T H E E L E M E N T S |
Book I Proposition 45 | |
And, since the straight line HG falls upon the parallels KM, FG, the the alternate angles MHG, HGF are equal to one another. [I.29] Let the angle HGL be added to each; therefore the angles MHG, HGL are equal to the angles HGF, HGL. [C.N.2] But the angles MHG, HGL are equal to two right angles [I.29]; therefore the angles HGF, HGL are also equal to two right angles. [C.N.1] Therefore FG is in a straight line with GL. [I.14] |
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