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 125
... centre of gravity of the triangle AMN . 34. Prove that the stereographic projection of any circle on the sphere is a circle ; and find the centre and radius of the circle . 35. If x1 , y1 , z , be the distances from the origin of the ...
... centre of gravity of the triangle AMN . 34. Prove that the stereographic projection of any circle on the sphere is a circle ; and find the centre and radius of the circle . 35. If x1 , y1 , z , be the distances from the origin of the ...
Σελίδα 147
... centre of gravity of a plane surface , bounded by a curve whose equation is given . 6. If a body be balanced upon a horizontal plane , and a slight motion be given to it , its centre of gravity will move . horizontally ; prove this ...
... centre of gravity of a plane surface , bounded by a curve whose equation is given . 6. If a body be balanced upon a horizontal plane , and a slight motion be given to it , its centre of gravity will move . horizontally ; prove this ...
Σελίδα 148
... centre of gravity of the quadrant a circular area . 10. When the same string passes over any number of pullies , and the parts of the string supporting any pulley at the lower block are not parallel to one another , find the proportion ...
... centre of gravity of the quadrant a circular area . 10. When the same string passes over any number of pullies , and the parts of the string supporting any pulley at the lower block are not parallel to one another , find the proportion ...
Σελίδα 149
... centre of gravity of a given isosceles triangle , making a given angle with the base , and terminated by the sides ... centre of the circle inscribed in the triangle DEF is the centre of gravity of the perimeter of the triangle ABC ...
... centre of gravity of a given isosceles triangle , making a given angle with the base , and terminated by the sides ... centre of the circle inscribed in the triangle DEF is the centre of gravity of the perimeter of the triangle ABC ...
Σελίδα 150
... centre of gravity of the area of a semi - parabola . 30. Determine the position of equilibrium of a uniform rod , one end of which rests against a plane perpendicular to the horizon , and the other on the interior surface of a given ...
... centre of gravity of the area of a semi - parabola . 30. Determine the position of equilibrium of a uniform rod , one end of which rests against a plane perpendicular to the horizon , and the other on the interior surface of a given ...
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.