## An Elementary Geometry |

### From inside the book

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William Frothingham Bradbury. BOOK I. ANGLES , LINES , POLYGONS . ANGLES . DEFINITIONS . 1. An Angle is the difference in direction of two lines . If the lines meet , the point of meeting , B , is called the vertex ; and the

William Frothingham Bradbury. BOOK I. ANGLES , LINES , POLYGONS . ANGLES . DEFINITIONS . 1. An Angle is the difference in direction of two lines . If the lines meet , the point of meeting , B , is called the vertex ; and the

**lines A B**, B C ... Page 5

... line DB meet the two

... line DB meet the two

**lines**,**AB**, BC , so as to make ABD + DBC = two right angles : then AB and BC form a straight line . A- B D E C For if A B and B C do not form a straight line , draw BE so that A B and B E shall form a straight line ... Page 6

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**Lines**are such as have the same direction ; as**A B**and CD .**A- -B**C- -D 14. Corollary . Parallel**lines**can never meet . For , since parallel**lines**have the same direction , if they coincided at one point , they would coincide throughout ... Page 7

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**line**cut two parallel**lines**, 1st . The opposite external and internal angles are equal . 2d . The alternate internal angles are equal . 3d . The internal angles on the same side are supplements of each other . Let EF cut the two parallels ... Page 8

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**lines A B**and CD so as to make E G B G H D , or AGH GHD , or BGH and GHD supplements of each other ; then A B is parallel to CD . For , if through the point G a line E G A B H D F C is drawn parallel to CD , it will make the opposite ...### Other editions - View all

### Common terms and phrases

A B C A B D ABCD adjacent adjacent angles altitude angle ABC apothem base and altitude centre chord circ circumference cone construct the triangle convex surface Corollary cylinder diagonals diameter distance divided dodecagon equal altitudes equally distant equilateral feet frustum given angle given circle given line given point given side half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining lines A B measured by half mutually equiangular number of sides opposite sides parallelogram parallelopiped perimeter perpendicular plane parallel quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VII trapezoid triangle ABC triangles are equal vertex