Plane and solid geometry . Given PC and PD quadrants of great ® of sphere 0, andACDB a great O passing through points C and prove P the pole of great O ACDB. Argument 1. Draw OCj OD, and OP. 2 PC = 90° and pB = 90°- 3. .*. A POC and POD are rt. A) OP ± OC and OD 4 .*. OP ± the plane of O ACDB. 5. .*. OP is the axis of O ACDB. 6 .*. P is the pole of great O ACDB. Reasons 1. § 54, 15. By hyp§358 4. § 622.§ 906.§907. Ex. 1479. Assuming the chord of a quadrant of a great circle of asphere to be given, construct with compasses an arc of a great circlethrough two given point
Plane and solid geometry . Given PC and PD quadrants of great ® of sphere 0, andACDB a great O passing through points C and prove P the pole of great O ACDB. Argument 1. Draw OCj OD, and OP. 2 PC = 90° and pB = 90°- 3. .*. A POC and POD are rt. A) OP ± OC and OD 4 .*. OP ± the plane of O ACDB. 5. .*. OP is the axis of O ACDB. 6 .*. P is the pole of great O ACDB. Reasons 1. § 54, 15. By hyp§358 4. § 622.§ 906.§907. Ex. 1479. Assuming the chord of a quadrant of a great circle of asphere to be given, construct with compasses an arc of a great circlethrough two given points on the surface of the sphere. Ex. 1480. If the planes of two great circles are perpendicular to eachother, each passes through the poles of the other. Ex. 1481. Find the locus of all points in space equidistant from twogiven points and at a given distance d from a third given point. Ex. 1482. Find the locus of all points in space at a distance d froma given point and at a distance m from a given plane. Ex. 1483
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
