Aristotle - The Organon - index for ANALYTICA POSTERIORA Book 1 Part 7

No demonstration may pass from one genus to another

Paragraph 1 It follows that we cannot in demonstrating pass from one genus to another.
Paragraph 2 (1) what is proved, the conclusion - an attribute inhering essentially in a genus;
Paragraph 3 (2) the axioms, i.e. axioms which are premisses of demonstration;
Paragraph 4 (3) the subject-genus whose attributes, i.e. essential properties, are revealed by the demonstration.
Paragraph 5 Arithmetical demonstration and the other sciences likewise possess, each of them, their own genera;

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