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and this figure, there is much resemblance, either kind having all sides equal; and likewise their angles in general quantity; but they differ in particular quality. A square has four right angles, while this has two obtuse and two acute angles; yet, they are in general quantity equal to four right angles: for by as much as the two acute angles are deficient (or wanting) of two right angles, by so much do the obtuse angles abound or exceed. This figure is described by the connection of two equilateral triangles, joined by any two of their sides, as appears by the dotted diagonal line B-C. Which being omitted and left out, this figure remains perfect, and has its acute angles equal to those of an equilateral—namely, 60 degrees—and the obtuse angles double thereunto. PRO. 57.

A geometric diagram showing a rhombus formed by two equilateral triangles joined at a common side, with a dotted diagonal line B-C.

DEFIN. XXVII.

A rhomboides (or diamond-like figure) is a figure whose opposite sides and opposite angles are only equal, and which has no right angles.

Euclid, Book 1, Def. 33. Ramus, 9. 14.

AS this figure A-B-C-D is a rhomboides, and has its sides A-B and C-D opposite and equal, and likewise A-C and B-D, but has no right angle. For the angles at the points A and D are acute, opposite, and equal; and likewise the angles at the points B and C are obtuse, opposite, and equal.

A geometric diagram of a rhomboid labeled A, B, C, D.

Note here, that the four figures last before defined—namely, a square, a figure of one side longer (rectangle), a rhombus, and a rhomboides—are commonly called parallelograms; of which four, the two former are called right-angled parallelograms. PROB. 90.