 | John Playfair - 1806 - 320 σελίδες
...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... | |
 | Jeremiah Day - 1815 - 388 σελίδες
...original figure. The area of the trianfle may then be found by multiplying its base into half its eight ; and this will be the contents of the field. In practice,...the area of a field measured by a chain 66.4 feet Jong, be computed to be 32.6036 acres ; what is the area as measured by the true'chain 66 feet long?... | |
 | Thomas Keith - 1817 - 306 σελίδες
...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 - 1822 - 394 σελίδες
...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 - 1824 - 440 σελίδες
...intersection G. Then the triangles DBC and DBG *re equal. (Eue. 37. 1.) Taking from each the common part OBH, there remains BGH equal to DCH. If then the triangle...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 - 1828 - 542 σελίδες
...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 - 1829 - 156 σελίδες
...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 - 1829 - 210 σελίδες
...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... | |
 | Ira Wanzer - 1831 - 408 σελίδες
...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... | |
 | Jeremiah Day - 1836 - 418 σελίδες
...of the field. In practice, it will not be necessary actually to draw the parallel lines BD, GC, Sic. It will be sufficient to lay the edge of a rule on...homologous sides. (Euc. 20. 6.) The proportion may be staled thus ; As the square of the true chain, to the square of that by which the survey was made ;... | |
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It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed, and the area computed, the chain is found to be too... 
