Elements of Geometry and Trigonometry |
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Page 14
... angle ACD + the angle DCB , be equal to two right angles . At the point C , erect CE perpendicular to AB . The angle ... A C B angle ACD must be equal to its adjacent an- gle DCB , and both of them must be right angles ( Def . 10 ...
... angle ACD + the angle DCB , be equal to two right angles . At the point C , erect CE perpendicular to AB . The angle ... A C B angle ACD must be equal to its adjacent an- gle DCB , and both of them must be right angles ( Def . 10 ...
Page 16
... angle ECB be equal to the angle ACD , and the angle ACE to the angle DCBВ ... ACB , BCD , A DCE , ECF , FCA , will be equal to four right angles : for ... ACB , BCD , DCE , ECF , FCA . D C F E PROPOSITION V. THEOREM . If two ...
... angle ECB be equal to the angle ACD , and the angle ACE to the angle DCBВ ... ACB , BCD , A DCE , ECF , FCA , will be equal to four right angles : for ... ACB , BCD , DCE , ECF , FCA . D C F E PROPOSITION V. THEOREM . If two ...
Page 21
... angle ACB ; then will the side AC be equal to the side AВ . 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 ...
... angle ACB ; then will the side AC be equal to the side AВ . 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
... 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 ...
... 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
... angles will be equal . Let BAC and DEF be the two angles , having AB ... angle DEF is equal to H G A -C E F DGC ( Prop . XX . Cor . 3. ) ; and since ... ACB ( Prop . XX . Cor . 3. ) ; in like manner , since AE , CB , are parallel ...
... angles will be equal . Let BAC and DEF be the two angles , having AB ... angle DEF is equal to H G A -C E F DGC ( Prop . XX . Cor . 3. ) ; and since ... ACB ( Prop . XX . Cor . 3. ) ; in like manner , since AE , CB , are parallel ...
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Common terms and phrases
adjacent altitude angle ACB 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 equal angles 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 parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex