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" It will be demonstrated art. 452, that every section of a sphere made by a plane is a circle. "
The Principles of Analytical Geometry: Designed for the Use of Students - Pągina 253
per Henry Parr Hamilton - 1826 - 326 pągines
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Practical Work in Geography: For the Use of Teachers and Advanced Pupils ...

Henry McCormick - 1885 - 424 pągines
...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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Illinois School Journal: A Monthly Magazine for Teachers and School ..., Volum 5

1886 - 636 pągines
...triangular 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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The Elements of Geometry

Webster Wells - 1886 - 392 pągines
...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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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - 1887 - 331 pągines
...every diameter is double the radius, all the diameters are equal. 20. Definition. It will be shown that every section of a sphere made by a plane is a circle; and, as the greatest possible section is one made by a plane passing through the centre, such a section...
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Lessons in Geometry: For the Use of Beginners

George Anthony Hill - 1888 - 200 pągines
...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 - 1888 - 202 pągines
...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 Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - 420 pągines
...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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The Elements of Coördinate Geometry: In Three Parts and an Appendix

De Volson Wood - 1890 - 372 pągines
...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...
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Elementary Geometry

William Chauvenet - 1893 - 340 pągines
...every diameter is double the radius, all the diameters are equal. 20. Definition. It will be shown that every section of a sphere made by a plane is a circle; and, as the greatest possible section is one made by a plane passing through the centre, such a section...
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The Elements of Solid Geometry

William C. Bartol - 1893 - 112 pągines
...to the sphere. The polyedrou is then circumscribed about the sphere. PROPOSITION XXVI. 173. THEOREM. Every section of a sphere made by a plane is a circle. The section through the centre is a circle (166). Let ABC be any section not through the centre 0;...
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