## Elements of Geometry and Trigonometry |

### From inside the book

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Page 41

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**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 chord , or subtense of an arc , is the straight line FG , which joins its ... Page 43

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**radii**We shall then have AD AC + CD ( Book I. Prop . VII . * ) ; or AD AB . Cor . Hence the greatest line which can be inscribed in a circle is its diameter . PROPOSITION III . THEOREM . A straight line cannot meet the circumference of ... Page 44

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**radii**AC , EO , to be equal , if the chord AD is equal to the chord EG , the arcs AMD , ENG will also be equal . For , if the**radii**CD , OG , be drawn , the triangles ACD , EOG , will have all their sides equal , each to each , namely ... Page 45

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**radii**CA , CB . Then the two right angled triangles ADC , CDB , will have AČ = CB , and CD com- mon ; hence , AD is equal to DB ( Book I. Prop . XVII . ) . Again , since AD , DB , are equal , CG is a perpendicular erected from the mid ... Page 47

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**radii**CA , CD . D M In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is equal to the side DG , the half of DE : hence the triangles are equal , and CF is equal to CG ...### 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 convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines 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 sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex