 III.), is a circle. If the plane pass through the centre, then, as every point in the surface of the sphere is equidistant from its centre, the section is a plane figure, every point of whose periphery is equidistant from a certain point within it, and...  A treatise on navigation, and nautical astronomy - Side 86av Edward Riddle - 1824 - 551 siderUten tilgangsbegrensning - Om denne boken
 | Thomas Curtis - 1829 - 814 sider
...dimensions. THEOREM LXX XI. — Every section of a sphere by a plane, as С DEGF (fig. 99, p. III.), is a circle. If the plane pass through the centre,...circle. But if the plane do not pass through the centre, from the centre A, let AB be a perpendicular to the plane ; take any two points, (.., I), in the circumference... | |
 | Thomas Curtis (of Grove house sch, Islington) - 798 sider
...dimensions. THEOREM LXX XL — Every section of a sphere by a plane, as CD EOF (fig. 99, p. III.), is a circle. If the plane pass through the centre,...periphery is equidistant from a certain point within it, aud the figure is therefore a circle. But if the plane do not pass through the centre, from the centre... | |
 | Euclides - 1845 - 546 sider
...comprised between the three semi-circumferences is equal to the circle whose diameter is DB. THEOREM III. Every section of a sphere by a plane is a circle. If the plane pass through the centre of the sphere, it is manifest that the section is a circle, having the same diameter as the generating... | |
 | William Thomas Read - 1862 - 144 sider
...formed on the surface of the sphere, by the intersection of three planes which meet in the centre of the sphere. Proposition I. Every section of a sphere by a plane is a circle. Let the sphere BFD be cut so as to expose the plane section BOED ; it is required to show that this... | |
 | Robert Potts - 1865 - 528 sider
...the three semi-circumferences is equal to the circle whose diameter is DB. THEOREM II1. Every lection of a sphere by a plane is a circle. If the plane pass through the center of the sphere, it is manifest that the section is a circle, having the same diameter as the... | |
 | Isaac Sharpless - 1879 - 282 sider
...Corollary.—Every diameter being equal to two radii, all diameters of a sphere are equal. 3. It will be proved that every section of a sphere by a plane is a circle. If the plane pass through the centre of the sphere, the circle is called a great circle; if not, a small circle. Corottary.—The diameter... | |
 | Eli Todd Tappan - 1868 - 454 sider
...every possible section of it is a curve. SECANT PLANES. 744. Theorem.- Every section of a sphere made by a plane is a circle. If the plane pass through the center of the sphere, every point in the perimeter of the section is equally distant from the center,... | |
 | George Anthony Hill - 1888 - 200 sider
...and AOB is a diameter. A 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 circle is called a small circle. 4 Define... | |
 | George Anthony Hill - 1888 - 202 sider
...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 circle is called a small circle. 4. Define... | |
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