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 |
From inside the book
Results 1-5 of 13
Page 31
... varies directly as y when x is constant , and in- versely as a when y is constant , then when x and y both vary ≈ ∞ 10 . y 00 • If x ∞ ∞ + y , u ∞ x -- y , and x ∞ u + % , then in general ya . What exception is there to this ...
... varies directly as y when x is constant , and in- versely as a when y is constant , then when x and y both vary ≈ ∞ 10 . y 00 • If x ∞ ∞ + y , u ∞ x -- y , and x ∞ u + % , then in general ya . What exception is there to this ...
Page 85
... varies inversely as the square of the dis- tance from the earth's centre ; so that if g ' be the value of gravity at a small height h above the earth's surface , and R the earth's radius , R2 h g ' = g ( R + hy8 ( 1-2 ) nearly . h ) 2 g ...
... varies inversely as the square of the dis- tance from the earth's centre ; so that if g ' be the value of gravity at a small height h above the earth's surface , and R the earth's radius , R2 h g ' = g ( R + hy8 ( 1-2 ) nearly . h ) 2 g ...
Page 115
... vary . Given that the area of an ellipse varies as either axis when the other is constant , and that the area of a circle of radius unity 3.14 ... , find the area of the = ellipse whose axes are 3 and 5 . 11. Find the sum to n terms of ...
... vary . Given that the area of an ellipse varies as either axis when the other is constant , and that the area of a circle of radius unity 3.14 ... , find the area of the = ellipse whose axes are 3 and 5 . 11. Find the sum to n terms of ...
Page 126
... varying as 1 ( dist . ) 2 ' › prove that if PSP be any focal chord of the body's path the sum of the squares of the velocities at P and p will be constant . A number of balls of given elasticity A , B , C ... are placed in a line ; A is ...
... varying as 1 ( dist . ) 2 ' › prove that if PSP be any focal chord of the body's path the sum of the squares of the velocities at P and p will be constant . A number of balls of given elasticity A , B , C ... are placed in a line ; A is ...
Page 138
... vary as the square of the time , shew that the space will vary as the cube of the time . 2. Define similar curves , and shew that all parabolas are similar to each other . Describe an instrument which is adapted for drawing curves ...
... vary as the square of the time , shew that the space will vary as the cube of the time . 2. Define similar curves , and shew that all parabolas are similar to each other . Describe an instrument which is adapted for drawing curves ...
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 |
Common terms and phrases
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.