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 ; there- fore CB is the ... ACB , BCD , DCE , ECF , FCA , will be equal to four right angles . For if , at the point C , four right angles ...
... angle ACD , and there will remain the part DCB equal to the whole DCE , which is impossible ; there- fore CB is the ... ACB , BCD , DCE , ECF , FCA , will be equal to four right angles . For if , at the point C , four right angles ...
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 ...
... 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 ...
Page 13
... angles is equal to two right angles . Demonstration . Let ABC ( fig . 35 ) be the proposed triangle , Fig . 35 in which we suppose * that AB is the greatest side , and BC the least , and that , consequently , ACB is the greatest angle ...
... angles is equal to two right angles . Demonstration . Let ABC ( fig . 35 ) be the proposed triangle , Fig . 35 in which we suppose * that AB is the greatest side , and BC the least , and that , consequently , ACB is the greatest angle ...
Page 14
... angle A is common , and the side AC = AB , and AK = AI . There- fore the third side CK is equal to the third BI ... ACB , and the angle KB'C ' = CAI . It hence follows , 1. that the angle AC'B ' , designated by C ' , is composed of ...
... angle A is common , and the side AC = AB , and AK = AI . There- fore the third side CK is equal to the third BI ... ACB , and the angle KB'C ' = CAI . It hence follows , 1. that the angle AC'B ' , designated by C ' , is composed of ...
Page 32
... 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 ...
... 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 ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition pyramid S-ABC radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence