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 41
... inversely as the perpendiculars let fall from them upon the opposite sides . 15. Find the number of different triangles into which a polygon of n sides may be divided by lines joining the angular points . 16. If through any point O ...
... inversely as the perpendiculars let fall from them upon the opposite sides . 15. Find the number of different triangles into which a polygon of n sides may be divided by lines joining the angular points . 16. If through any point O ...
Σελίδα 69
... inversely as the sines of the angles which they make with the lines drawn to either focus . 9. A triangle is described about an ellipse : prove that the products of the alternate segments of the sides , made by the points of contact ...
... inversely as the sines of the angles which they make with the lines drawn to either focus . 9. A triangle is described about an ellipse : prove that the products of the alternate segments of the sides , made by the points of contact ...
Σελίδα 70
... inversely as the square of the sign of the angle at which the corresponding ordinates are inclined to it . 24. If ay2 + bxy + cx2 + dy + ex + ƒ 0 , be the equation to a curve of the second order ; prove that the angles which its ...
... inversely as the square of the sign of the angle at which the corresponding ordinates are inclined to it . 24. If ay2 + bxy + cx2 + dy + ex + ƒ 0 , be the equation to a curve of the second order ; prove that the angles which its ...
Σελίδα 82
... inversely as the nth power of the radius vector . 30. Explain the method of drawing asymptotes to spirals , and apply it to the hyperbola considered as a spiral having the pole in the focus . 31. Investigate the differential expression ...
... inversely as the nth power of the radius vector . 30. Explain the method of drawing asymptotes to spirals , and apply it to the hyperbola considered as a spiral having the pole in the focus . 31. Investigate the differential expression ...
Σελίδα 150
... inversely as the perpendicular let fall from the centre of force on the tangent at that point . Required proof . 33. Determine the point in the curve surface on which a semi - paraboloid will rest on a horizontal plane . 34. A given ...
... inversely as the perpendicular let fall from the centre of force on the tangent at that point . Required proof . 33. Determine the point in the curve surface on which a semi - paraboloid will rest on a horizontal plane . 34. A given ...
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Mathematical Problems and Examples: Arranged According to Subjects, from the ... Πλήρης προβολή - 1837 |
Mathematical Problems and Examples: Arranged According to Subjects, From the ... University of Cambridge Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
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.