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" The volumes of similar solids are to each other as the cubes of their like dimensions. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 38
by Nathan Scholfield - 1845
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A Philosophical and Mathematical Dictionary: Containing an ..., Volume 2

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...
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A Treatise on Practical Gauging

Anthony Nesbit, W. Little - Measurement - 1822
...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...
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A treatise of practical mensuration

Anthony Nesbit - Measurement - 1824 - 434 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...
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The British gunner

James Morton Spearman - Artillery - 1844 - 416 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,...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845
...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...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

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...
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An Elementary Arithmetic ...: Serving as an Introduction to the Higher ...

George Roberts Perkins - Arithmetic - 1846 - 258 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...
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A Complete Treatise on Practical Land-surveying: In All Its Departments ...

Anthony Nesbit - Plane trigonometry - 1847 - 426 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,...
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Higher Arithmetic: Designed for the Use of High Schools, Academies, and ...

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...
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Key to the American Common-school Arithmetic

Rufus Putnam (Arithmetician) - 1849 - 162 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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