Circular segments in continuous proportion
Turning 3 similar arcs into 7 equal ones, and 7 into 3 in continuous proportion
In ink (mirror script) with pen diagrams, this page poses a problem on similar circular segments. Given three similar segments a, b and c in continuous proportion, the note asks to make seven equal segments similar to each; a fan of seven nested arcs on a single chord and a row of seven small segments work the transformation, and the text adds the converse, from seven equal segments to make three in continuous proportion. The problem belongs to the notebook's Euclidean geometry of proportional figures.
On this page
From 3 similar arcs (a, b, c) to 7 equal ones
Given three similar circular segments a, b and c standing in continuous proportion, the problem is to construct seven equal segments each similar to those first proposed. The three lettered arcs at the top pose the data.
Seven nested arcs and the converse problem
A fan of seven arcs sharing one chord, and a row of seven separate segments, carry out the equalisation. A note then reverses the task: from seven equal and similar portions make three similar ones in continuous proportion.