## Elements of Geometry and Trigonometry |

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Page 59

... angle DAB will be equal to the

... angle DAB will be equal to the

**given angle**K. For , the two arcs BD , LI , have equal radii , and equal chords ; hence they are equal ( Prop . IV . ) ; therefore the angles BAD , IKL , measured by them , are equal . PROBLEM V. To divide a ...Page 60

... angles of a triangle being given , to find the third . Draw the indefinite line DEF ; at any point as E , make the an- gle DEC equal to one of the

... angles of a triangle being given , to find the third . Draw the indefinite line DEF ; at any point as E , make the an- gle DEC equal to one of the

**given angles**, and the angle CEH equal to the other : the remaining angle HEF will be IC the ...Page 65

... angle ADO = AFO ; hence the third angle AOD is equal to the third AOF ( Book I. Prop . XXV . Cor . 2. ) . Moreover , the side AO is com- mon to the two triangles AOD , AOF ; and the angles ...

... angle ADO = AFO ; hence the third angle AOD is equal to the third AOF ( Book I. Prop . XXV . Cor . 2. ) . Moreover , the side AO is com- mon to the two triangles AOD , AOF ; and the angles ...

**given angle**were a right angle BOOK III . 65.### Contents

BOOK | 7 |

Problems relating to the First and Third Books 57 | 57 |

BOOK IV | 68 |

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### 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 consequently convex surface cosine Cotang 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex