## Elements of Geometry and Trigonometry |

### From inside the book

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**secant**line : AGO , DÓG , are alternate angles ; and so also are the angles COG , BGO . Alternate exterior angles lie without the parallels , and on dif- ferent sides of the**secant**line : EGB , COF , are alternate exte- rior angles ... Page 27

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**secant**line . The sum OGB + GOD is equal to two right angles . But the sum OGB + OGA is also equal to two right angles ( Prop . I. ) . Taking from each , the angle OGB , and there remains CGA GOD . In the same manner we may prove that ... Page 42

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**secant**is a line which meets the circum- ference in two points , and lies partly within and partly without the circle . AB is a**secant**. 8. A tangent is a line which has but one point in common with the circumference . CD is a ... Page 48

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**secant**. PROPOSITION X. THEOREM . Two parallels intercept equal arcs on the circumference . There may be three cases . H DIN M PB First . If the two parallels are se- cants , draw the radius CH perpendicu- lar to the chord MP . It will ... Page 56

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**secants**, is measured by half the diffe- rence of the arcs included between its sides . Let AB , AC , be two**secants**: then will the angle BAC be measured by half the difference of the arcs BEC and DF . Draw DE parallel to AC : then ...### Other editions - View all

### Common terms and phrases

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