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MANUAL OF CHRISTIAN ANTIQUITIES; Or, An Account of the Constitution, Ministers, Worship, Discipline, and Customs of the Early Church : with a Complete Analysis

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DESCRIPTIVE GEOMETRY.

1. The object of Descriptive Geometry is the invention of methods by which we may represent upon a plane, having only two dimensions, length and breadth, the form and position of a body which possesses three dimensions, length, breadth, and height.

This definition of the chief object of descriptive geometry includes its application to points and lines situated above or below the plane, to which they are to be referred ; and thus gives us means of drawing such lines and points with an accuracy unnecessary and unknown to common geometry. For the results obtained in plane geometry do not depend upon the faithfulness with which the figures are drawn, but upon the accuracy with which the reasoning in conducted. But even in these problems we often make assumptions with regard to the mechanical drawing of lines, which we should find it extremely difficult to execute. Thus in Proposition XI. of the Introduction we say, draw AD I Bc; but the practical difficulty of drawing, AD IE ** great as that of drawing ah, the objsct of the problem,

The means by which descriptive gestry attaissa isa object is the method of Projections, which we ww progui to explain.

2. The projection of a pris un 3 puts it cle ius of the perpendicular let 120 425 the utmo1 plane.

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