## Elements of Geometry and Trigonometry |

### From inside the book

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**proportional**, their squares or cubes will also be**proportional**. Let and then will For since and or N m therefore , PROPOSITION XII . THEOREM . M : NP : Q , M2 : N2 : : P2 : Q2 M3 : N3 P3 : Q3 therefore , M2 : N ° :: P2 : Q ° and M3 ...Page 98

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**proportionally**in C and I ( Prop . XV . ) . But AC is the fifth part of AG , hence AI is the fifth part of AB , D M B Pr Secondly . Let it be proposed to divide the line AB into parts**proportional**to the given lines P , Q , R. Through A ...Page 99

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**proportional**required . F A E B D PROBLEM III . I PROBLEM IV . A BCICor . A third**proportional**to two given lines A , B , may be found in the same manner , for it will be the same as a fourth**proportional**to the three lines A , B , B ...### Contents

Ratios and Proportions | 34 |

The Circle and the Measurement of Angles | 41 |

Problems relating to the First and Third Books | 57 |

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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 logarithm M.
M. Sine 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism vertex