Plane And Solid Geometry

Cover Plane And Solid Geometry
Plane And Solid Geometry
James Howard Gore
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1. To construct a right triangle, given an acute angle and the base ; given an acute angle and the hypotenuse.
2. To divide an angle into four equal parts.
3. Given an angle, to construct its complement ; to construct its sup- plement. See 40, 41.
PROPOSITION XIX. PROBLEM. 188. Given two angles of a triangle, to find the third.
E Let A and B be the given angles.
To find the third angle.
It is known (from 79) that the three angles of a triangle are equal to two right angles.
It is also known (fr
...om 46) that the sum of the angles around a point on one side of a straight line is equal to two right angles.
Therefore, if the two angles be added together so that their vertices may coincide and both fall on the same side of a straight line, then the remaining angle on that side will be the angle required.
Hence at a point, say E in the line CD, construct (by 187) an angle, say CEO- equal to Z B, and an angle FED equal to Z A y then the remaining Z GEF will be the third angle re- quired.
EXERCISES.


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