## A Text-book of Geometry |

### From inside the book

Results 1-5 of 10

Page 77

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**radii**; for they will coincide if one is applied to the other ; conversely , two equal circles have equal**radii**. Two circles are concentric if they have the same cer PROPOSITION I. THEOREM . genere . 227. The diameter of a circle is ... Page 80

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**radii**OR and OS the**radii**O'R ' and O ' .. A ROSA R'O'S ' , ( three sides of the one being equal to three sides of the ot ..20 = 20 ' , .. arc RS arc R'S ' , ( in equal © , equal △ at the centre intercept equal arc CONVERSELY : To ... Page 81

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**radii**OA , OF , and OB . Since Fis between A and B , OF will fall between OA and OB , and △ AOB be greater than △ AOF . Hence , in the AAOB and AOF , the**radii**OA and OB the**radii**OA and OF , but AOB is greater than △ AOF . .. AB ... Page 106

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**radii**gre OB , describe two arcs intersecting at R. Join OR . Then the line OR is the required . Proof . Since O and R are two points at equal dista H and B , they determine the position of a perpend the line HB at its middle point O ... Page 107

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**radii**greater than MK , describe two arcs intersecting at O. Draw CO , and produce it to meet AB at M. CM is the required . Proof . Since Cand O are two points equidistant from Hand K , they determine a 1 to HK at its middle point ...### 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.