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

Find the two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.
In a square box that contains 1000 marbles, how many will it take to reach across the bottom of the box in a straight row?
Determine the greatest cylinder that can be inscribed in a given cone.
Given a wooden log of diameter 2 feet 5 inches from which a 7 inch thick board is to be cut, what is the maximum possible width of the board?
There are many historical sessions during the 2007 summer meeting of the Mathematical Association of America.
A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. How many did he have?
I wish to find three numbers of such nature that the first and the second with 1/2 of the third makes 20...

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