## 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

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**arithmetical mean**between a and b is greater than the geometrical . 6. If quantities are in geometrical progression , their differences are in geometrical progression . 7 . There are three numbers in geometrical progres- sion 34 ALGEBRA . Page 35

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**arithmetical mean**exceeds the geometrical by 18. Find the numbers . 9. In any geometrical series , consisting of an ... means of 4 numbers in geometrical progression is 2 , and the difference of the extremes is 7 ; find the numbers ... Page 36

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**arithmetical mean**between two numbers ex- ceeds the geometrical by 13 , and the geometrical exceeds the harmonical by 12 , what are the numbers ? 5. The arithmetical , geometrical , and harmonical means between a and b form a ... Page 51

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**arithmetical mean**between a and B. 7. If tan 0 = tan3 , and 3 cos2 = m2 - 1 , then 2 cos3 0 + sin30 213 = m 8 . 8 , Given sin 0 = m sin , and tan 0 = n tan o , find sin and cos p . 9. Given sin ( 0 + a ) = m sin 0 , find 0 in terms ... Page 55

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**arithmetical**pro- gression , and the distance of the centres of the inscribed and circumscribed circles is a**mean**proportional between the greatest and the least ; shew that the sides are in the proportion of √5-1 : √5 : √5 +1 . 14 ...### 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.