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Convergence articles

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Benjamin Banneker solved some trigonometry problems in his extant notebooks. One of them is discussed here. The authors have also discovered the probable source of Banneker's trigonometry table.
The three sides of a triangular piece of land, taken in order, measure 15, 10, and 13 chains respectively.
A brief outline of policies for submission of articles to Loci.
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

Illustration of a counting board in Strasbourg
Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the length of those sides.
I am a brazen lion; my spouts are my 2 eyes, my mouth, and the flat of my foot. My right eye fills a jar in 2 days, my left eye in 3, and my foot in 4.
This is an invited working conference as part of the ICMI Study Series.

Three images from Kepler's 1609 Astronomia Nova, the text in which he introduced his first two laws of planetary motion