## Elements of Geometry and Trigonometry |

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**THEOREM**. The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short ...Page 36

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**THEOREM**. If the product of two quantities be equal to the product of two other quantities , two of them will be the extremes and the other two the means of a proportion . Let MxQ = Nx P ; then will M : N :: P : Q. For , if P have not ...Page 83

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**theorem**, we shall have AD DB :: AO : OC . But by hypothe- sis , we have AD : DB :: AE : EC : hence we must have AO : OC :: AE : EC , or AO : AE :: OC : EC ; an impossible result , since AO , the one antecedent , is less than its ...### 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