## Elements of Geometry |

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Page vi

This work is divided into eight sections ,

This work is divided into eight sections ,

**four**of which treat of plane geometry , and**four**of solid geometry . The first section , entitled first principles , & c.contains the properties of straight lines which meet those of ... Page xiv

If we multiply the proportion A : B :: C : D by A : B :: C : D we shall have ( II ) A : B2 :: C2 : D , whence it follows , that the squares of

If we multiply the proportion A : B :: C : D by A : B :: C : D we shall have ( II ) A : B2 :: C2 : D , whence it follows , that the squares of

**four**proportional quantities form a new proportion . By multiplying the proportion A : B2 ... Page 2

The polygon of three sides is the most simple of these figures , and is called a triangle ; that of

The polygon of three sides is the most simple of these figures , and is called a triangle ; that of

**four**sides is called a quadrilateral ; that of five sides , a pentagon ; that of six , a hexagon , & c . Fig . 7 . 15. Page 4

Take the

Take the

**four**distances CA , CB , GE , GF , equal to each other , the distance AB will be equal to the distance EF , and the line EF may be applied to AB , so that the point E will fall upon A , and the point F upon B. These two lines ... Page 6

The

The

**four**angles , formed about a point by two straight lines which cut each other , are together equal to**four**right angles ; for the angles ACE , BCE , taken together , are equal to two right angles ; also the other angles ACD ...### What people are saying - Write a review

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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