## Elements of Geometry and Trigonometry |

### From inside the book

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**radii**of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any part of a circumference . 5. A CHORD is a straight line joining the extremities of an arc . Any chord belongs to two ... Page 63

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**radii**CD and OG . The triangles ACD and EOG have all the sides of the one equal to the cor- responding sides of the other ; they are , therefore , equal in all their parts : hence , the angle ACD is equal to EOG . If , now , the sector ... Page 64

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**radii**CA and CB . Then , the right - angled triangles CDA and CDB will have the hypothenuse CA equal to CB , and the side CD common ; the triangles are , therefore , A B D G equal in all their parts : hence , AD is equal to DB . Again ... Page 71

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**radii**. Let the circumferences , whose centres are C and D , intersect at A : then will CD be less than the sum , and greater than the difference of the**radii**of the two circles . For , draw AC and AD , forming the triangle ACD . Then ... Page 72

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**radii**, one will be tangent to the other internally . Let C and D be the centres of two circles , and let the distance between these centres be equal to the difference of the**radii**: then will the one be tangent to the other in ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence

### Popular passages

Page 28 - If two triangles have two sides of the one equal to two sides of the...

Page 100 - The area of a triangle is equal to half the product of its base by its altitude.

Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.

Page 59 - A chord is a straight line joining the extremities of an arc.

Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.

Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.

Page 123 - Similar triangles are to each other as the squares of their homologous sides.

Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...