T. Frankel's The Geometry of Physics - an Introduction (revised, PDF

By T. Frankel

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Additional resources for The Geometry of Physics - an Introduction (revised, corrected)

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The statement of the problem is apparently incomplete and the proof is faulty. What seems incomplete is an unannounced line-segment required for an operation. The fault lies in concluding that because corresponding sides of two triangles are proportional, the triangles are congruent, as Background xxxv the Latin text states. In fact they are only similar, as I corrected the text. The error is so obvious that it suggests to me that someone else added the two paragraphs. Inasmuch as both are at the end of a major section, I wonder if they were not slipped in by an over-eager instructor or copyist who thought he had successfully captured Fibonacci’s method.

To touch the right ankle bone from the same side with the tip of the left foot means 5. The 18 Fibonacci’s De Practica Geometrie other five signs are made in the same order with the right foot on the left. The sign for 11 is made by placing the heel of the right foot over the left ankle bone. We do not need additional signs because 12 deniers make one soldus that can be kept in the left hand. Nothing need be said about manual signs because everyone who knows how to calculate knows them. We return to what was proposed: you will multiply again 2 feet by 12 rods to get 12 solmdi.

Some gather by multiplying from these areal measures a certain quantity which they call iugerum or aripennium or carrucam or tornaturam or culturam or other quantities which require other words. I, however, follow the custom at Pisa beginning with the rod. The Pisan linear rod is six linear feet long. A linear foot consists of 18 linear points. The square or areal rod consists of six areal feet. An areal foot is one rod long and six parts of a rod wide. An areal inch is one rod long and an eighteenth part of a long foot wide.

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The Geometry of Physics - an Introduction (revised, corrected) by T. Frankel


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