 | George G. Carey - 1818 - 602 pages
...of the other, and then extract the cube root of each product for the mean proportionals sought. 2. Similar solids are to one another as the cubes of their like linear tides. 3. Spheres are to one another as the cabes of their diameters ; and their surfaces as the sqnares... | |
 | John Playfair - 1829 - 210 pages
...diameter, it will be a mean proportional between the segments of the diameter. -* Similar triangles, and all similar figures, are to one another as the squares of their corresponding sides. Equiangular parallelograms, and also equiangular triangles, are to one another... | |
 | Ireland commissioners of nat. educ - 1834 - 370 pages
...content.f 1. What is the solidity of an octaedron, when the linear side is 1 ? Geometry, viz. that similar solids are to one another as the cubes of their like sides ; and the tabular number being the contents of solids whose sides are 1 ; therefore the cube... | |
 | 1837 - 136 pages
...is the rule. The reason of the second rule is obvious, from a property in Solid Geometry, viz. that similar solids are to one another as the cubes of their like sides ; and the tabular numbers being the content of solids whose sides are 1 ; therefore, the cube... | |
 | Denison Olmsted - 1838 - 376 pages
...gravity at E, is to the force of gravity at A, as EFGH to ABCD inversely. But EFGH and ABCD, being similar figures,* are to one another as the squares of their homologous sides, that is, asEF 3 to AB3-'- the forces of gravity at E and A, are inversely as EF 3 : AB 3 . Again,... | |
 | Scottish school-book assoc - 1845 - 444 pages
...SOLIDS. RULE. Since similar surfaces are to one another as the squares of their like sides, and since similar solids are to one another as the cubes of their like sides, the surfaces in the table above, multiplied by the square of the length of the edge of any similar... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pages
...ratios of the homologous edges terminating in those angles. PROPOSITION XL Similar parallelopipeds are to one another as the cubes of their like linear dimensions ; Or again, As the cubes of any homologous lines of the two figures. PROPOSITION XII. Triangular pyramids... | |
 | Euclides - 1861 - 464 pages
...tides, any three be given, the fourth may readily be found. The principle employed is. that the areas of similar figures^ are to one another as the squares of their homologous sides, and vice versa. For (fig 20, VI.) Д ABE : д FGL = AB2 : FG2; ' ^ g Д BCЕ : Д GHL = BО*... | |
 | Olinthus Gregory - 1863 - 482 pages
...the same proportion, aa any two homologous sides of the figure: viz. BE:QT::BC:QR::AB:PQ::AD:PS. 19. All similar figures are to one another as the squares of their homologous sides. 20. Any figure described on the hypothenuse of a right-angled triangle, is equal to two similar... | |
 | Thomas Baker (C.E.) - 1865 - 174 pages
...triangle AED as the square A. B is to the square of AE: that is, similar triangles are to one another iu the duplicate ratio of their homologous sides. (Euc....cubes of their like linear dimensions. (Euc. VI. 24.) " EXPLANATION OF THE PRINCIPAL MATHEMATICAL CHARACTERS USED IN THIS WORK. The sign for equality = is... | |
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AE : that is, similar triangles are to one another iii the duplicate ratio of their homologous sides. (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of their homologous, or like, sides. 
