## Second-year Mathematics for Secondary Schools, Volume 2 |

### From inside the book

Results 1-5 of 14

Page viii

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**geometrical**notions already begun , it develops the customary topics of first - year algebra well into quadratics . Toward the close of the first year**geometrical**ideas are revived and considerable preliminary**geometrical**work is done ... Page ix

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**geometrical**reasoning . More than 90 per cent . of the theorems of school geometry are proved by them . The early part of four of the first five chapters thus adds a new**geometrical**tool to the equipment of the pupil . Furthermore ... Page 1

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**geometrical**figure without reference to a proof . CONSTRUCTION I 5. To draw a circle of given center and radius . Let O ( Fig . 1 ) be the given center and let the line , r , be the given radius . Spread the compasses until the distance ... Page 10

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**Geometrical**figures that have the same shape are similar figures . 18.**Geometrical**figures that have the same size , but not the same shape , are equal or equivalent figures . 19.**Geometrical**figures , that have both the same size and ... Page 15

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**geometrical**study is to learn how to find out things , how to discover new truths , i . e . , how to find out what is likely to be true and to state it in form for logical proof or disproof . In this work of**geometrical**exploration and ...### Other editions - View all

### Common terms and phrases

acute angle adjacent sides algebra altitude angle equal angles are equal arc A B axiom base bisects central angle chord circumference circumscribed circle congruent construct a line construct a triangle construct the triangle cosine decagon denoted diagonals diameter distance divided divisor Draw a circle drawn equally distant equilateral triangle EXERCISES expressed exterior angle Find the area Find the side formula geometrical given angle given circle given line given triangle graph Hence homologous sides hypotenuse inches inscribed angle intersecting isosceles triangle line-segment mean proportional number of degrees number of sides parallel parallelogram pentagon perimeter perpendicular bisector Problem Proof PROPOSITION VIII Prove quadratic equation quadrilateral radii radius ratio rectangle regular inscribed regular polygon remainder rhombus right angle right triangle root secant segment similar polygons similar triangles sine square straight angle straight line tangent Theorem unequal vertex

### Popular passages

Page 41 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Page 169 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.

Page 150 - THEOREM If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.

Page 77 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.

Page 141 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 223 - Pythagorean theorem, which states that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides.

Page 214 - I label the two new points e and /." FIG. 2 With the help of this figure he then proceeds to the usual proof of the theorem that the area of a parallelogram is equal to the product of the base by the altitude, establishing the equality of certain lines and angles and the congruence of the pair of triangles.

Page 215 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.

Page 10 - If two sides and the included angle of one triangle are equal respectively to two sides and the included angle of another triangle, then the triangles are congruent.

Page 268 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R