## Elements of Geometry and Trigonometry |

### From inside the book

Results 6-10 of 32

Page 41

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**included**between an arc and its chord . 5. A sector is the part of the circle**included**between an arc DE , and the two radii CD , CE , drawn to the extremities of the arc . 6. A straight line is said to be inscribed in a circle , when ... Page 54

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**included**between its sides . Let BAD be an inscribed angle , and let us first suppose that the centre of the cir- cle lies within the angle BAD . Draw the diameter AE , and the radii CB , CD . The angle BCE , being exterior to the ... Page 55

... two right angles . PROPOSITION XIX . THEOREM . The angle formed by two chords , which intersect each other , is measured by half the sum of the arcs

... two right angles . PROPOSITION XIX . THEOREM . The angle formed by two chords , which intersect each other , is measured by half the sum of the arcs

**included**between its sides . Let AB , CD , be two chords intersecting each BOOK III . 55. Page 56

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**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 will the arc EC be equal to DF , and the angle BDE equal to ... Page 57

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**included**between its sides . PROBLEMS RELATING TO THE FIRST AND THIRD BOOKS . PROBLEM I. To divide a given straight line into two equal parts . Let AB be the given straight line . From the points A and B as centres , with a radius ...### 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 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 produced proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE 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