Items related to Constructive Text-Book of Practical Mathematics (Volume...
Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1914. Excerpt: ... BOOK X THE SPHERE 1. Every section Sph 2. Line Jng Center Sph 3. Os = Dist Fr Center 4. Nearer O 5. Thru 2 Pts 1-6. Thru 3 Pts 7. Os 8. Great Os = 9. Great O Bis Sph 10. Great Os Bis 11. Great Os Pls-L 12. Shortest Dist Bet 2 Pts 13. Pts Circum = Dist Fr Pole 14. Polar Dist Quad 15. Pt at Quad Dist 16. PI-L Rad 17. PI Tan 18. Line in Tan PI 19. PI of 2 St Lines Ea Tan 20. Line Tan O of Sph 21. Sph Circum 22. Sph Inscr 23. 6 Pls Bis 24. Sph Z ZZI X Theorem 1 Every section of a sphere, formed by a plane, is a circle whose center is the projection of the center of the sphere, on the plane. Locate any two points on the line of intersection of the surface of the sphere with the plane. To each of these points, draw radii of the sphere. Project the center of the sphere, on the plane. Connect the projection with each of the points marked on the line of intersection previously named. X Theorem 2 The line joining the center of a sphere to the center of a circle of the sphere is perpendicular to the plane of the circle. X Theorem 3 Circles of a sphere made by planes equally distant from the center, are equal. X Theorem 4 Of circles made by planes unequally distant from the center of a sphere, the one nearer to the center is the larger. Draw a radius of each circle. Connect the center of the sphere with the extremity of each radius. Prove by square of the hypotenuse. X Theorem 5 Through any two points on the surface of a sphere, (1) An arc of a great circle can be drawn. (2) When the two points are not the extremities of a diameter of the sphere, only one can be drawn. After demonstrating, show how many can be drawn when the two points are the extremities of a diameter. X Theorem 6 Through any three points on the surface of a sphere, one circle may be passed, and o...
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