Text-book of Euclid's elements for the use of schools : books I - VI and XI (1900)
Hall, H. S. (Henry Sinclair), 1848-1934, Stevens, F. H. (Frederick Haller), 1853-1933 · MacMillan : London · leaf 362
d 3.] one of them must be the greater. Let the l EDF be greater than the L BAC. At D in ED make the L EDF equal to the l BAC. [Fig. 3.] Then the As BAC, EDF are equiangular, . . BA AC : : ED DF; but, by hypothesis, BA AC : : ED DF; m . ED DF : : ED DF, .. DF=DF,.-. the L DFF = the L DFF.But the… … Three cases of this theorem deserve special attention. It has been proved that if the angles ACB, DFE are not supple-mentary, they are equal. Hence, in addition to the hypothesis of this theorem, (i) If the angles ACB, DFE, opposite to the two homo-logous sides AB, DE are both acute or both obtuse,…
Geometry · Mathematics
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