## A Text-book of Geometry |

### From inside the book

Results 1-5 of 15

Page 76

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**subtends**two arcs whose sum is th ference ; thus , the chord AB ( Fig . 3 )**subtends**the sn AB and the larger arc BCDEA . If a chord and i spoken of , the less arc is meant unless it is otherwise . D A SEGMENT B QUADRANT 0 SEMICIRCLE N ... Page 79

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**subtend**equal angles at the centre . A R B Α R P P ' In the equal circles ABP and A'B'P ' let 20 = 20 . To prove Proof . arc RS : = arc R'S ' . Apply O ABP to © A'B'P ' , so that shall coincide with O ' . R will fall upon R ' , and S ... Page 80

George Albert Wentworth. 230. In the same circle , or equal circles chords

George Albert Wentworth. 230. In the same circle , or equal circles chords

**subtend**equal arcs ; CONVERSELY , equ are**subtended**by equal chords . A R B RA P P ' In the equal circles ABP and A'B'P ' , let ch chord R'S ' . To prove Proof ... Page 81

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**subtended**by the greater chord ; CONVERSELY , the greater chord**subtends**the greater arc . M F B A In the circle whose centre is 0 , let the arc AMB be greater than the arc AMF . To prove Proof . chord AB greater than chord AF . Draw ... Page 82

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**subtended**by it . E M 0 B S Let AB be the chord , and let the radius 0 . pendicular to AB at M. Το prove AM BM , and arc AS - arc BS . Proof . Draw OA and OB from O , the centre of t In the rt . A OAM and OBM the radius OA : and OM ...### Other editions - View all

### Common terms and phrases

AB² ABCD AC² 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.