Solar Rays, Squaring the Circle, and a Letter to a Friend
Light through an aperture, columns of calculation, and geometric problems
This crowded sheet is dominated by studies of sunlight passing through a small aperture: at the top a fan of rays runs from a solar disc through the opening, with small camera-obscura demonstrations, and a long note analyses how the beam's 'strikings' (percussioni) are mixed with the light of the surrounding air and darken toward their edges. A second large X-shaped ray diagram fills the centre, surrounded by dense columns of squares and products. At the head of the page Leonardo begins a letter — 'Most faithful friend, I let you know how here in the past days there was a …' — while at the foot two small figures pose the classic problems of finding the square of a circle and the circle of a square. Legibility is partial and much of the numerical matter is faint.
On this page
Strikings of the solar ray mixed with the light of the air
The first striking (percussione) of the solar ray is lit toward its centre b by the bare body of the sun, but along a b and b c it is mixed with the light of the surrounding air o p, n m, so it is no longer the pure light of the sun. Toward the edges a c the spaces darken strongly, where the sun's light fails and only the weaker light of the air remains. In the second striking, a c sees the whole solar body and would be very bright but for the darkness of the lateral air.
Figure of shadows and lights
A separate figure of shadows and lights is laid out with the labels e d c b a, m n and i h g f. It accompanies the analysis of graded illumination behind the aperture.
Draft of a letter to a faithful friend
At the head of the sheet Leonardo begins a letter: 'Most faithful friend, I let you know how here in the past days there was a …'. The draft breaks off after the opening.
Columns of squares and products
The right half of the page is filled with columns of numbers — pairs and their squares such as 17 and 11, 289 and 121, 324 and 144 — worked down the sheet. A further short table in the upper right corner runs 1·2·5, 2·4·128, 3·6·45 and so on.
To find the square of a circle
A triangle inscribed in a circle is captioned with the problem 'for the circle, to find its square' — the quadrature of the circle.
To find the circle of a square
A companion figure of a triangle inscribed in a square is captioned 'for the square, to find its circle' — the inverse problem.