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PROPOSITIONS 1—26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS.

PROPOSITION XXIII.

At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.

the given

Let be the given straight line, and the given point in it, and rectilineal angle.

It is required, at the given point in the given straight line that shall be equal to the given rectilineal angle

to make an angle

In,

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take any points

and join ; on

make the triangle

the sides of which shall be equal to the three straight lines

be equal to

to

and

to

Then the angle

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equal to the angle

Because

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to the base ; therefore the angle

are equal to

each to each, and the base is equal to the angle Wherefore, at the given point in the given straight line

is equal

, the angle

is

made equal to the given rectilineal angle

PROPOSITIONS 1—26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS.

PROPOSITION XXII.

To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third.

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be the three given straight lines, of which any two whatever are greater

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It is required to make a triangle of which the sides shall be equal to

to each.

each

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; then the triangle

make

; from the centre at the dis

where the circles cut each other, draw

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describe

to the points

shall have its sides equal to the three straight lines

Because the point

is the centre of the circle

therefore

is equal to ;

but

is equal to the straight line ; therefore

is the centre of the circle

; therefore also

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