Turning a rectangle into a square, and changing its sides
Problems on how a rectangle's length and width change when it is stretched or narrowed.
A set of paired geometrical problems on transforming a long rectangle ('tetragono lungo') into a square and back again. Each problem fixes one dimension to a given size and asks by how much the other dimension must grow or shrink, exploring the reciprocal relation of length and width under a constant area. A small rectangle is drawn beside the second block of text.
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Transforming a rectangle into a square and back
Leonardo lists the operations: from a long rectangle make a square, and from a square make the long rectangle. He then asks, for a square narrowed to a given width, how much it grows in length; and for a square stretched to a given length, how much it narrows in width.
How much a rectangle's sides change when widened or narrowed
Widening a rectangle to the limit of a given distance, one seeks how much length it loses. Narrowing a rectangle to a given narrowness, he asks how much it grows in length.