How the three triangles derive from three quadrangles
Square, rectangle and rhombus halved by their diagonals; the square defined
Folio 1v shows how each kind of triangle is obtained by halving a quadrangle along its diagonal. A square, a rhombus and a rectangle (long tetragon) are each divided by a diagonal, yielding right and obtuse triangles as the captions record. The page closes with a formal definition of the square as a four-sided figure of equal sides composing four right angles.
On this page
Each quadrangle divided by its diagonal
In series a square, a rhombus and a rectangle are each cut by a diagonal and captioned with the triangle each half yields - square and right triangle, long tetragon and right triangle, rhombus and obtuse triangle.
Triangles produced by halving quadrangles
The right triangle with two equal sides comes from half a square; the right triangle with three unequal sides from half a long tetragon; and the obtuse triangle from half a rhombus cut along its greater length.
Definition of the square
The square is a figure of four sides equal among themselves composing four right angles, the lines that form the angles being equal to one another.