Sir IsaacNewto n’s Book I.

104.

79. A cone is thus defined by Euclidehi his ele-ments of geometry a . If to the straight line A B (in fig.62..)another straight line, as A C, be drawn perpendicular, and thetwo extremities B and C be joined by a third straight linecomposing the triangle A C B ( for so every figure is called,which is included under three straight lines:) then the twopoints A and B being held fixed, as two centers, and the trian-gle A C B being turned round upon the line A B, as on an axis;the line A C will describe a circle, and the figure A C B willdescribe a cone, of the form represented by the figure BCDEF( fig. 6z.) in which the circle CDEF is usually called thebase of the cone, and B the vertex.

80. N o w by this figure may several problems be resolved,which cannot by the simple description of straight lines andcircles upon a plane. Suppose for instance, it were requiredto make a cube, which should bear any assigned proportionto some other cube named. I need not here inform my read-ers, that a cube is the figure of a dye. This problem wasmuch celebrated among the ancients, and was once inforcedby the command of an oracle. This problem may be per-formed by a cone thus. First make a cone from a triangle,whose side AC shall be half the length of the side BC.Then on the plane A B C D (fig. 64. ) let the line E F beexhibited equal in length to the side of the cube proposed;and let the line F G be drawn perpendicular to E F, and ofsuch a length, that it bear the fame proportion to E F, as the

» Lib. XI. Des.

cube