## Elementary geometry |

### Inni boken

Side 71

All the points which satisfy a single given geometrical condition lie in general in a

line or lines : and this line , or these lines , are called the

the given condition . Hence we get the following definition of a

All the points which satisfy a single given geometrical condition lie in general in a

line or lines : and this line , or these lines , are called the

**locus**of the point underthe given condition . Hence we get the following definition of a

**locus**: Def . Side 72

In order that a line or group of lines A may be properly termed the

satisfying an assigned condition X , it is necessary and sufficient to demonstrate

the two following associated Theorems : If a point is on A , it satisfies X . If a point

...

In order that a line or group of lines A may be properly termed the

**locus**of a pointsatisfying an assigned condition X , it is necessary and sufficient to demonstrate

the two following associated Theorems : If a point is on A , it satisfies X . If a point

...

Side 73

The

lines , at right angles to one another , which bisect the angles made by the given

lines . Let AB , DC intersect in 0 ; it is required to find a point equally distant from ...

The

**locus**of a point equidistant from two intersecting straight lines is the pair oflines , at right angles to one another , which bisect the angles made by the given

lines . Let AB , DC intersect in 0 ; it is required to find a point equally distant from ...

Side 74

In the same manner every point in the bisector of any one of the four angles at O

is equally distant from AB and CD ; that is , the

two straight lines which intersect , is the bisectors of the angles between the ...

In the same manner every point in the bisector of any one of the four angles at O

is equally distant from AB and CD ; that is , the

**locus**of points equally distant fromtwo straight lines which intersect , is the bisectors of the angles between the ...

Side 75

( 7 ) Find part of the

subtend equal angles . ( 8 ) Find the

of a rectangle subtend supplementary angles . INTERSECTION OF Loci . When a

point ...

( 7 ) Find part of the

**locus**of points at which two adjacent sides of a squaresubtend equal angles . ( 8 ) Find the

**locus**of a point at which two adjacent sidesof a rectangle subtend supplementary angles . INTERSECTION OF Loci . When a

point ...

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### Vanlige uttrykk og setninger

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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