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2. Take H on DF such that AH = OE (= ~b); draw CH; draw AI parallel to C H. 28[Eutocius CommSphrCyl] pp. 615-620. 34 2. The legitimation of geometrical procedures before 1590 3. By "neusis" draw a line H J K through H, intersecting AI and DA prolonged in J and K, respectively, and such that JK = DE (= ~b). 4. Draw and prolong KG, it intersects DB prolonged in L. 5. x = H J and y = AK are the required proportionals. 6. Moreover, LB = x, so Nicomedes' construction yields the same configurations as Heron's.

Finally, there were the mathematicians who simply were not interested in the (6) matter. This attitude was probably rather common, but in individual cases it Non-interest is difficult to distinguish it from the attitude listed above under (1). One major figure in the category of non-interest is Fermat, who, despite his important contributions to methods for analyzing geometrical problems, seems to have had very little affinity to questions of the acceptability of the constructions found by these methods (Chapter 13).

He may shorten it where modern insight makes the result obvious and no lessons can be learned from going into detail through elaborate and unfamiliar notation and terminology, and he does well to unify the presentation where differences are unessential. On the other hand, he may need to expand certain now unfamiliar steps in the argument. In accordance with these general remarks I have not hesitated to modify the presentation of mathematical argument with respect to notation, symbols, and figures, in such cases where this makes the essence more clear and does not change the meaning.

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3-D Shapes by Marina Cohen

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