Pure Mathematics Including Arithmetic Algebra Geometry And Plane Trigonometr

Cover Pure Mathematics Including Arithmetic Algebra Geometry And Plane Trigonometr
Pure Mathematics Including Arithmetic Algebra Geometry And Plane Trigonometr
Edward Atkins
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Proof. — Because ABC is a CBE is equal to the angle EBA C the angle CD as ra- dius.
Bisect FG inH.
straight line, (Def. 10).
Also, because ABD is a straight line, the angle DBE is equal to the angle EBA (Def. 10).
Therefore the angle DBE is equal to the angle CBE. The less to the greater; which is impossible.
Therefore two straight lines cannot have a common seg- ment.
Proposition 12. — Problem.
To draw a straight line perpendicular to a given straight line of unlimited lengthy from, a given po
...int without it.
Let AB be the given straight line, which may be produced to any length both ways, and let C be a point without it.
It is requii-ed to draw from the point C, a straight line perpendicular to AB.
Construction. — Take any point D upon the other side of AB.
From the centre C, at the distance CD, describe the circle EGF, meet- ing AB in F and G (Post. 3). Bisect FG in H (I. 10). Join CF, CH, CG. Then CH shall he jyerpetulicular to AB. Proof* — Because FH is equal to HG (Const.


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