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" The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C... "
New Elementary Geometry: With Practical Applications : a Shorter Course Upon ... - Page 100
by Benjamin Greenleaf - 1874 - 176 pages
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Catalogue - Harvard University

Harvard University - 1876 - 554 pages
...polygons are to eaoli other as the squares of their homologous sides. 7. The circumferences of two circles are to each other as their radii, and their...areas are to each other as the squares of their radii. PROBLEMS. 8. To divide a given straight line in extreme and mean ratio. 9. To find a fourth proportional...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...similar sectors and similar segments are like parts of the circles to which they belong, their arcs are to each other as their radii, and their areas are to each other as the squares of their radii. PROPOSITION VII. PROBLEM. Let ACDE be the given circle. 1°. Draw two diameters, AD and CE, perpendicular...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...of the sector ACB is equal to the product of its arc AEB by half of AC. PROPOSITION XIII. THEOREM. The circumferences of circles are to each other as their radii, and their areas are as the squares of their radii. Let R and r denote the radii of two circles ; C and c their circumferences...
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Cornell University Register and Catalogue

Cornell University - 1880 - 868 pages
...proportional. 5. To construct a triangle equivalent to a given polygon. 6. The circumferances of two circles are to each other as their radii, and their...areas are to each other as the squares of their radii If the areas of two circles be as 16 to 25, and the diameter of the first circle be twenty inches,...
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The System of Calculating Diameter, Circumference, Area, and Squaring the ...

James Morton - Circle-squaring - 1881 - 236 pages
...by the altitude, and take half the product, or multiply one of these dimensions by half the other. The circumferences of 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...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1882 - 262 pages
...the polygons. For the apothems are to each other as the sides of the polygons (351). 371. COR. 2. — The circumferences of circles are to each other as their radii, and as their diameters ; since they may be considered as regular polygons of the same number of sides (352)....
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...the same number of sides we to each other as the apothems of the polygons (382)417. COROLLARY 2. — The circumferences of circles are to each other as their radii, and as their diameters (390). PROPOSITION X. 418. Problem. — To find the relation between the chord of...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...PROPOSITION XIII. THEOREM. The circumferences of circles are to each oiher as their radii, and the areas are to each other as the squares of their radii. Let C and O be the centres of two circles whose radii are CA and OB : then the circumferences are to each...
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The Philosophy of Mathematics: With Special Reference to the Elements of ...

Albert Taylor Bledsoe - Mathematics - 1886 - 253 pages
...example, in one of the most extensively used text-books in America, the following demonstration : * " The circumferences of circles are to each other as their radii, and the areas are as the squares of their radii" Let us designate the circumference of the circle whose...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 342 pages
...the circle is the limit of the areas of these polygons. PROPOSITION VIII. The circumferences of two circles are to each other as their radii, and their...areas are to each other as the squares of their radii. Corollary I. The circumferences of circles are to each other as their diameters, and their areas are...
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