Abstract
I QUITE agree with Prof. Alfred Lodge as to the order of propositions he proposes, which is practically the order I adopted in my “Foundations of Geometry.” But he does not in his letter refer to what seems to me the chief reason for it, which is that the elementary geometry of straight lines and angles should precede the geometry of plane surfaces, including any propositions about areas. And to carry out this idea, the fundamental propositions which Euclid gives so badly in his XIth. book (props. 1–9) ought to be taken before such propositions as his I. 35 and 36. On the other hand, there are important propositions in the XIth. book, notably prop. 10 (if this is not included in the definition of parallelism) and props. 20 and 21, which come properly in what Prof. Lodge calls the first part of Book I.
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DIXON, E. Rearrangement of Euclid Book I., Pt. i.. Nature 65, 559 (1902). https://doi.org/10.1038/065559b0
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DOI: https://doi.org/10.1038/065559b0
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