## Elements of Geometry and Trigonometry |

### From inside the book

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**diameter**. From the definition of a circle , it follows that all the radii are equal ; that all the**diameters**are equal also , and each double of the radius . 3. A portion of the circumference , such as FHG , is called an arc . The ... Page 42

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**diameter**divides the circle and its circumference into two equal parts . Let AEDF be a circle , and AB a**diameter**. Now , if the figure AEB be applied to AFB , their common base AB retaining its position , the curve line AEB must fall ... Page 43

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**diameter**. Let AD be any chord . Draw the radii CA , CD , to its extremities . We shall then have AD AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Cor . Hence the greatest line which can be inscribed in a circle is its**diameter**... Page 44

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**diameters**AB , EF , are equal , the semi- circle AMDB may be applied M H N DO • exactly to the semicircle ENGF , and the curve line AMDB will coincide entirely with the curve line ENGF . But the part AMD is equal to the part ENG , by ... Page 54

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**diameter**AE , and the radii CB , CD . The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles , the angle CAB ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex