## Elements of Geometry |

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In general , A ?, being an abbreviation of AX A , indicates the second power or square of A. VĀ indicates the square root of A , or the number which , being multiplied by itself ,

In general , A ?, being an abbreviation of AX A , indicates the second power or square of A. VĀ indicates the square root of A , or the number which , being multiplied by itself ,

**produces**the number represented by A. A , being an ... Page 2

5 ) , when , being situated in the same plane , and

5 ) , when , being situated in the same plane , and

**produced**ever so far both ways , they do not meet . 13. A plane figure is a plane terminated on all sides by lines . If the lines are straight , the space which they contain is Fig . Page 5

Now let us suppose , if it be possible , that the lines , when

Now let us suppose , if it be possible , that the lines , when

**produced**, separate from each other at a point C , the one becoming CD and the other CE . At the point C , let CF be drawn , so as to make the angle ACF a right angle ... Page 6

For if CB is not the line AC

For if CB is not the line AC

**produced**, let CE be that line**produced**; then , ACE being a straight line , the angles ACD , DCE , are together equal to two right angles ( 28 ) ; but , by hypothesis , the angles ACD , DCB , are together ... Page 8

24 ) , within a triangle ABC , there be drawn straight lines OB , OC , to the extremities of BC , one of its sides , the sum of these lines will be less than that of AB , AC , the two other sides . Demonstration . Let BO be

24 ) , within a triangle ABC , there be drawn straight lines OB , OC , to the extremities of BC , one of its sides , the sum of these lines will be less than that of AB , AC , the two other sides . Demonstration . Let BO be

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### Common terms and phrases

ABC fig ABCD adjacent altitude applied base called centre chord circ circle circumference circumscribed common cone consequently construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces feet figure follows formed four give given greater half hence inclination inscribed intersection isosceles join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM produced proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment similar solid angle Solution sphere spherical square straight line suppose surface taken tangent THEOREM third triangle ABC vertex vertices whence