## Elements of Geometry |

### From inside the book

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**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 11

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**gle**DCB would be a right angle as well as BCE ; and a part would be equal to the whole . THEOREM . 52. If , from a point A ( fig . 31 ) , without a straight line DE , a Fig . 31 . perpendicular AB be drawn to that line , and also ... Page 13

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**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 19

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**gle**EFZ , will meet AB . 2. Let us suppose that the sum of the interior angles AEF + CFE is greater than two right angles ; if we produce AE to- ward B , and CF toward D , the sum of the four angles AEF , BEF , CFE , EFD , will be equal ... Page 21

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**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 ...### Other editions - View all

### 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