 | Alexander Ewing - 1771 - 342 pages
...6,anditsarea.7&5398 1633, or. 7854. . j. The diameter of a circle being given, to find its circumference. Becaufe the -circumferences of circles are to each other as their diameters, and the circumference of a circle, whofe diameter is r,is 3.1416 ; therefore, as X is to 3.1416, fo is... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...by 2, and of the second by 4, we shall have and circ. CA area CA circ. OB area OB 2CA 4CA* that is, the circumferences of circles are to each other as...are to each other as the squares of their diameters. 151 PBOPOSITION XIV. THEOEEM. Similar arcs are to each other as their radii: and similar sectors are... | |
 | James Smith - Mathematics - 1865 - 168 pages
...perimeter of a regular six sided inscribed polygon to the circle B; and, 172-3 : 130 : : 3 : 3-125. Now, the circumferences of circles are to each other as their diameters ; and the perimeters of regular polygons are to each other as the circumferences of their circumscribing... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...(III. 9) the same as I,' P] C_ C' and the proportion [2] is the same as 4.R2 S' 4R'* (2R'y therefore, the circumferences of circles are to each other as...are to each other as the squares of their diameters. 39. Corollary II. Similar arcs, as AB, A'B', are those which subtend equal angles at the centres of... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
.../~1 O JJ — = — •-, [3 C' 2R' L and the proportion [2] is the same as - A o, S' 4R'2 therefore, the circumferences of circles are to each other as...are to each other as the squares of their diameters. 39. Corollary II. Similar arcs, as AB, A'B', are those which subtend equal angles at the centres of... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...which was to be proved. Cor. 1. The circumferences of two circles are to each other as their radii, or as their diameters, and their areas are to each other as the squares of their radii, or as the squares of their diameters. Cor. 2. Because similar sectors and similar segments... | |
 | William Chauvenet - Geometry - 1879 - 380 pages
...same as C_ = 2R_ C' ~~ 2R' and the proportion [2] is the same as 8 4R * (2.8)* . ~~ [3] therefore, th& circumferences of circles are to each other as their...are to each other as the squares of their diameters. 39. Corollary II. Similar arcs, as AJB, A'B', are those which subtend equal angles at the centres of... | |
 | James Morton - Circle-squaring - 1881 - 236 pages
...circles are to each other as their radii, and the areas are to each other as the squares of their radii. The circumferences of circles are to each other as...are to each other as the squares of their diameters. The circumference o£ the circle is the limit of all inscribed polygons ; in fact, the circle is but... | |
 | James Morton - Mathematics - 1887 - 236 pages
...circles are to each other as their radii, and the areas are to each other as the squares of their radii. The circumferences of circles are to each other as...are to each other as the squares of their diameters. The circumference of the circle is the limit of all inscribed polygons ; in fact, the circle is but... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...Limits, these limits are equal, and we have or C 7 = W In the same way we may prove 19. COROLLARY I. The circumferences of circles are to each other as...are to each other as the squares of their diameters. 20. COROLLARY II. The ratio of the circumference of a circle to its diameter is constant ; that is,... | |
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L and the proportion [2] is the same as - A o, S' 4R'2 therefore, the circumferences of circles are to each other as their diameters, and their areas are to each other as the squares of their diameters. 
