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Caption: Mathematical Models Catalog of a Collection of Models of Ruled Surfaces
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Catalogue of a Collection of Models of Ruled Surfaces* constructed by M . Pabre de Lagrange, with an Appendix, containing an account of the application of Analysis to their investigation and classification. By 0. W . M E B R I F I E L D , F.K.S., Principal of the Royal School of Naval Architecture and Marine Engineering;, and Superintendent of the Naval M u s e u m at South Kensington, INTRODUCTION", This collection illustrates the principal types of the class of surfaces which can be traced out in space by the motion of a straight line. These surfaces, on account of the facility with which they can be constructed and represented, and of the ease with which their intersections can be determined, are of more consequence than any others in the geometry of the Industrial Arts. It is only in small work, which can be put into the lathe, that the class of surfaces of revolution approaches them in respect of general utility, T h e most important surfaces of all, the plane, the right cylinder, the right cone, and the c o m m o n screw, belong to both classes, The representation of the surfaces by means of silk threads is of course only approximate; an approximation of the same character as the representation of a curve by a dotted or chain line, or by a series of right lines touching the actual curve. / mathematics library; .£>5Uu Fig. 2. A 2
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