## 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 1851J. Deighton, 1851 - 173 pages |

### From inside the book

Results 1-5 of 16

Page 77

... plane ? 3 . In an inverted parabola the time of descending down any chord from a point in the

... plane ? 3 . In an inverted parabola the time of descending down any chord from a point in the

**curve**to the vertex , is equal to the time of falling freely to a horizontal line which is at a distance below the vertex equal to DYNAMICS . 77. Page 82

...

...

**curve**; determine the latus rectum of the parabola described . The position of a ball on a triangular billiard table being given ; it is required to shew that there are three directions , in any one of which if the ball be struck , it ... Page 84

...

...

**curve**passes through the other ex- tremity , then sin 0 = √ . e 1+ e ( e the modulus of elasticity . ) 18. If two perfectly elastic balls , the masses of which are in the ratio of 1 : 3 , meet directly with equal velocities , the ... Page 108

... after two reflexions at the

... after two reflexions at the

**curve**meets the ordinate again ; prove that the length of the path described will be the same from whatever point in the ordinate the ray proceeds . 7. Find the point at which a ray of light 108 OPTICS . Page 113

...

...

**curve**at P. For what position of P is the angle SPH greatest ? 13 . State when diameters of an ellipse or hyperbola are conjugate . Prove that all parallelograms whose sides touch an ellipse at the ends of conjugate diameters are equal ...### 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.