Elements of plane and solid free-hand geometrical drawing, with lettering; and some elements of geometrical ornamental design, including the principals of harmonic angular ratios, etcIn three parts ..for draughtsmen and artisans; and teachers and students of industrial and mechanical drawing . as centres, C theintersection of their radii, being the centre of the arc E F G. 74. Hays comjposite elli])se.—Still, it is desirable, both forthe sake of conformity to Nature, and of completing a systemof geometric beauty, that an oval curve should be found, asnaturally and intimately associated with th
Elements of plane and solid free-hand geometrical drawing, with lettering; and some elements of geometrical ornamental design, including the principals of harmonic angular ratios, etcIn three parts ..for draughtsmen and artisans; and teachers and students of industrial and mechanical drawing . as centres, C theintersection of their radii, being the centre of the arc E F G. 74. Hays comjposite elli])se.—Still, it is desirable, both forthe sake of conformity to Nature, and of completing a systemof geometric beauty, that an oval curve should be found, asnaturally and intimately associated with the various harnionjc 112 FREE-HAND GEOMETEICAL DBA WING. triangles (37-39) as the circle is with the square, or the ellipsewith the rectangle. Hay perceived and stated this want, and, in his search tosupply it, devised the egg-curve which he called the compositeellipse, Fig. 21. Here, the points A, B, C, are foci, and D isthe describing point. That is, pins being set at A, B, C, Dand an inelastic string tied tightly around the four, the pin atD is then replaced by a moving pencil point, as at P, Fig. 14,and this pencil, moved so as to keep the string tense, will de-scribe the egg-curve shown in Fig. 21. Comparing this withFig. 20, the curve will evidently consist of several elliptical. arcs; first mJ)n, with B and C for its foci; second no, withA and B for foci; third, op, with A and C for foci; next, theshort arc pq with B and C again as foci, etc. The curves thusformed are divided by Hay into five classes, according asthe angle at D is 90°, 108°, 120°, 135°, 144°, these all havingsimple ratios to 180°. Each class is then divided into as many degrees as there may be angles chosen at A having simpleratios to the fixed class angle at D. Thus a great variety of egg-forms, or ovals, including manyoblate ones, are formed; as when, for example, the angles atA and D are made 90° and 135° respectively. All these can CUEVILINEAK GEOMETRIC BEAUTY. OVALS. 113 readily be traced,
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Keywords: ., bo, bookcentury1800, bookdecade1870, booksubjectmechanicaldrawing
