## Elementary geometry |

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Resultat 1-5 av 45

Side 3

two Theorems that are independent of one another , and two others that are

always and necessarily true if the former are true ; consequently it will never be ...

**Hence**the four associated Theorems ( i ) ( ii ) ( iii ) ( iv ) resolve themselves intotwo Theorems that are independent of one another , and two others that are

always and necessarily true if the former are true ; consequently it will never be ...

Side 9

The bisector of an angle is the straight line that divides it into two equal angles .

Def . 14 . When one straight line stands upon another straight line and makes the

adjacent angles equal , each of the angles is called a right angle . OBS .

The bisector of an angle is the straight line that divides it into two equal angles .

Def . 14 . When one straight line stands upon another straight line and makes the

adjacent angles equal , each of the angles is called a right angle . OBS .

**Hence**... Side 35

but DGF is supplementary to DGE , that is , to ACB , and therefore the angle Fis

supplementary to the angle C . Q . E . D . COR .

all respects( 3 - 2 SECT . II . ] 35 : TRIANGLES . Part. En. Let ABC, DEF be the ...

but DGF is supplementary to DGE , that is , to ACB , and therefore the angle Fis

supplementary to the angle C . Q . E . D . COR .

**Hence**the triangles are equal inall respects( 3 - 2 SECT . II . ] 35 : TRIANGLES . Part. En. Let ABC, DEF be the ...

Side 36

right angles or obtuse angles . For then the remaining angles must be acute , and

therefore cannot be supplementary , and must therefore be equal by the ...

**Hence**the triangles are equal in all respects( 1 ) If the two angles given equal areright angles or obtuse angles . For then the remaining angles must be acute , and

therefore cannot be supplementary , and must therefore be equal by the ...

Side 46

corresponding angles are equal , and the interior angles on the same side are

supplementary ; and conversely . THEOREM 24 . Straight lines which are parallel

to ...

**Hence**if two parallel straight lines are intersected by a third straight line , thecorresponding angles are equal , and the interior angles on the same side are

supplementary ; and conversely . THEOREM 24 . Straight lines which are parallel

to ...

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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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