## Elements of Geometry and Trigonometry |

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Page 51

... angles contained by the radii will also be equal . Let C and C be the centres of equal circles , and the

... angles contained by the radii will also be equal . Let C and C be the centres of equal circles , and the

**angle ACB**= DCE . First . Since the**angles ACB**, DCE , are equal , they may be placed upon each other ; and since their sides are ...Page 52

... angle M , which may serve as a common measure , is contained times in the

... angle M , which may serve as a common measure , is contained times in the

**angle ACB**, and 4 times in DCE M E The seven partial angles ACm , mCn , nCp , & c . , into which ACB is divided , being each equal to any of the four partial ...Page 53

...

...

**angle ACB**: angle ACI :: arc AB arc AI . Comparing these two proportions with each other , we see that the antecedents are the same : hence , the conse- quents are proportional ( Book II . Prop . IV . ) ; and thus we find the angle ACD ...### 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