## Elements of Geometry and Trigonometry |

### From inside the book

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**angle**ECB be equal to the**angle**ACD , and the**angle**ACE to the**angle**DCB ...**ACB**, BCD , DCE , ECF , FCA , will be equal to four right**angles**: for , if ...**ACB**, BCD , DCE , EČF , FCA . per- PROPOSITION V. THEOREM . T E If two ... Page 21

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**angle ACB**; then will the side AC be equal to the side AB . D For , if these sides are not equal , suppose AB to be ... angle B equal to the**angle ACB**, by hypothesis ; B and the side BC common : therefore , the two triangles , BDC ... Page 22

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**angle ACB**= BCF ( Prop . V. Cor . ) . But the**angle ACB**is a right angle , by hypothesis ; therefore , BCF must likewise be a right angle . But if the adja- cent angles BCA , BCF , are together equal to two right angles , ACF must be ... Page 29

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**angles**will be equal . Let BAC and DEF be the two**angles**, having AB ...**angle**DGC is equal to BAC ; hence the**angle**DEF is equal to BAC ( Ax . 1 ...**ACB**( Prop . XX . Cor . 3. ) ; in like manner , since AE , CB , are parallel ... 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 ...### Other editions - View all

### 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 convex surface Cosine 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex