## Elementary geometry |

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Side 109

If one angle of a triangle is equal to the sum of the other two , the greatest side is

locus of a point , given the sum or difference of its distances from two fixed lines .

If one angle of a triangle is equal to the sum of the other two , the greatest side is

**double**of the distance of its middle point from the opposite angle . 29 . Find thelocus of a point , given the sum or difference of its distances from two fixed lines .

Side 110

Produce a given straight line to such a distance that the square on the produced

part may be

line to such a distance that the square on the whole line may be

Produce a given straight line to such a distance that the square on the produced

part may be

**double**of the square on the given line . 40 . Produce a given straightline to such a distance that the square on the whole line may be

**double**of the ... Side 112

A medium of a triangle is the line drawn from an angle to the point of bisection of

the opposite side . 58 . The square on the base on an isosceles triangle is

the rectangle contained by either side , and the projection on it of the base . 59 .

A medium of a triangle is the line drawn from an angle to the point of bisection of

the opposite side . 58 . The square on the base on an isosceles triangle is

**double**the rectangle contained by either side , and the projection on it of the base . 59 .

Side 136

therefore the angle AOQ is

difference of the angles AOQ , QOB is

and ...

therefore the angle AOQ is

**double**of the angle OPA . Similarly the angle QOB is**double**of the angle OPB . Hence in figs . ( 1 and 2 ) the sum , or ( in fig . 3 ) thedifference of the angles AOQ , QOB is

**double**of the sum or difference of OP : Aand ...

Side 17

Shew how to find the sum and difference of two straight lines : and prove that

their sum and difference together are

lines . 11 . Given the sum and difference of two straight lines ; find the lengths of

the ...

Shew how to find the sum and difference of two straight lines : and prove that

their sum and difference together are

**double**of the greater of the two straightlines . 11 . Given the sum and difference of two straight lines ; find the lengths of

the ...

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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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