## 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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**shew**that pn 1 . 28 . -**Shew**that the middle term of the expansion of 1.3.5 ......... ( 2n - 1 ) ( 1 + x ) 2n = 1 .2.3 . 2 " x " . n LOGARITHMS . 1 . Solve the equations : aby = c ab1 = = a * by c d = ab , c , * = d1 a , b , c , * 1 da ... Page 42

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**Shew**that ymn - 1 is divisible by either of the quan- tities y TM – 1 or y " -1 without remainder , m and n being positive integers . - 2. Of the two quantities a + a1b2 + a2ba + bˆ and ( a3 + b3 ) , determine which is the greater . 3 ... Page 44

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**Shew**that + is greater than - + b2 D 1 1 a b · 19 .**Shew**that a + b2 / c + d2 is greater than ac + bd . 20.**Shew**that abc is greater than ( a + b - c ) ( a + c −b ) ( b + ca ) unless a = b = c . 21 .**Shew**that a3 + 1 is greater than a2 ... Page 47

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**Shew**that as the angle increases each of the trigonometrical functions changes sign whenever it passes through the value 0 or ∞o , and for no other value . FORMULE INVOLVING FUNCTIONS OF ONE ANGLE . 1. Prove the following formula : sin ... Page 55

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**shew**that the sides are in the proportion of √5-1 : √5 : √5 +1 . 14. In a right - angled triangle , if the hypothenuse be divided into two segments x and y , by the line which bisects the right angle , and t = the tangent of half the ...### 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.