## Elementary geometry |

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Resultat 6-10 av 26

Side 96

If a straight line is divided internally or externally at any point , the sum of the

squares on the segments is

the line between the point of division and the middle point of the line * . Let AB be

...

If a straight line is divided internally or externally at any point , the sum of the

squares on the segments is

**double**the sum of the squares on half the line and onthe line between the point of division and the middle point of the line * . Let AB be

...

Side 97

... sides of the parallelogram , then , the difference of the parallelograms DO , BO

is

The diagonals of a parallelogram ABCD intersect in SECT . I . ] EXERCISES . :

... sides of the parallelogram , then , the difference of the parallelograms DO , BO

is

**double**of the triangle OAC . . . w . will be unes be drawn to in the diagonal of II .The diagonals of a parallelogram ABCD intersect in SECT . I . ] EXERCISES . :

Side 98

Shew that the sum of the squares on the lines joining the angular points of a

square to any point within it is

perpendiculars from that point on the sides . 14 . If the sides of a quadrilateral

figure be ...

Shew that the sum of the squares on the lines joining the angular points of a

square to any point within it is

**double**of the sum of the squares on theperpendiculars from that point on the sides . 14 . If the sides of a quadrilateral

figure be ...

Side 99

... CDF = E , and through B draw BFH parallel to AC , and draw CH parallel to DF

. FDCH will be the parallelogram required . Proof . If BD be joined , it will be clear

that the triangle BAC and the parallelogram FHCD are each of them

... CDF = E , and through B draw BFH parallel to AC , and draw CH parallel to DF

. FDCH will be the parallelogram required . Proof . If BD be joined , it will be clear

that the triangle BAC and the parallelogram FHCD are each of them

**double**of ... Side 105

... that is , the square on AK is equal to the rectangle ABxBK . Q . E . D .

EXERCISES . 1 . Construct a square

square equal to two , or three , or any number of given squares . 3 . Divide a

straight line into ...

... that is , the square on AK is equal to the rectangle ABxBK . Q . E . D .

EXERCISES . 1 . Construct a square

**double**of a given square . 2 . Construct asquare equal to two , or three , or any number of given squares . 3 . Divide a

straight line into ...

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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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