Plane and solid geometry . Given trihedral A F-^5(7 and v-a!b!c^ Z AVB = Z aVb\Z B vc = Z B vc, Z CVA = Z C va, and the equal face anglesarranged in the same order. To prove trihedral Z F-^5C= trihedral Z v-Abc\ Outline of Proof 1. Since, by hyp., any two face A of V-ABC, as A AVBand BVC, are equal, respectively, to the two corresponding faceA of f-^^c, it remains only to prove the included dihe-dral A VB and FJ5 equal. § 702, II. (See also § 705.) 2. Let face A AVB and BVC be oblique A\ then from anypoint E in Fj5, draw ED and EF, in planes AVB and BVC, respec-tively, and ± VB. 3. Since A AVB
Plane and solid geometry . Given trihedral A F-^5(7 and v-a!b!c^ Z AVB = Z aVb\Z B vc = Z B vc, Z CVA = Z C va, and the equal face anglesarranged in the same order. To prove trihedral Z F-^5C= trihedral Z v-Abc\ Outline of Proof 1. Since, by hyp., any two face A of V-ABC, as A AVBand BVC, are equal, respectively, to the two corresponding faceA of f-^^c, it remains only to prove the included dihe-dral A VB and FJ5 equal. § 702, II. (See also § 705.) 2. Let face A AVB and BVC be oblique A\ then from anypoint E in Fj5, draw ED and EF, in planes AVB and BVC, respec-tively, and ± VB. 3. Since A AVB and BVC are oblique Z, ED and EF willmeet VA and VC in D and F, respectively. Draw FD. 4. Similarly, lay off Ve^ = VE and draw A def\ 5. Prove rt. Ai)F^ = rt. Ai>F£; then F/)= fZ), ZZ) = ZZ)^ 6. Prove rt. A ^FF= rt. A zVf; then VF= V^F, EF=ef*. 7. Prove A FVD = A Fvd ; then FD = Fd. 8. . DEF = A DeF* ; then Z DEF = Z DEF\ BOOK VI 339 9. But A DBF and D^E^F^ are the plane A of dihedral A VBand V^b\ respectively.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
