## A Text-book of Geometry |

### From inside the book

Results 1-5 of 9

Page 75

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**secant**is a straight line which intersects the circum- ference in two points ; as , AD , Fig . 1 . 213. A tangent is a straight line which touches the circum- ference but does not intersect it ; as , BC , Fig . 1. The point in which the ... Page 87

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**secants**. Fig . 2 . § 102 § 232 Suppose EF drawn || to CD and tangent to the circle at M. Then and - arc AM arc BM arc CM = arc DM = arc BD .. by subtraction , arc AC CASE III . When AB and CD are tangents . Fig . 3 . Suppose the**secant**... Page 103

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**secants**are drawn through the point of contact , the chords joining their extremities are parallel HINT Draw the common tangent 270. An angle formed by two**secants**, two ta PROPOSITION XIX . THEOREM . Page 104

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**secant**, intersecting with circumference , is measured by one - half the dij of the intercepted arcs . E B FIG . 1 . M FIG . 2 . B D FIG . 3 . CASE I. Angle formed by two**secants**. Let the angle 0 ( Fig . 1 ) be formed by the cants OA ... Page 105

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**secant**. Let the angle 0 ( Fig . 3 ) be formed by the tangent OB and the**secant**OA . To prove 40 is measured by ( ADS — CES ) . Proof . Draw CS . = ZACS 20 + 2 CSO , § 145 ( the exterior of a △ is equal to the sum of the two opposite ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē acute angle adjacent angles altitude angle formed angles are equal base bisector bisects called centre chord circumference circumscribed coincide construct a square decagon diagonals diameter Draw equal respectively equiangular equiangular polygon equidistant equilateral polygon equilateral triangle exterior angle feet figure Find the area given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches intersecting isosceles triangle legs length line drawn line joining measured by arc middle points number of sides obtuse opposite sides parallel parallelogram perimeter perpendicular PROPOSITION prove Proof quadrilateral radii ratio rectangle regular inscribed regular polygon rhombus right angle right triangle SCHOLIUM secant segments similar polygons square equivalent straight angle subtended tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertices

### Popular passages

Page 46 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...

Page 69 - The exterior angles of a polygon, made by producing each of its sides in succession, are together equal to four right angles.

Page 187 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 64 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.

Page 201 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.

Page 215 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.

Page 161 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.

Page 135 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.

Page 156 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3.