 | Charles Hutton - 1816 - 610 sider
...8)1 is equal to the rectangle of the half base AD and the altitude CD. conseconsequently the whole polygon, or all the triangles added together which...rectangle of the radius and half the circumference. 4. BD OF PLANES AND SOLIDS, DEFINITIONS. DBF. 88. The common Section of two Planes, is the line in... | |
 | Charles Hutton - 1822 - 616 sider
...the halves of all the sides, or the half perimeter of the polygon. Now, conceive the number of tides of the polygon to be indefinitely increased ; then...CD will become equal to the radius, and the whole polygen equal to the circle. Consequently the space of the circle, or of the polygon in that state,... | |
 | Charles Hutton - 1825 - 608 sider
...added together which compose it, is equal to the rectangle of the common altitude CD. and the halve? of all the sides, or the half perimeter of the polygon....rectangle of the radius and half the circumference. %. ED OF PLANES AND SOLIDS. DEFINITIONS. DBF. 88. The common Section of two Planes, is the line in... | |
 | John Playfair - 1829 - 210 sider
...to be increased indefinitely, and consequently the length of each side to be decreased indefinitely; then will its perimeter coincide with the circumference of the circle, and the perpendicular from the centre on one of its sides will become equal to the radius. Hence the surface... | |
 | Charles Hutton - 1831 - 632 sider
...cor. 2), is equal to the rectangle of the half base AD and the altitude CD ; consequently the whole polygon, or all the triangles added together which...radius, and the whole polygon equal to the circle. Censequently the space of the circle, or of the polygon in that state, is equal to the rectangle of... | |
 | Charles William Hackley - 1847 - 248 sider
...the triangles added together which compose it, is equal to the rectangle of the common altitude OG, and the halves of all the sides, or the half perimeter...coincide with the circumference of the circle, and the altitude OG will become equal to the radius, and the whole polygon equal to the circle. Consequently,... | |
 | Elias Loomis - 1849 - 252 sider
...sides. The area of the polygon will be equal to its perimeter multiplied by half of CD (Prop. VII.). Conceive the number of sides of the polygon to be indefinitely increased, by continually bisecting the arcs which subtend the sides; its perimeter will ultimately coincide with... | |
 | Ramchundra - 1850 - 222 sider
...triangle ABC is equal to a rectangle of half the base AD and the altitude CD, consequently; the whole polygon, or all the triangles added together which...rectangle of the radius and half the circumference. QED (8.) EVERY SPHERE IS TWO-THIRDS OF ITS CIRCUMSCRIBING CYLINDER. (Fig. ?•) By prop. 12 of Euclid,... | |
 | Elias Loomis - 1858 - 256 sider
...The area of the polygon will be equal to its perimeter multiplied A. B by half of CD (Prop. VII.). Conceive the number of sides of the polygon to be indefinitely increased, by continually bisecting the arcs subtended by the sides ; its perimeter will ultimately coincide with... | |
 | Rāmachandra (son of Sundara Lāla.) - 1859 - 250 sider
...triangle ABC is equal to a rectangle of half the base AD and the altitude CD; consequently, the whole polygon, or all the triangles added together which...rectangle of the radius and half the circumference. QED (8.) EVERY SPHERE IS TWO-THIRDS OF ITS CIRCUMSCRIBING CYLINDER. (Fig. 7.) By prop. 12 of Euclid,... | |
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CD. conseconsequently the whole polygon, or all the triangles added together which compose it, is equal to the- rectangle of the common altitude CD, and the halves of all the sides, or the half perimeter of the polygon. Now, conceive the number of sides... 
