## Elementary geometry |

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Resultat 6-10 av 34

Side 96

If a straight line is

squares on the segments is double the sum of the squares on half the line and on

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 thesquares on the segments is double the sum of the squares on half the line and on

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

...

Side 97

The diagonals of a parallelogram

any point in the diagonal of a parallelogram : straight lines be drawn to the

angles , then the parallelogram will be

triangles .

The diagonals of a parallelogram

**divide**it into four equivalent triangles . 7 . If fromany point in the diagonal of a parallelogram : straight lines be drawn to the

angles , then the parallelogram will be

**divided**into two pairs of equivalenttriangles .

Side 102

Therefore VQ * = ABCDE , and the square described on VQ is the square

required * . PROBLEM V . To construct a rectilineal figure equal to. Remark . If the

given figure is not rectilineal , it cannot be

impossible ...

Therefore VQ * = ABCDE , and the square described on VQ is the square

required * . PROBLEM V . To construct a rectilineal figure equal to. Remark . If the

given figure is not rectilineal , it cannot be

**divided**into triangles : hence it isimpossible ...

Side 104

First , to

on AB ; bisect AC in E . Join BE ; produce EA to F , making EF = EB ; on AF

describe a square AFGH . AH and HB are the parts required , so that the

rectangle AB ...

First , to

**divide**it internally . T . . . . . . . . 11B Construction . Draw a square ACDBon AB ; bisect AC in E . Join BE ; produce EA to F , making EF = EB ; on AF

describe a square AFGH . AH and HB are the parts required , so that the

rectangle AB ...

Side 111

... drawn to the opposite angles of the square on AB , the difference of the

squares on these two lines will equal the difference of the squares on A Cand BC

. 54 . AB is

, & c .

... drawn to the opposite angles of the square on AB , the difference of the

squares on these two lines will equal the difference of the squares on A Cand BC

. 54 . AB is

**divided**into two unequal parts in II . ) MISCELLANEOUS THEOREMS, & c .

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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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