles which they make with that axis is constant ; prove that the locus of their ...
... constant . 29. Two straight lines , which are always tangents to a given parabola , are so inclined to the axis of x that the sum of the cotangents of the angles which they make with that axis is constant ; prove that the locus of their ...
Side 69
... constant quantity : ( 2 ) , that SP be to HP in the given ratio of n to 1 ; prove that in each case the locus of the point P is a circle . 12. If a right cone whose vertical angle is 90 ° , be cut by a plane which is parallel to one ...
... constant quantity : ( 2 ) , that SP be to HP in the given ratio of n to 1 ; prove that in each case the locus of the point P is a circle . 12. If a right cone whose vertical angle is 90 ° , be cut by a plane which is parallel to one ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 255 - If a body be projected from a given point in a given direction with a given velocity...
Side 4 - If a solid angle be contained by three plane angles, any two of them are greater than the third.
Side 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.
Side 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.
Side 314 - ... varies inversely as the square of the distance of the particle from the centre.