Plane and solid geometry . cV. a C Given spherical A ABC with sides denoted by a, h, and prove /.A + + /.G> 180° and < 540°. Argument 1. Let A abc, with sides denoted by a\b, and c, be the polar of A ABC, Then Z ^ + a = 180°, Z^ + 5 = 180°,Z(7+c=180°. .•.Z^ + Z5+Z(7 + (a+6+c)=540°. But a + 6 + c 0°. .. Za + Zb + Zc< 640°. 2. 7. Reasons 1. §943. 2. § 947. 3. § 64, 2. 4. § § 64, 6. 6. § 938. 7. § 64, 6. 950. Cor. 7/2/ a spherical triangle there can he one,two, or three right angles; there can he one, two, or threeobtuse angles. 951. Note. Throughout the S
Plane and solid geometry . cV. a C Given spherical A ABC with sides denoted by a, h, and prove /.A + + /.G> 180° and < 540°. Argument 1. Let A abc, with sides denoted by a\b, and c, be the polar of A ABC, Then Z ^ + a = 180°, Z^ + 5 = 180°,Z(7+c=180°. .•.Z^ + Z5+Z(7 + (a+6+c)=540°. But a + 6 + c 0°. .. Za + Zb + Zc< 640°. 2. 7. Reasons 1. §943. 2. § 947. 3. § 64, 2. 4. § § 64, 6. 6. § 938. 7. § 64, 6. 950. Cor. 7/2/ a spherical triangle there can he one,two, or three right angles; there can he one, two, or threeobtuse angles. 951. Note. Throughout the Solid Geometiy the students attentionhas constantly been called to the relations between definitions and theoremsof solid geometry and the corresponding definitions and theorems of planegeometry. In the remaining portion of the geometry of the sphere therewill likewise be many of these comparisons, but here the student must beparticularly on his guard for co
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
