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 55
... fixed point in it , affected with their proper algebraic signs ? Upon this principle trace the sign of the secant of an arc through 360 ° , and of the chord through 720 ° . 137. Prove the formulæ 2 sin x = √1 + sin 2x + √I - 2 cos x ...
... fixed point in it , affected with their proper algebraic signs ? Upon this principle trace the sign of the secant of an arc through 360 ° , and of the chord through 720 ° . 137. Prove the formulæ 2 sin x = √1 + sin 2x + √I - 2 cos x ...
Σελίδα 62
... fixed point ( C ) . At the same instant B begins to move in a direction perpendicular to P's first motion : P is always found in the line joining C and B ; but can only accelerate her rate of sailing so as to retain the same distance ...
... fixed point ( C ) . At the same instant B begins to move in a direction perpendicular to P's first motion : P is always found in the line joining C and B ; but can only accelerate her rate of sailing so as to retain the same distance ...
Σελίδα 64
... fixed point is equal to the perpendicular drawn from the same point in the curve upon a given line . 20. Having given the equation to a straight line , find the equation to another straight line drawn perpendicular to it from a given ...
... fixed point is equal to the perpendicular drawn from the same point in the curve upon a given line . 20. Having given the equation to a straight line , find the equation to another straight line drawn perpendicular to it from a given ...
Σελίδα 73
... fixed point S be 1830 in a given ratio to its distance PM from a fixed line , find the rectangular equation to the locus of P , according as SP is equal to , less than , or greater than PM . PV.VG CP2 49. In the ellipse , = QV2 CD2 50 ...
... fixed point S be 1830 in a given ratio to its distance PM from a fixed line , find the rectangular equation to the locus of P , according as SP is equal to , less than , or greater than PM . PV.VG CP2 49. In the ellipse , = QV2 CD2 50 ...
Σελίδα 74
... fixed diameter AB = n : 1 . Prove that the locus of p is a conic section . 60. In a given equilateral parallelogram inscribe an ellipse of given eccentricity . 61. Prove that the locus of the points of bisection of any number of chords ...
... fixed diameter AB = n : 1 . Prove that the locus of p is a conic section . 60. In a given equilateral parallelogram inscribe an ellipse of given eccentricity . 61. Prove that the locus of the points of bisection of any number of chords ...
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.