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The volumes of similar solids are to each other as the cubes of their like dimensions.
An Elementary Arithmetic Designed for Academies and Schools: Also Serving as ... - Σελίδα 310
των George Roberts Perkins - 1855 - 347 σελίδες
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## A Philosophical and Mathematical Dictionary: Containing an ..., Τόμος 2

Charles Hutton - 1815
...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...

## A Treatise on Practical Gauging

Anthony Nesbit, W. Little - 1822 - 533 σελίδες
...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 ; for having...

## A Treatise on Practical Mensuration in Eight Parts ...

Anthony Nesbit - 1824 - 434 σελίδες
...they 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. AN EXPLANATION OF THE Principal Mathematical Characters. THE sign or character = (called equality)...

## Higher Arithmetic: Designed for the Use of High Schools, Academies, and Colleges

George Roberts Perkins - 1841 - 252 σελίδες
...PRINCIPLES OF THE CUBE ROOT. 80. It is an established theorem of geometry, that all similar solida are to each other as the cubes of their like dimensions. 1. If a cannon ball, 3 inches in diameter, weighs 8 pounds, what will a ball of the same metal weigh, whose...

## The British gunner

James Morton Spearman - 1844 - 416 σελίδες
...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,...

## Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
...diameter of its base is necessarily = 1 that of the larger, and since they are similar solids ; for similar solids are to each other as the cubes of their like sides, (Prop. XXXV. B. II, El. S. Geom.) and cube of 1 is 1, cube of 2 is 8 ; hence 1:8:: cone dMS...

## A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - 1845
...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 of their like sides, (Prop. XXXV, B. II, El. S. Geom.) and cube of 1 is 1, cube of 2 is 8 ; hence 1:8:: cone dMS...

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

George Roberts Perkins - 1846 - 258 σελίδες
...nearly. 6. What is the cnbe root of § ? .« EXAMPLES INVOLVING THE PRINCIPLES OF THE CUBE ROOT. 121. It is an established theorem of geometry, that all...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...

## A Complete Treatise on Practical Land-surveying, in All Its Departments ...

Anthony Nesbit - 1847 - 426 σελίδες
...they 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, AND FIELD-BOOK...

## Higher Arithmetic: Designed for the Use of High Schools, Academies, and ...

George Roberts Perkins - 1849 - 342 σελίδες
...root of ?|T to 8 decimals 1 Ans. 0-13992727. EXAMPLES INVOLVING THE PRINCIPLES OF THE CUBE ROOT. 79. IT is an established theorem of geometry, that all...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 weigh, whose diameter...