 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...and GO ; wherefore the circumscribed * It is one of the ^anftavo/ieva, or axioms, of ABCHIMEDKS, that the circumference of a circle is greater than the perimeter of any rectilineal figure inscribed in it ; and less than the perimeter -»f any rectilineal figure described... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...the radius being unity ich. 97 (G) Of the Circumference and Area of Ihn Circle, III. § 4, 5. [(a) The circumference of a circle is greater than the perimeter of any inscribed polygon, and less than that of any circumscribed polygon ; so also • The diagonals, also,... | |
 | Mathematics - 1835 - 684 pages
...the radius being unity «cA. 9Г (G) Of the Circumference and Area of the Circle, III. § 4, 5. [(a) The circumference of a circle is greater than the perimeter of any inscribed polygon, and less than that of any circumscribed polygon ; so also * The diagonals, also,... | |
 | Euclides - 1842 - 316 pages
...sum of the straight lines AB, вc, and less than the sum of the straight lines AТИ, me, cc. Also the circumference of a circle is greater than the perimeter of any polygon inscribed within it, and less than that of any polygon described about it. Again. If DE, EF were sides of a regular... | |
 | William Scott - Measurement - 1845 - 288 pages
...approximation. 2nd. Let it be required to find the ratio of the circumference to the diameter of a circle. The circumference of a circle is greater than the perimeter of any regular polygon inscribed in the circle, and less than the perimeter of any regular polygon described... | |
 | Samuel Hunter Christie - 1847 - 172 pages
...AD, DB. Wherefore, if the chord of any arc of a circle, &c.: which was to be demonstrated. Cor. Hence the circumference of a circle is greater than the perimeter of any polygon inscribed in the circle, and less thap the perimeter of any polygon described about the circle. PKOP. IV. THEOK. The perimeters... | |
 | James Hamblin Smith - Trigonometry - 1870 - 286 pages
...one of the sides of a. regular polygon of n sides the perimeter of the polygon will be n . AB. 15. The circumference of a circle is greater than the perimeter of any polygon which can be inscribed in the circle, but as the ELEMENTARY TRIGONOMETRY. number of sides of such a... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...This proposition is true when .the enveloping line is a curve line of any species whatever. 26. Cor. The circumference of a circle is greater than the perimeter of any polygon inscribed in it. 27. Diedral angles. . When two. planes intersect, the space about the line of intersection is divided... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...enveloping line, is not the least, or shortest line. Therefore the arc ABC is the least. 39. Corollary. The circumference of a circle is greater than the perimeter of any polygon inscribed in it, and less than the perimeter of any polygon circumscribed about it. DEFINITIONS. 40. A constant... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...enveloping line, is not the least, or shortest line. Therefore the arc ABC is the least. 39. Corollary. The circumference of a circle is greater than the perimeter of any polygon inscribed in it, and less than the perimeter of any polygon circumscribed about it. DEFINITIONS. !0. A constant... | |
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The circumference of a circle is greater than the perimeter of any inscribed polygon. 
