## Elementary geometry |

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Side 86

All rectangles being identically equal which have two adjoining sides equal to

two given straight lines , any such rectangle is spoken of as the

given ...

All rectangles being identically equal which have two adjoining sides equal to

two given straight lines , any such rectangle is spoken of as the

**rectangle****contained**by those lines . In like manner , any square whose side is equal to agiven ...

Side 87

The

Part . En . Let A and BC be the two given lines , of which BC is divided into any ...

The

**rectangle contained**by two given lines is equal to the sum of the**rectangles****contained**by one of them and the several parts into which the other is divided .Part . En . Let A and BC be the two given lines , of which BC is divided into any ...

Side 88

therefore the

divided into two parts , the

parts is equal ...

therefore the

**rectangle contained**by A and BC is equal to the**rectangles****contained**by A and BD , A and DE , A and EC * . Cor . 1 . If a straight line isdivided into two parts , the

**rectangle contained**by the whole line and one of theparts is equal ...

Side 89

Then the figures AL , PH , LE , MF are rectangles by construction ; and PH , MF

are the squares on PB , AP respectively ; and AL , LE are each of them the

figures , it ...

Then the figures AL , PH , LE , MF are rectangles by construction ; and PH , MF

are the squares on PB , AP respectively ; and AL , LE are each of them the

**rectangle contained**by AP , PB . Hence , since ADEB is made up of these fourfigures , it ...

Side 90

And AE is less than MF + HP by MP + HF ; that is , the square on AB is equal to

the squares of AP , PB diminished by twice the

THEOREM 8 . The difference of the squares on two lines is equal to the rectangle

...

And AE is less than MF + HP by MP + HF ; that is , the square on AB is equal to

the squares of AP , PB diminished by twice the

**rectangle contained**by AP , PB .THEOREM 8 . The difference of the squares on two lines is equal to the rectangle

...

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ABCD adjacent angle ABC angle APB angle BAC base bisect bisector Book called centre chord circle circumference coincide College common Constr construct converse Crown 8vo diagonals diameter difference distance divided double draw drawn Edition ELEMENTARY equal angles Euclid Examples exterior angle extremities fall figure Find follows four Geometry given angle given line given point given straight line greater half Hence Illustrations inscribed interior intersect isosceles triangle Join length less Let ABC line drawn locus magnitudes measure meet middle point minor arc opposite sides parallel parallelogram pass perpendicular placed polygon PROBLEM produced Professor Proof proportional quadrilateral radius ratio rectangle contained rectilineal figure regular required to prove respectively right angles School segment Shew sides similar Similarly square supplementary tangent THEOREM third touch triangle ABC unequal

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