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" THEOREM. Every section of a sphere, made by a plane, is a circle. "
Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ... - Page 196
by James Bates Thomson - 1844 - 237 pages
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Senate Documents, Otherwise Publ. as Public Documents and ..., Volume 3

United States. Congress. Senate - United States - 1880 - 1302 pages
...Si MOR PUPIL TEACHEHS — SIXTH YEAR. SPHERICAL TRIGONOMETRY. (Timo allowed, 3 hours.) 1. Prove that every section of a sphere made by a plane is a circle. 2. In spherical triangle А В С, given a = 87░ 10' 15", Ь = 62░ 36' 45", and с = 100^ 10' 15";...
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Practical Work in Geography: For the Use of Teachers and Advanced Pupils ...

Henry McCormick - Geography - 1885 - 424 pages
...The diameter of a sphere is a straight line drawn through the center and terminating in the surface. Every section of a sphere made by a plane is a circle. If an orange be cut into two parts, each cut surface is a circle. A great circle of a sphere is one...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 346 pages
...linear dimen sions. THKOREM XX. Every sect1on oj a sphere, made by a plane, 1s a circle. Let AMB be a section, made by a plane, in the sphere whose centre is C. From the centre C draw CO, perpendicular to the plane AMB, and also draw the lines CA, CM, &c., to the points...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...sphere. In this case the sphere is circumscribed about the polyedron. 316 PROPOSITION V. THEOREM. 623. Every section of a sphere made by a plane is a circle. P Let ABC be a plane section of the sphere APC. To prove that ABC is a circle. Let 0 be the centre...
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Illinois School Journal: A Monthly Magazine for Teachers and ..., Volume 5

Education - 1886
...pyramid is onethird of a triangular prism of the same base and altitude. ' ' 10. (80) Demonstrate that "every section of a sphere made by a plane is a circle." achy ILLINOIS SCHOOL JOURNAL. [DECEMBER, 1 ILLINOIS SCHOOL JOURNAL A MONTHLY EDUCATIONAL MAGAZINE....
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 322 pages
...plane of the circle; and this diameter is called the axis of the circle. PROPOSITION V.—THEOREM. 22. Every section of a sphere made by a plane is a circle. 1st. If the plane passes through the centre of the sphere, the lines joining points on the perimeter...
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Lessons in Geometry: For the Use of Beginners

George Anthony Hill - Geometry - 1888 - 182 pages
...sphere. In Fig. 169 OA is a radius, and AOB is a diameter. AP 3. Define great circles and small circles. Every Section of a sphere made by a plane is a circle. If the plane pass through the centre, the circle is called a great circle ; in all other cases the...
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Lessons in Geometry: For the Use of Beginners

George Anthony Hill - Geometry - 1888 - 182 pages
...sphere. In Fig. 169 OA is a radius, and AOB is a diameter. AP 3. Define great circles and small circles. Every section of a sphere made by a plane is a circle. If the plane pass through the centre, the circle is called a great circle ; in all other cases the...
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The Elements of Co÷rdinate Geometry: In Three Parts and an Appendix

De Volson Wood - Geometry, Analytic - 1890 - 642 pages
...sphere, and equations (1), (2), (3), of Article 386 will be the equation of a tangent plane. EXAMPLES. 1. Every section of a sphere made by a plane is a circle. Let fi be a vector perpendicular to the plane, d the scalar of S, r the radius of the sphere, p the vector...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 393 pages
...on which the student should draw the diagrams of spherical surfaces. Proposition 1 . Theorem. 664. Every section of a sphere made by a plane is a circle. Hyp. Let ACB be a plane section of the sphere whose centre is 0. To prove that ACB is a Q. Proof. Draw...
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