Plane and solid geometry . Fig. Given A ABC and A^B^Cf, with AB, BC, and CA II (Fig- 1)or ± (Fig. 2) respectively to A^B\ B^C, and (/^. To prove A ABC ^ A AB^Cf, Argument 1. AB, BC, and CA are II or X respectively to A^b\ bc, and cW. 2. .-. Aa,B, and C are equal respectively or are sup. respectively to A a, b\ and c\ Keasons 1. By hyp. 2. §§198,201 BOOK III 183 Argument 3. Three suppositions may be made, there- fore, as follows: (1) +ZA=2TtA,ZB+^ = 2 rt. A, Za + = 2 rt. A. (2) Za^Za^Ab + ZB = , ZC + Z& =: 2 It. A. (3) Za = Za,Zb = Zb*, hence, also, Zc= Zc\ 4. According to (
Plane and solid geometry . Fig. Given A ABC and A^B^Cf, with AB, BC, and CA II (Fig- 1)or ± (Fig. 2) respectively to A^B\ B^C, and (/^. To prove A ABC ^ A AB^Cf, Argument 1. AB, BC, and CA are II or X respectively to A^b\ bc, and cW. 2. .-. Aa,B, and C are equal respectively or are sup. respectively to A a, b\ and c\ Keasons 1. By hyp. 2. §§198,201 BOOK III 183 Argument 3. Three suppositions may be made, there- fore, as follows: (1) +ZA=2TtA,ZB+^ = 2 rt. A, Za + = 2 rt. A. (2) Za^Za^Ab + ZB = , ZC + Z& =: 2 It. A. (3) Za = Za,Zb = Zb*, hence, also, Zc= Zc\ 4. According to (1) and (2) the sum of the A of the two A is more than four rt. A. 5. But this is impossible. 6. .-. (3) is the only supposition admissible; the two A are mutually equi-angular. 7. .. AABC^Aa^B^C\ Reasons3. §161, a. 4. §54,2. 5. §204. 6. 161, b. I 7. §420. 430. Question. Can one pair of angles in Prop. XVII be supple-mentary and the other two pairs equal ? SUMMARY OF CONDITIONS FOR SIMILARITY OF TRIANGLES
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
