| Charles Hutton - Astronomy - 1815 - 686 pages
...SIMILAR Solids, are such as are contained under the same number of similar planes, alike situated. — **Similar solids are to each other as the cubes of their like** linear dimensions. SIMILAR Solid Numbers, are those whose little cubes may be so ranged, as to form... | |
| Anthony Nesbit, W. Little - Measurement - 1822 - 916 pages
...DIAGONAL ROD. The construction of this instrument is founded upon Theo. XX, Part III.; namely, that **similar solids are to each other as the cubes of their like** dimensions. Hence, it appears that the original construction of the diagonal line was extremely easy... | |
| Anthony Nesbit - Surveying - 1824 - 476 pages
...nearly the same as the General Rules. Its construction is founded upon Theo. 20, Part I. ; viz. that **similar solids are to each other as the cubes of their like** dimensions. tfote I. Those who have not a diagonal rod, may nevertheless find the content of a cask... | |
| James Morton Spearman - Artillery - 1844 - 446 pages
...determined by means of its specific gravity. But a shot, four inches in diameter, weighs 9.0029 pounds, and **similar solids are to each other as the cubes of their like** linear dimensions. Also, the specific gravity of gunpowder, in a closely shaken mass, is 920, — Consequently,... | |
| Nathan Scholfield - Conic sections - 1845 - 542 pages
...vertices of the ungulas, is = to | of the cone BDS, since the diameter of its base is necessarily = ^ **that of the larger, and since they are similar solids...cone be cut by a plane perpendicular to the plane** of its buse, the convex surface of the cone, and the plane of the base, will be divided in the same... | |
| Nathan Scholfield - Geometry - 1845 - 506 pages
...vertices of the ungulas, is = to £ of the cone BDS, since the diameter of its base is necessarily = ^ **that of the larger, and since they are similar solids...for similar solids are to each other as the cubes** <>f their like sides, (Prop. XXXV, B. II, El. S. Geom.) and cube of 1 is 1, cube of 2 is 8 ; hence... | |
| George Roberts Perkins - Arithmetic - 1846 - 266 pages
...INVOLVING THE PRINCIPLES OF THE CUBE ROOT. 121. It is an established theorem of geometry, that all **similar solids are to each other as the cubes of their like** dimenswns. 1. If a cannon-ball, 3 inches in diameter, weigh 8 pounds, what will a ball of the same... | |
| Anthony Nesbit - Plane trigonometry - 1847 - 492 pages
...are inscribed ; or as the squares of the diameters of those circles. (Em. IV. 36.) THEOREM XX. All **similar solids are to each other, as the cubes of their like** dimensions. (Em. VI. 24.) PART THE SECOND. A DESCRIPTION OF THE CHAIN, CROSS-STAFF, OFFSETSTAFF, COMPASS,... | |
| George Roberts Perkins - Arithmetic - 1849 - 356 pages
...EXAMPLES INVOLVING THE PRINCIPLES OF THE CUBE ROOT. 79. IT is an established theorem of geometry, that all **similar solids are to each other as the cubes of their like** dimensions. 1. If a cannon ball 3 inches in diameter weigh 8 pounds, what will a ball of the same metal... | |
| Rufus Putnam (Arithmetician) - 1849 - 164 pages
...cube root of the solidity of the latter. The whole truth may be thus expressed. • The contents of **similar solids are to each other as the cubes of their like** dimensions ; and like dimensions of similar solids are to each other as the cube roots of their contents.... | |
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