 | Adrien Marie Legendre - 1863 - 464 σελίδες
...frustum, and a mean proportional between them ; which was to be proved. PROPOSITION VII. THEOREM. Any section of a sphere made ~by a plane, is a circle. Let C be the centre of a sphere, CA one of its radii, and AMB any section made by a plane : then will this... | |
 | Eli Todd Tappan - 1864 - 288 σελίδες
...motion of a straight line, every possible section of it is a curve. SECANT PLANES. 744. Theorem. — Every section of a sphere made by a plane is a circle. 252 But if the section do not pass through the center, as DGF, then from the center C let CI fall perpendicularly... | |
 | Euclides - 1864 - 448 σελίδες
...two great circles of a sphere, is measured by the arc of a great circle which joins their poles. 35. Every section of a sphere made by a plane is a circle : and if two parallel planes cut a sphere so that the sections are equal, they are equidistant from... | |
 | William Harris Johnston - 1865 - 478 σελίδες
...and a line passing through tho centre and meeting the surface in two opposite points, is a diameter. Every section of a sphere, made by a plane, is a circle. A section through tho centre is termed a great circle of tho sphere ; any other, a small circle. A... | |
 | Gerardus Beekman Docharty - 1867 - 474 σελίδες
...all the diameters are equal, and each double of the radius. 3. It will be demonstrated (Prop. 1) that every section of a sphere made by a plane is a circle ; this being assumed, A great circle of a sphere is the section made by a plane passing through the... | |
 | Edward Brooks - 1868 - 284 σελίδες
...expression for the volume of a frustum of a cone is (*& -f nr* + *B X r) X i .2". THE SPHERE. THEOREM VII. Every section of a sphere made by a plane is a circle. Let C be the centre of a sphere whose radius is CA, and ADB any section made by a plane; then will this... | |
 | Robert Potts - 1868 - 434 σελίδες
...two great circles of a sphere, is measured by the arc of a great circle which joins their poles. ,35. Every section of a sphere made by a plane is a circle : and if two parallel planes cut a sphere so that the sections are equal, they are equidistant from... | |
 | Eli Todd Tappan - 1868 - 444 σελίδες
...the motion of a straight line, every possible section of it is a curve. 8ECANT PLANE8. 744. Theorem.- Every section of a sphere made by a plane is a circle. But if the section do not pass through the center, as DGF, then from the center C let CI fall perpendicularly... | |
 | Benjamin Greenleaf - 1868 - 340 σελίδες
...the pyramid is the spherical polygon intercepted by the same planes. PROPOSITION I. — THEOREM. 515. Every section of a sphere made by a plane is a circle. BOOK IX. B The oblique lines CA, CB, CE are equal, being radii of the sphere ; therefore they are equally... | |
 | Isaac Stone - 1869 - 272 σελίδες
...4. The solidity of a Cone is equal to its base multiplied by a third of its altitude. PBB VIII. 5. Every section of a sphere, made by a plane, is a circle. P. VII. B. vm. 6. The solidity of a sphere is equal to its surface multiplied by a third of its radius.... | |
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It will be shown that every section of a sphere made by a plane is a circle... 
