## Elementary geometry |

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Resultat 1-5 av 23

Side 78

( 1 ) It is required to draw a line to

angles with two given intersecting lines . Let O be the given point , AB , AC the

given lines . We reason as follows ( analysis ) : suppose POQ were the line

required ...

( 1 ) It is required to draw a line to

**pass**through a given point and make equalangles with two given intersecting lines . Let O be the given point , AB , AC the

given lines . We reason as follows ( analysis ) : suppose POQ were the line

required ...

Side 97

Of all triangles having the same vertical angle , and whose bases

given point , the least is that whose base is bisected in that point . 6 . The

diagonals of a parallelogram divide it into four equivalent triangles . 7 . If from any

point ...

Of all triangles having the same vertical angle , and whose bases

**pass**through agiven point , the least is that whose base is bisected in that point . 6 . The

diagonals of a parallelogram divide it into four equivalent triangles . 7 . If from any

point ...

Side 109

... construct an equilateral triangle so that two of its sides shall

given points , and the third shall be in the given straight line . 31 . Construct an

isosceles triangle having the angle at the vertex double of the angles at the base

.

... construct an equilateral triangle so that two of its sides shall

**pass**through thegiven points , and the third shall be in the given straight line . 31 . Construct an

isosceles triangle having the angle at the vertex double of the angles at the base

.

Side 126

The straight line drawn perpendicular to a chord of a circle through its middle

point

The straight line drawn perpendicular to a chord of a circle through its middle

point

**passes**through the centre of the ... The locus of the centres of all circles that**pass**through twò given points is the straight line that bisects at right angles the ... Side 129

it is required to prove that one circle , and only one , can be drawn to

through A , B , C . Proof . Because the locus of the centres of all circles A that

Cor . ) ...

it is required to prove that one circle , and only one , can be drawn to

**pass**through A , B , C . Proof . Because the locus of the centres of all circles A that

**pass**through A and B is a straight line that bisects AB at right angles ; ( 111 . 8 ,Cor . ) ...

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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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