Similar triangles, a common chord, and mirror incidence
Proportion of triangle bases and legs; the angle of incidence in mirrors
Beside lettered figures this opening states that similar triangles have their bases in the same proportion as their legs (catheti), and sets up a problem of two different irrational heights joined by a single chord running between their opposite ends. On the facing leaf a marginal note argues that the angle of incidence in mirrors always has the potential to form two further angles with two further sides, placing it between two similar but unequal triangles. Faint geometric and perspective-like constructions of converging lines and triangles fill both leaves.
On this page
Bases of similar triangles follow their legs
Such will be the proportion of the bases that similar triangles have between them as is that of their catheti (legs). The rule links the triangles' bases directly to their corresponding sides.
Two irrational heights joined by one chord
He takes two different irrational heights, somewhat distant from one another, from which descends one and the same chord, its opposite ends joined to those heights. The setup prepares a proportional comparison between the two.
Angle of incidence in mirrors and unequal triangles
Always the angle of incidence in mirrors has the potential to have two other angles with two other sides, and so it lies between two similar but unequal triangles, and this inequality... The note breaks off as it develops the geometry of reflection.