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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.
If 40 oranges are worth 60 apples, and 75 apples are worth 7 dozen peaches, and 100 peaches are worth 1 box of grapes and three boxes of grapes are worth 40 pounds of pecans, how many peaches can be bought for 100 oranges?
Relationships between Architecture and Mathematics
Three equal circumferences with radii 6" are tangent to each other. Compute the area enclosed between them.
An oblong garden is a half yard longer than it is wide and consists entirely of a gravel walk...
Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 7 months.
The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".
A detailed study of the cycles of the Mayan calendar, along with some other ancient calendars.
Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By looking at the line of vision, determine, to the nearest mile, the radius of the earth.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.

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