 | Thomas Keith - 1817 - 306 σελίδες
...BD, the base of the triangle, is a chord, or diameter, of the circular base AB c » of the cone. 4. If a cone be cut by a plane parallel to the base, the section will be 11 circle. Thus, if the cone ABE, be cut by a plane parallel to AB, the section will be a circle,... | |
 | 1829 - 522 σελίδες
...science which treats of the proper, ties of certain curve» that arc formed by 1> the cutting of a cone. If a cone be cut by a plane parallel to the base, the section (or flat surface of the cut) will be a circle; and if it be cut by a plane passing through the vertex,... | |
 | Timothy Walker - 1829 - 156 σελίδες
...the prism. We shall divide the reasoning into four distinct propositions. DEM. 1. — If a pyramid be cut by a plane parallel to the base, the section is a polygon similar to the base. Let GHIKL (fig. 93) be a section F 93 parallel to the base BCDE F. We... | |
 | A. Bell - 1837 - 180 σελίδες
...the solids between each of them and the base, are cylinders. • COR. 3. — If a cone or cylinder be cut by a plane parallel to the base, the section is a circle. COR. 4. — Any plane touching the axis of a cone or cylinder, cuts every parallel section in its diameter.... | |
 | Thomas Holliday - 1838 - 404 σελίδες
...through the vertex A of the cone, to any part of the base, the section will be a triangle, as ABC. 3. If a cone be cut by a plane parallel to the base, the section will be a circle, as D—E. 4. If a cone be cut by a plane which passes through its two slant sides... | |
 | Charles Davies - 1840 - 262 σελίδες
...by one-third of the altitude. Thus, the solidity of the cone C—AED is equal to base Q.BEsT. — 7. If a cone be cut by a plane parallel to the base, what will the section be 1 If the upper part be taken away what is the lower part called 1 8. What... | |
 | Isaac Wilber Jackson - 1845 - 116 σελίδες
...denominated the upper and lower nappes of the cone respectively. PROPOSITION I. THEOREM. If a conic surface be cut by a plane parallel to the base, the section is the circumference of a circle having its centre in the axis. Let ACBD (Fig. 29) be the base, S the... | |
 | Charles Davies - 1846 - 254 σελίδες
...or altitude of the cone, and the point C the vertex of the cone. 37- What is the frustum of a cone ? If a cone be cut by a plane parallel to the base, the section will be a circle. Thus, the section FKHI is a circle. If from the cone S — CDB, the cone S — FKH... | |
 | Samuel Hunter Christie - 1847 - 172 σελίδες
...as the cubes of the diameters of their bases, or as the cubes of their altitudes. PROP. LXXI. THEOR. If a cone be cut by a plane parallel to the base, the section will be a circle; and this section and the base will be to one another in the duplicate ratio of their... | |
 | 1847 - 648 σελίδες
...side of the the prism or pyramid ; or again in the pyramid beyond the vertex, as PROP. V " cylinder or cone be cut by a plane parallel to the base, the section will be a circle ; and in the cylinder, this circle will be equal to the base. (1.) Let ABC be the... | |
| |
... be cut by a plane parallel to the base, the section is a figure parallel and similar to the base. The one point a... 
