## An elementary treatise on descriptive geometry, with a theory of shadows and of perspective: extr. [by B. Brisson. Tr.]. To which is added, a description of the principles and practice of isometrical projection, by J.F. Heather. [With] Atlas of plates |

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axis body which casts bright brilliant point casts the shadow circumference colour conceived cone conic section conical surface consequently cube curve of double curved surfaces cutting plane cylindrical surface descriptive geometry developed surface diagonal direction distance double curvature draw a tangent drawing the straight edges ellipse equal faces given curve given plane given point given straight line hori horizontal and vertical horizontal plane horizontal projection horizontal trace indefinite straight line isometric axes isometric planes isometric projection let fall line parallel luminous body luminous point manner meets L M method pendicular perspective plane passing planes of projection point H point of intersection points of contact Prob produced projecting the point radius rays of light remitted required intersection respect right angles second surface sphere straight line A B suppose surface of revolution tangent plane tion twisted surface vertex vertical plane vertical projection vertical trace visual ray

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Página i - DESCRIPTIVE GEOMETRY, an Elementary Treatise on; with a Theory of Shadows and of Perspective, extracted from the French of G. MONGE. To which is added, a description of the Principles and Practice of Isometrical Projection ; the whole being intended as an introduction to the Application of Descriptive Geometry to various branches of the Arts.

Página 115 - The surfaces may be divided into two classes, according to the manner in which they receive and remit the light ; viz., polished surfaces and dull surfaces.

Página 134 - ... sinister distance, and its altitude. And it is manifest they need not be taken in this order, but in any other that may be more convenient to the artist, there being six ways in which this operation may be varied. If any point in the same isometrical plane with the point required to be found, is already represented in the picture, that point may be assumed as a new regulating point, and the point required found by taking two distances ; and if the new assumed regulating point is in the same isometrical...

Página 84 - ... AM produced, and the parallelogram MPEQ, be completed, the diagonal ME of this parallelogram will be the direction of the motion of the generating point at M, and consequently the tangent to the curve at this point. It is clearly seen from this, that in the ellipse the tangent bisects the angle BMP, formed by one of the focal distances and the production of the other...

Página 82 - Moreover, each of the series of spherical surfaces will cut the second surface of revolution in the circumference of a circle, the plane of which will be perpendicular to the vertical plane of projection, and of which the vertical projection will be obtained by drawing through the pointy a...

Página 83 - ... vector can be determined by elementary trigonometry ; and in its application to many other curves, of high and low degree, a like simplicity characterizes this elegant process. Nevertheless, in his treatise on Descriptive Geometry, Mr. JF Heather makes this curious remark : " This method, which Roberval invented before Descartes had applied algebra to geometry, is implicitly comprehended in the processes of the differential calculus, on which account it is not noticed in elementary mathematics";...

Página 84 - FIG. 13. point. It is clearly seen from this, that in the ellipse, the tangent bisects the angle BPN formed by one of the focal distances and the production of the other," etc., etc. Mr. Heather elsewhere explicitly states that if the components in two directions are given, whatever their relative magnitudes, the method of Roberval consists in " completing the parallelogram and drawing the diagonal.

Página 10 - These three examples are sufficient to make it evident that all curved surfaces may be generated by the movement of certain curved lines, and that there is not any surface whose form and position cannot be completely determined by an exact and complete definition of its mode of generation.

Página 1 - DESCRIPTIVE geometry has two objects in view : the first to determine methods for representing on a sheet of paper which has only two dimensions, viz., length and breadth, the forms of solid bodies which have three, length, breadth, and thickness, provided that these bodies can be rigorously defined.

Página 84 - AP produced, and the parallelogram /WKWbe completed, the diagonal PO of this parallelogram will be the direction of the motion of the generating point at P, and consequently the tangent to the curve at this point. It is clearly seen from this, that in the ellipse the tangent bisects the angle BPN, formed by one of the focal distances and the production of the other, '