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RELFE BROTHERS EUCLID SHEETS.
PROPOSITIONS 1–26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS.
At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Let be the given straight line, and the given point in it, and
the given rectilineal angle.
It is required, at the given point in the given straight line to make an angle that shall be equal to the given rectilineal angle
In , take any points
make the triangle the sides of which shall be equal to the three straight lines
Then the angle be equal to
, so that
equal to the angle
are equal to
each to each, and the base
to the base ; therefore the angle is equal to the angle
Wherefore, at the given point in the given straight line
made equal to the given rectilineal angle
RELFE BROTHERS' EUCLID SHEETS.
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.
be the three given straight lines, of which any two whatever are greater than the third, namely, and
and greater than
It is required to make a triangle of which the sides shall be equal to
; then the triangle
shall have its sides equal to the three straight lines
; therefore also
is equal to
is equal to ;
therefore the three are respectively equal to the three,
; and therehas its three sides
equal to the three given
fore the triangle