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This is the title page of the 1640 printing of Galileo's Operation of the Geometrical and Military Compass, originally published privately in 1606. Galileo had invented a version of this geometrical compass a few years earlier and evidently gave copies of this manual to those who bought the compass. The compass had many uses, from performing square root calculations to determining ranges of cannons to solving surveying problems.
What is the perpendicular height of a cloud when it's angles of elevation were 35 degrees and 64 degrees as taken by two observers?
If an arc of 45 degrees on one circumference is equal to an arc of 60 degrees on another circle, what is the ratio of the areas of the circle?
Determine the radii of three equal circles decribed within and tangent to a given circle, and also tangent to each other
A man entered an orchard through 7 gates, and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples he had and 1 apple more.
Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?
After a terrible battle it is found that 70% of the soldiers have lost an eye.

A detailed study of the cycles of the Mayan calendar, along with some other ancient calendars.

Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
What is the value of X...

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