Elements of Geometry |
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Page 6
... angle ACD , and there will remain the part DCB equal to the whole DCE , which is impossible ; therefore CB is the ... ACB , BCD , DCE , ECF , FCA , will be equal to four right angles . For , if at the point C , four right angles be formed by ...
... angle ACD , and there will remain the part DCB equal to the whole DCE , which is impossible ; therefore CB is the ... ACB , BCD , DCE , ECF , FCA , will be equal to four right angles . For , if at the point C , four right angles be formed by ...
Page 10
... angle BAD = DAC , and that the angle BDA = ADC ; therefore these two last are right angles . Hence a straight line ... ACB ( fig . 29 ) , the side AC will be equal to the side AB . For , if these sides are not equal , let AB be the greater .
... angle BAD = DAC , and that the angle BDA = ADC ; therefore these two last are right angles . Hence a straight line ... ACB ( fig . 29 ) , the side AC will be equal to the side AB . For , if these sides are not equal , let AB be the greater .
Page 18
... ACB , DAE , consid- ered with reference to the line CAD , are equal , being ... angle ; for if there were two , the third angle must be nothing ; still less then can a ... angles , so that if a right angle be 18 Elements of Geometry .
... ACB , DAE , consid- ered with reference to the line CAD , are equal , being ... angle ; for if there were two , the third angle must be nothing ; still less then can a ... angles , so that if a right angle be 18 Elements of Geometry .
Page 30
... angle ACB is equal to the angle DCE , these two angles may be placed the one upon the other , and as their sides are equal , it is evident , that the point A will fall upon D , and the point B upon E. But in this case the arc AB must ...
... angle ACB is equal to the angle DCE , these two angles may be placed the one upon the other , and as their sides are equal , it is evident , that the point A will fall upon D , and the point B upon E. But in this case the arc AB must ...
Page 31
... angles ACB , DCE . 121. Scholium . Reciprocally , if the arcs AB , DE , are to each other , as two entire numbers , the angles ACB , DCE , will be to each other , as the same numbers , and we shall have always ACB : DCE :: AB : DE ; for ...
... angles ACB , DCE . 121. Scholium . Reciprocally , if the arcs AB , DE , are to each other , as two entire numbers , the angles ACB , DCE , will be to each other , as the same numbers , and we shall have always ACB : DCE :: AB : DE ; for ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence