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## Search Loci: Convergence:

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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.

In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

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# Van Schooten's Ruler Constructions

## Solution to Problem X

Problem X:   Given three straight lines AG, BC and AD, to find a fourth proportional DE, that is so that AB is to BC as AD is to DE.

This problem can be done in the manner of Euclid, putting the first two lines AB, BC in a straight line AC, and the third on another line AE, which forms an angle CAE with AC.  If BD is drawn parallel to CE, then DE is the fourth proportional being sought.

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