Triangle Subdivisions, Concentric Circles, and Eyeglasses
Equilateral triangles divided by medians within paired circles; a note on how eyeglasses magnify
Most of the sheet is geometric: an equilateral triangle repeatedly subdivided by lines from each vertex to the midpoints of the opposite sides, producing a nested smaller triangle, and two 'coronas' of concentric circles in which equilateral triangles are inscribed on shared radii. A note records that the chord a b enters five times into the smaller circle and c d seven times into the larger, while the triangle's bases each enter six times. A final paragraph on eyeglasses states that the farther eyeglasses (of the kind made for fifty-year-olds) are held from the eye the larger they make things appear: of two equal objects two hundred braccia away, the one seen through the eyeglass looks large and the other small.
On this page
Equilateral triangle subdivided by medians into a nested triangle
An equilateral triangle is divided by lines drawn from each vertex to the midpoint of the opposite side, and by further lines from the apex to the midpoints of the halved base; parallels to the base pass through the intersections, the uppermost forming the base of a new, smaller equilateral triangle that repeats the same subdivision.
Concentric circles with inscribed equilateral triangles (a, b, c, d)
Two radii of the outer circle form the sides of an equilateral triangle whose base is a chord tangent to the inner circle, and a parallel forms a second triangle within. The chord a b enters five times into the smaller circle, c d seven times into the larger, and each triangle's base enters its circle six times.
How eyeglasses magnify with distance from the eye
The farther eyeglasses (of the kind for fifty-year-olds) are set from the eye, the larger they show things. Of two equal objects at two hundred braccia, the one seen through the eyeglass appears large and the one seen outside it small.