A Collection of Problems and Examples Adapted to the "Elementary Course of Mathematics.": With an Appendix Containing the Questions Proposed During the First Three Days of the Senate-House Examinations in the Years 1848, 1849, 1850, and 1851 |
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Page 31
... radius ; compare the inner and outer radii , having given that the weight of a sphere varies as the cube of its radius . 14. There are two vessels , A and B , each containing a mixture of water and wine , A in the ratio of 2 : 3 , B in ...
... radius ; compare the inner and outer radii , having given that the weight of a sphere varies as the cube of its radius . 14. There are two vessels , A and B , each containing a mixture of water and wine , A in the ratio of 2 : 3 , B in ...
Page 53
... cot + cot = cot · 2 2 2 2 2 sin ( 4 a + b - B ) : sin C :: a2 - b2 : c2 , C sin2 = cos A + cos B , C 2 1 . ( a + b ) cos C + ( a + c ) cos B + ( b + c ) cos A = a + b + c . 2. If R be the radius of the circle circumscribed TRIGONOMETRY .
... cot + cot = cot · 2 2 2 2 2 sin ( 4 a + b - B ) : sin C :: a2 - b2 : c2 , C sin2 = cos A + cos B , C 2 1 . ( a + b ) cos C + ( a + c ) cos B + ( b + c ) cos A = a + b + c . 2. If R be the radius of the circle circumscribed TRIGONOMETRY .
Page 54
... radius of the circle circumscribed about a given triangle ABC , and r the radius of the inscribed circle , then A B C 2 2 r = 4R sin — sin sin 2 3. In a plane triangle ABC , given the sum of the sides AC , BC ; the perpendicular from ...
... radius of the circle circumscribed about a given triangle ABC , and r the radius of the inscribed circle , then A B C 2 2 r = 4R sin — sin sin 2 3. In a plane triangle ABC , given the sum of the sides AC , BC ; the perpendicular from ...
Page 55
... radius of the inscribed circle , determine the sides . 16. The triangle ABC has its angles A , B , C in the proportion of 2 : 3 : 4. Prove that cos 17 . A a + c 2 2b The angles of a triangle are as the numbers 1 , 2 , 3 ; and the ...
... radius of the inscribed circle , determine the sides . 16. The triangle ABC has its angles A , B , C in the proportion of 2 : 3 : 4. Prove that cos 17 . A a + c 2 2b The angles of a triangle are as the numbers 1 , 2 , 3 ; and the ...
Page 60
... radius Find the circular measure of 1 ' . - 03 6. It may be shewn , that if a very small angle ◊ is expressed according to the circular measure sin 0 = 0 nearly ; what change must be made in the formula if 0 is expressed in seconds ? 6 ...
... radius Find the circular measure of 1 ' . - 03 6. It may be shewn , that if a very small angle ◊ is expressed according to the circular measure sin 0 = 0 nearly ; what change must be made in the formula if 0 is expressed in seconds ? 6 ...
Other editions - View all
A Collection of Problems and Examples, Adapted to the Elementary Course of ... Harvey Goodwin No preview available - 2019 |
A Collection of Problems and Examples Adapted to the 'Elementary Course of ... Harvey. Goodwin No preview available - 2015 |
A Collection of Problems and Examples, Adapted to the 'Elementary Course of ... Harvey Goodwin No preview available - 2010 |
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angular points arithmetical arithmetical mean arithmetical series axis base bisects centre of gravity chord circle concave convex lens cos² cosec curve cylinder Describe determine diameter direction distance Divide drawn elastic balls ellipse equal equation equilibrium feet find the height Find the number find the position Find the velocity fluid focal length force geometrical focus geometrical progression geometrical series given point given velocity given weight horizontal plane hyperbola immersed inches incident inclined plane inscribed latus rectum luminous point mirror motion moving Multiply observed parabola parallel parallelogram pencil of rays perpendicular placed pressure proportional prove pullies quantities radii radius ratio reflexion refracted respectively right angle shew sides sin² specific gravity sphere spherical square St John's College straight line string passing Subtract surface tangent tower triangle vertex
Popular passages
Page 111 - If two triangles have two sides of the one equal to two sides of the...
Page 128 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.
Page 111 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 112 - EQUAL straight lines in a circle are equally distant from the centre ; and those which are equally distant from the centre, are equal to one another.
Page 144 - ... a circle. The angle in a semicircle is a right angle: the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 160 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Page 112 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 160 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.