Caption: Mathematical Models Catalog of a Collection of Models of Ruled Surfaces
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9 15. Hyperboloid of one Sheet. A slight variation from No. 14. The paraboloid only shows one system of right line generators, and the tangent plane is made by parallel instead of radiating lines. 16. Hyperboloid of one Sheet, and its tangent paraboloid. This shows the transformation of a cylinder and its tangent plane into a hyperboloid and i s tangent paraboloid. t 17. Conoid with its director plane. The director curve i plane curve. By shifting the position of the brasses, the conoids deform into different conoids or other allied surfaces. IB. Conoid with a director cone. The director curve is o double curvature. B y shifting the position of the brasses the conoids deform into different conoids or other allied surfaces. 19. Conoid showing both sheets of the surface. B y shifting the position of the brasses the conoids deform into different conoids or other allied surfaces. 20. Conoids. Model showing the transformation of a cylinder into a conoid and back again. Also model showing the transformation of a cone into a conoid and back again. It is to be noticed that the head-lines of the two conoids, that i to say, the right line in which s the two sheets of each conoid meet, are perpendicular to one another. The transformation is effected by making the upper semicircle turn through two right angles. 21. Conoids. Intersection of two equal conoids having a common director plane. The horizontal intersection is a plane ellipse. 22. Conoid, in contact with a hyperbolic paraboloid. 23. Conoids. Two equal circles in parallel planes, divid equi-distantly, are connected by threads, so as to form four surfaces. A cylinder. A conoid. A cone. A second conoid. The director planes, as well as the head lines, of these conoids are at right angles to one another.
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