| John Playfair - Mathematics - 1806 - 320 pages
...is the same with the duplicate ratio of their sides ; and hence, also, any two similar rectilineal figures are to each other as the squares of their homologous sides. PROP. XXI. THEOR. Book VI. RECTILINEAL figures, which are similar to the same rectilineal figure, are... | |
| Thomas Keith - 1817 - 306 pages
...I = 7- X VD — d 3/ \D — d 3/ a — d 3 the solidity of the frustum ABD c. Now all similar plane figures are to each other as the squares of their homologous sides. Therefore A 1 a : : D* : d* or — = — , put each off these equal to m ; then A — * D* and a —... | |
| Adrien Marie Legendre - Geometry - 1822 - 394 pages
...polygon, we shall have S' =p'2? : (A, B, A' B', &c.) Hence S : S': :p2 :p's ; hence the surfaces of similar figures are to each other as the squares of their homologous sides. Let us now proceed to polyedrons. We may take it for granted, that a face is determined by means of... | |
| Jeremiah Day - Geometry - 1824 - 440 pages
...original figure. The area of the triangle may then be found by multiplying its base into half its height ; and this will be the contents of the field. In practice...other as the squares of their homologous sides. (Euc. 20.6.) The proportion may be stated thus ; As the square of the true chain, to the square of that by... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...polygon, we shall have S' = ^/i0 : (A, B, A', B', &c.) Hence S : S' : : p2 : p'1 ; hence the surfaces of similar figures are to each other as the squares of their homologous sides. Let us now proceed to polyedrons. We may take it for granted, that a face is determined by means of... | |
| Timothy Walker - Geometry - 1829 - 156 pages
...ABCDE:FGHIK::ABC:FGH. But ABC : FGH : : AB* : p G*. Therefore ABCDE : FGHIK : : AB* : FG*. In other words, similar figures are to each other as the squares of their homologous sides. 117. THEOREM. — Circles are to each other as the squares of their radii. No diagram is necessary... | |
| John Playfair - Geometry - 1829 - 210 pages
...other is the same with the duplicate ratio of their sides; and hence, also, any two similar rectilineal figures are to each other as the squares of their homologous sides. CoR. 3. Two similar triangles, or two similar polygons, are to each other as any rectilineal figure... | |
| Jeremiah Day - Logarithms - 1831 - 418 pages
...original figure. The area of the triangle may then be found by multiplying its base into half its height ; and this will be the contents of the field. In practice,...the area of a field measured by a chain 66.4 feet long, be computed to be 32.6036 acres ; what is the area as measured by the true chain 66 feet long... | |
| Jeremiah Day - Measurement - 1831 - 394 pages
...original figure. The area of the triangle may then be found by multiplying its base into half its height ; and this will be the contents of the field. In practice,...the area of a field measured by a chain 66.4 feet long, be computed to be 32.6036 acres ; what is the area as measured by the true chain 66 feet long... | |
| Ira Wanzer - Arithmetic - 1831 - 408 pages
...the polygon ; then multiply that square by the multiplier set against the name *This rule depends on the principle, that similar figures are to each other as the squares oftluir llke sides. The multipllers in the table are the areas of the respective figures to the side... | |
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