A Sector is a very old tool to graphically lay out proportions with dividers. Based on the principles of similar triangles, it’s mainly used for scaling drawings but can be directly applied to a project if necessary. The tool opens to a wide V where you can, on the Line of Lines, see that the distance between the “6” markings is half the distance between the “12” markings, and the “4” marking separation is a third of the “12” separation. That much is intuitive, useful for scaling a drawing up by say, a third. Quick – how tall is a 7 1/2” drawer front if scaled up by a third? Set your dividers to the height of the front, open the sector so the divider just spans the “9” markings, then open your dividers to span the “12”. No math involved, and mathematicians were scarce in the 17th century.
There is also a scale labeled “Line of Circles”. It has markings for “Radius”, Diameter”, and “Circumference”. These are also intuitive proportions. Diameter = 2 X Radius and Circumference = Pi X Diameter. Linear relationships.
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