Letter to his family, July 1507, among lune quadratures
A personal letter to mother, sisters and brother-in-law surrounded by sickle-shaped (lune) geometry
A heavily stained sheet dominated at the top by a personal letter dated July 1507, addressed to a beloved mother, sisters and brother-in-law: it reports the writer's good health, gives instructions to sell a sword left behind by taking it to Maso delle Viole at the Piazza degli Strozzi, commends certain garments and a woman named Dianira, and promises a visit by the end of September. The rest of the page is filled with small curvilinear triangles and sickle-shaped figures (falcate, i.e. lunes) studied for their quadrature, with numeric and lettered labels. A pen trial reading 'Sunday, Sunday' sits inverted near the left margin.
On this page
Letter to mother, sisters and brother-in-law, July 1507
In the name of God, on a day of July 1507, the writer greets his dear mother, sisters and brother-in-law, reports himself well by God's grace, and reminds them to take a sword he left with them to Maso delle Viole at the Piazza degli Strozzi and sell it. He commends some garments and a woman Dianira, and promises to come by the end of September, stay a few days, and settle Piero's affair to his contentment.
Lune with the middle line as a half-circle
A curvilinear triangle labelled a-edcba-o accompanies numbers 4 3 4. The middle line a b o must belong to a circle half the size of the other lines, and Leonardo balances what he removes and gives back at each lune (falcata).
Squaring the lune: c squared equals a sector
In a two-triangle figure, a c is equal to b d o and the a b are equal to one another; therefore c squared is equal to the sector o d, which is squarable.