Elements of Geometry |
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Page 6
... gles , ACB , BCD , DCE , ECF , FCA , will be equal to four right angles . For if , at the point C , four right angles be formed by two lines perpendicular to each other , they will comprehend the same space as the successive angles ...
... gles , ACB , BCD , DCE , ECF , FCA , will be equal to four right angles . For if , at the point C , four right angles be formed by two lines perpendicular to each other , they will comprehend the same space as the successive angles ...
Page 13
... gles being equal ( 36 ) , AG = DF ; and , by hypothesis , DFAC ; whence AG AC . But AG cannot be equal to AC ( 52 ) ; therefore it is impossible that BC should be unequal to EF , that is , it is equal to it , and the triangle ABC is ...
... gles being equal ( 36 ) , AG = DF ; and , by hypothesis , DFAC ; whence AG AC . But AG cannot be equal to AC ( 52 ) ; therefore it is impossible that BC should be unequal to EF , that is , it is equal to it , and the triangle ABC is ...
Page 21
... gles ( 76 ) , are equal ; also , since the straight lines EG , FH , are perpendicular to the same straight line AB , and consequently parallel to each other , the angles EHF , HEG , considered with reference to the parallels GE , FH ...
... gles ( 76 ) , are equal ; also , since the straight lines EG , FH , are perpendicular to the same straight line AB , and consequently parallel to each other , the angles EHF , HEG , considered with reference to the parallels GE , FH ...
Page 42
... gles of a triangle , meet in the same point . PROBLEM . Fig . 88 , 89 . 155. Upon a given straight line AB ( fig . 88 , 89 ) to describe a segment capable of containing a given angle C , that is , a segment such , that each of the ...
... gles of a triangle , meet in the same point . PROBLEM . Fig . 88 , 89 . 155. Upon a given straight line AB ( fig . 88 , 89 ) to describe a segment capable of containing a given angle C , that is , a segment such , that each of the ...
Page 48
... gles ABCD , AEHD , have the same altitude AD ; they are , con- sequently , to each other as their bases AB , AE . Likewise the two rectangles AEHD , AEGF , have the same altitude AE ; these are therefore to each other as their bases AD ...
... gles ABCD , AEHD , have the same altitude AD ; they are , con- sequently , to each other as their bases AB , AE . Likewise the two rectangles AEHD , AEGF , have the same altitude AE ; these are therefore to each other as their bases AD ...
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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 construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces 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 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