## A Text-book of Geometry |

### From inside the book

Results 11-15 of 16

Page 87

...

...

**bisects**the chord and its subtended arc ) . CASE II . When AB and CD are secants . Fig . 2 . 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 ... Page 102

... the hypotenuse of a rt . A , to the vertex of the rt . 4 ,

... the hypotenuse of a rt . A , to the vertex of the rt . 4 ,

**bisects**the right angle . HINT . Describe a circle upon the hypotenuse as diameter . PROPOSITION XIX . THEOREM . 269. An angle formed by 102 BOOK II . PLANE GEOMETRY . Page 108

...

...

**bisect**the line AB . Construction . From A and B as centres , with equal radii greater than AB , describe arcs intersecting at Cand E. Join CE . Then the line CE**bisects**AB . Proof . C and E are two points equidistant from A and B ... Page 109

...

...

**bisect**the arc ACB . Construction . Draw the chord AB . From A and B as centres , with equal radii greater than AB ...**bisects**the arc of the chord . $ 234 Q. E. F. Ex . 91. To construct a circle having a given radius and passing ... Page 110

...

...

**bisect**AEB . Construction . From E as a centre , with any radius , as EA , describe an arc cutting the sides of ...**bisects**the E. Proof . In the A AEC and BEC and EC - EC . = AE BE , and AC = BC , Cons . Iden . = § 160 ..A AEC A ...### Other editions - View all

### Common terms and phrases

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

### Popular passages

Page 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 144 - The areas of two triangles which have 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 130 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.

Page 128 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.

Page 211 - 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 157 - 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 152 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 187 - ... upon the sum of two straight lines is equivalent to the sum of the squares described on the two lines plus twice their rectangle. Note. By the "rectangle of two lines" is here meant the rectangle of which the two lines are the adjacent sides.

Page 136 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

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.