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 5
... EQUATIONS . 1. THE number 803 expressed in a different scale of nota- 1821 tion becomes 30203 ; required the radix of the scale . 2. Prove that n- 1 n " — n . ( n − 1 ) " + n 2 ( n − 2 ) " - & c . 1.2.3 .... n . 3. Find a from the ...
... EQUATIONS . 1. THE number 803 expressed in a different scale of nota- 1821 tion becomes 30203 ; required the radix of the scale . 2. Prove that n- 1 n " — n . ( n − 1 ) " + n 2 ( n − 2 ) " - & c . 1.2.3 .... n . 3. Find a from the ...
Σελίδα 30
... the roots of the original equation . 6. Prove that Waring's solution of a biquadratic equation fails when all the roots are impossible , and of the form a + b√1 . 7. The roots of the equation 6x1 — 43x3 + Nature of Algebraic Equations.
... the roots of the original equation . 6. Prove that Waring's solution of a biquadratic equation fails when all the roots are impossible , and of the form a + b√1 . 7. The roots of the equation 6x1 — 43x3 + Nature of Algebraic Equations.
Σελίδα 31
... equation have two equal roots , and the terms are multiplied by the terms of an arithmetic progression , the result will = 0 . 9. In an equation of n dimensions , the second and third terms may be taken ... equation NATURE OF EQUATIONS . 31.
... equation have two equal roots , and the terms are multiplied by the terms of an arithmetic progression , the result will = 0 . 9. In an equation of n dimensions , the second and third terms may be taken ... equation NATURE OF EQUATIONS . 31.
Σελίδα 32
... equation in terms of the inferior powers . 18. If a be an approximate value of x in any equation , and b , c be the results , when a is substituted for x in the original and in the limiting ... equation 1 x2 - 32 NATURE OF EQUATIONS .
... equation in terms of the inferior powers . 18. If a be an approximate value of x in any equation , and b , c be the results , when a is substituted for x in the original and in the limiting ... equation 1 x2 - 32 NATURE OF EQUATIONS .
Σελίδα 33
... equation - x2 - pxn − 1 + qx2 - 2 — & c . + qx2 — px + 1 = 0 , - whose roots are a , b , c , & c .; prove that C2 a2 b2 b2 b2 + 02 a2 a2 + + c2 b2 a2 + c2 + b2 + & c . c2 b2 = ( p2 - 2q + ... equation has at least NATURE OF EQUATIONS . 33.
... equation - x2 - pxn − 1 + qx2 - 2 — & c . + qx2 — px + 1 = 0 , - whose roots are a , b , c , & c .; prove that C2 a2 b2 b2 b2 + 02 a2 a2 + + c2 b2 a2 + c2 + b2 + & c . c2 b2 = ( p2 - 2q + ... equation has at least NATURE OF EQUATIONS . 33.
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.