A Compendious Course of Practical Mathematics; Particularly Adapted to the Use of the Gentlemen of the Army and Navy - Softcover

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1769. Excerpt: ... 3. Extension is to be considered in three different respects, which we call Dimensions, viz, 1. Length. 2. Breadth. 3. Thickness, or Depth. 4. A Solid, is a magnitude considered under three dimensions; as if the tonnage of a Ship is demanded, the Ship is considered as a Solid; and the question requires that we examine its length, its breadth, and its depth; for the longer, the broader, and the deeper it is, the greater will be its tonnage. 5. A Superficies, or Surface, is a magnitude comprehended under two dimensions, viz. length, and breadth; as when we measure a field, we take it for a Surface, which the longer, and broader it is, the more acres it contains, without any regard to the depth, or thickness of the earth. 6. A Line is a magnitude Considered only as length; thus when it is afk'd, how far one place is distant from another, we consider the space between the two places as a line, which, the longer it is, the farther distant are the places; but the breadth or thickness of the space, makes no difference in the distance of the places. 7. A Point is that in which we consider neither length, breadth, nor thickness, as in the foregoing instance, the two places are taken for two Points; for it is not at all necestary to know the length, breadth, or thickness of the two places, (0 determine the distance between them. 8. The 8. The extreams of a Line are Points: a Line being only a continuation of the motion of a Point. So Lines are the boundaries of a Superficies. In like manner also, Superficies are the boundaries of a solid body. 9. Two similar Surfaces are faid to be equal, when the one being laid upon the other, perfectly covers it. In like manner, two similar Solids are accounted equal, when one being supposed to penetrate the other, is persectly c...

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