Caption: Mathematical Models Catalog of a Collection of Models of Ruled Surfaces
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7 6 Hyperbolic Paraboloid. . A skew quadrilateral,- with its opposite sides equal in length, and pierced with holes at equal distances. Nearly similar to N o . 5, but differently mounted, and with the sides of different lengths, the alternate sides only being equal. It is virtually a slightly different aspect of the same surface as N o . 5. 7. Hyperbolic Paraboloid. A skew quadrilateral, with all its sides equal, and pierced holes at equal distances. A s far as the curved surface is concerned, the same as N o . 5. B u t the hinges are altered in direction, and the model shows plans and elevations of the right line generators of the surface. T h e rings also show parabolic sections of the surface. In consequence of the alteration in the direction of the hinges, the spacing of the inclined bars, although equidistant, is at a different pitch from that of the horizontal bars. 8. Hyperbolic Paraboloid, A skew quadrilateral with all its sides equal, and pierced with holes at equal distances. It shows the plans and elevations of the right line generators. T h e rings show the parabolas of the principal sections. N o . 7 represents one quarter of what is shown in N o . -8. T h e upper corners of Nos. 7 and 8 correspond; but the lower corner of N o . 7 corresponds with the middle ring of N o . 8. 9. Hyperbolic Paraboloid, A skew quadrilateral with all its sides unequal. The surface is the same as Nos. 7 and 8, but the proportions and the portion of the surface chosen for representation are different. T h e quadrilateral base being irregular, the strings alter in length as the surface is deformed by closing the hinges. 10. Hyperbolic Paraboloid. Skew quadrilateral, pivoting on a single hinge. Intended to show the construction of the parabola connecting two roads which meet obliquely. This construction is used by engineers in laying out roads.
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