 | 1861 - 420 pages
...hexagon be inscribed in a circle, its side will be equal to the radius. 3. Book V, Proposition XIV. Similar arcs are to each other as their radii; and...sectors are to each other as the squares of their radii. 4. Book VI, Proposition IV. If a straight line be perpendicular to two straight lines at their point... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...second proportion by 4, or 2 squared, we have A: A' : : 4 K2 : 4r2. PROPOSITION XIV. — THEOREM. 379. Similar arcs are to each other as their radii; and...sectors are to each other as the squares of their radii. Let AB, DE be similar arcs ; ACB, D0E, similar sectors ; and denote the radii CA and 0D by K and r... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...second proportion by 4, or 2 squared, we have A: A': : 4 R2 : 4r2. PROPOSITION XIV. — THEOREM. 379. Similar arcs are to each other as their radii; and...sectors are to each other as the squares of their radii. Let AB, DE be similar arcs ; ACB, DOE, similar sectors ; and denote the radii CA and OD by R and r... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...4, or 2 squared, we have Л: A' : : 4 R3 : 4r3. PROPOSITION XIV. — THEOREM. 379. Similar arcs arc to each other as their radii; and similar sectors are to each other as the squares of their radii. Let AB, DE be similar arcs ; А С В, DOE, similar sectors ; and denote the radii С A and 0 D by... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...to which they belong, and similar sectors, as ACB and DOE, are like parts of the circles to wliich they belong : hence, similar arcs are to each other...squares of their radii. Scholium. The term infinite^ employed above, is to be understood in its limited technical sense. When it is proposed to make the... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...second proportion by 4, or 2 squared, we have A: A' : : 4 R* : 4r2. PROPOSITION XIV. — THEOREM. 879. Similar arcs are to each other as their radii; and...sectors are to each other as the squares of their radii. Let AB, DE be similar arcs ; ACB, DOE, similar sectors ; and denote the radii CA and 0D by B and r... | |
 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...length of its diameter? 4. The diameter of a circle is 16: what its area? 5. Prove that the areas of similar sectors are to each other as the squares of their radii. 6. Prove that the area of a circle equals the square of its radius multiplied by 3.14159. SEC. XII.—... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...second proportion by 4, or 2 squared, we have A: A' : : 4 R2 : 4r\ PROPOSITION XIV. — THEOREM. 379. Similar arcs are to each other as their radii; and...sectors are to each other as the squares of their radii. Let AB, DE be similar arcs ; ACB, D0E, similar sectors ; and denote the radii CA and 0D by R and r... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...of the circumferences to which they belong, and similar sectors, as A CH and 'D OE, are like parts of the circles to which they belong : hence, similar...proposed to make the number of sides of the polygons infinite, by the method indicated in the scholium of Proposition X., it is simply meant to express... | |
 | Adrien Marie Legendre - Geometry - 1871 - 490 pages
...and DE, are like parts of the circumferences to which they belong, and similar sectors, as A CH and D OE, are like ports of the circles to which they belong...proposed to make the number of sides of the polygons infinite, by the method indicated in the scholium of Proposition X., it is simply meant to express... | |
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DE, are like parts of the circumferences to which they belong, and similar sectors, as A CH and 'D OE, are like parts of the circles to which they belong : hence, similar arcs are to each other as their radii, and similar sectors are to each other as... 
