## Elements of Geometry and Trigonometry |

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**proportional**, their squares or cubes will also be**proportional**. M : NP : Q , M2 : N2 :: P2 : Q2 M3 : N3 :: P3 : Q3 Let then will and For , or , and M2 × Q2 = N2 × P2 , MxQ = Nx P , since M : N :: P : Q M3x QN3x P3 , therefore , M2 ...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 , Secondly . Let it be pro- posed to divide the line AB into parts**proportional**to the given lines P , Q , R. Through A , draw ...Page 99

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**proportional**required . Cor . 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. PROBLEM III . To find a mean**proportional**...### 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