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 24
... determine the sum of the coeffi- cients . Write down the coefficient of 24 in the expansion of ( 1 + x + x2 ) 6 . 87968 214. Form the continued fraction corresponding to 277288 ' and determine the first five converging fractions . 215 ...
... determine the sum of the coeffi- cients . Write down the coefficient of 24 in the expansion of ( 1 + x + x2 ) 6 . 87968 214. Form the continued fraction corresponding to 277288 ' and determine the first five converging fractions . 215 ...
Σελίδα 39
... determine a superior limit of the roots of an equation . Ex . x4 2x3 3x2 15x 3 = 0 . - 83. Every equation of an even number of dimensions , and whose last term is negative , has at least two real roots . 84. Take away the third term ...
... determine a superior limit of the roots of an equation . Ex . x4 2x3 3x2 15x 3 = 0 . - 83. Every equation of an even number of dimensions , and whose last term is negative , has at least two real roots . 84. Take away the third term ...
Σελίδα 48
... Determine the breadth of the river . log sin 7 ° 9.08589 , log sin 35 ° = 9.75859 , - log sin 48 ° 9.87107 , = log 1.0493.02089 . log 3 = 47712 , 85. Determine the distance between two inaccessible objects , by observations made at two ...
... Determine the breadth of the river . log sin 7 ° 9.08589 , log sin 35 ° = 9.75859 , - log sin 48 ° 9.87107 , = log 1.0493.02089 . log 3 = 47712 , 85. Determine the distance between two inaccessible objects , by observations made at two ...
Σελίδα 59
... determine the remaining angle and sides . Is there any ambiguity in the determination of the side opposite to the given angle ? 34. In a spherical triangle -- COS A + B tan 2 a b 2 C = cot a + b 2 ' COS 2 35. Having given the three ...
... determine the remaining angle and sides . Is there any ambiguity in the determination of the side opposite to the given angle ? 34. In a spherical triangle -- COS A + B tan 2 a b 2 C = cot a + b 2 ' COS 2 35. Having given the three ...
Σελίδα 61
... determine also the cosine of a side in terms of a and B. 53. In a spherical triangle , determine the limits of the sum of the angles . Prove also that the difference between any angle and the sum of the other two is less than 180 ° . 54 ...
... determine also the cosine of a side in terms of a and B. 53. In a spherical triangle , determine the limits of the sum of the angles . Prove also that the difference between any angle and the sum of the other two is less than 180 ° . 54 ...
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.