## Elements of Geometry and Trigonometry |

### From inside the book

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Page 139

... angle ASD ASC ( Book I. Prop . IX . Sch . ) . Adding BSD = BSC , we shall have ASD + BSD or ASB < ASC + BSC . PROPOSITION XX . THEOREM . The sum of the plane angles which form a

... angle ASD ASC ( Book I. Prop . IX . Sch . ) . Adding BSD = BSC , we shall have ASD + BSD or ASB < ASC + BSC . PROPOSITION XX . THEOREM . The sum of the plane angles which form a

**solid angle**is always less than four right angles . Cut the ...Page 141

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**solid angles**, these angles will be equal , and they will coincide when applied the one to the other . We have ... angle , formed by the plane angles A , B , C , D , E , and another**solid angle**, formed by the same angles in an inverse ...Page 204

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**solid angles**at their vertices . From this , some consequences are deduced . First . Two triangular spherical ... angle of the tri - rectangular pyramid is formed by three planes at right angles to each other : this angle , which may be ...### 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