The objects next presented, were three vases of very dissimilar appearance, all produced from the same diagram of the oval; each in a separate drawing. The first was like a Greek vase with handles; its character established by employing certain proportions of quantities, in seven parts. The body has four parts, the foot or pedestal one; the neck two. The handles were regulated in the position and projection by lines drawn from the bottom of the vase, through the ovals which compose the outline of the two sides; and passing through the transverse diameter. These handles were made from an oval that was the length of half the line of the transverse diameter, _Fig._ 16. The skeleton of angles that [p008] govern the shape of this vase, is a very pretty figure of itself. The form does not proceed from any caprice of irregularity, but is consistent with rational organization, and symmetrical proportions. The figure of the plate sufficiently describes the mode of making the diagram without entering into the detail. _Fig._ 17 represents a tazza with handles: the same disk is apparent, by the dotted lines that made the first vase. The ovals [p009] are placed right and left of a central perpendicular line, dividing the cup in two parts; the transverse diameters meet in one line parallel to the base of the tazza; a dotted outline expresses the angular position of the handles: the concave lip of the tazza is made by the same oval disk, whose transverse diameter leads to the under line of the folding edge of the cup. The leg of the tazza is produced by the same small disk that served for the handles of the first vase. The body of the vase and the leg form two equal parts; the whole upper extent ought to be seven parts, so that it is seven and two[2]; the width of the base of the leg measures two parts, and the altitude three, of the seven parts. These proportions cannot produce any other than agreeable appearances, apply them as we may. [Illustration: _Fig._ 18.] The third vase, exhibited an Hebe cup, with a handle, which presented a totally different appearance in form to the two previous ones. It was proportioned by similar principles: the larger disk made the body, inclined right and left upon the end of the oval. The neck and the leg were both made from the smaller oval disk; the dotted lines to the ovals of the leg sufficiently show the fact. The handle and concave lip of the cup were made by an application of the same disk. The altitude contained four parts. The body two parts, the leg one part, and the neck one other part; the handle rises one-eighth above: every portion of this figure is created by the two disks previously named. The foliage rises from below and descends from above, one-fourth of the whole height of the body [p010] to the commencement of the concavity of the neck, where the beading runs round.