## Elements of Geometry |

### From inside the book

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... angles DCE , BCE . Fig . 3 . Fig . 4 . Fig . 5 . 10. When a straight line AB ( fig . 3 ) meets another straight line CD in such a manner that the

... angles DCE , BCE . Fig . 3 . Fig . 4 . Fig . 5 . 10. When a straight line AB ( fig . 3 ) meets another straight line CD in such a manner that the

**adjacent angles**BAC , BAD , are equal , each of these angles is called a right angle , and ... Page 3

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**angles**not**adjacent**, as AC ( fig . 42 ) . 19. An equilateral polygon is one which has all its sides equal ; an equiangular polygon is one which has all its**angles**equal . 20. Two polygons are equilateral with respect to each other ... Page 4

... angles are equal . Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH ...

... angles are equal . Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH ...

**adjacent angles**ACD , BCD , which , taken together , are equal to two right angles . Demonstration . At the point C ... Page 5

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**adjacent angle**DCB , and that they are both right angles . But , since the angle ACD is a right angle , it fol- lows that its**adjacent angle**ACE is also a right angle ; therefore the angle ACE = ACD , and AB is perpendicular to DE . 31 ... Page 6

Adrien Marie Legendre. Fig . 20 . THEOREM . 33. If two

Adrien Marie Legendre. Fig . 20 . THEOREM . 33. If two

**adjacent angles**ACD , DCB ( fig . 20 ) , are together equal to two right angles , the two exterior sides AC , CB , are in the same straight line . Demonstration . For if CB is not ...### Other editions - View all

### 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