Jevons's Elementary Lessons in Logic, Lesson XV, "The Rules of the Syllogism" (pp.126–131), is the text behind the eight numbered rules Aikins reproduces in his Ch. XVI footnote

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Jevons's Lesson XV states that the rules of the syllogism "are eight in number" and lists them: (1) every syllogism has three and only three terms; (2) every syllogism contains three and only three propositions; (3) the middle term must be distributed once at least, and must not be ambiguous; (4) no term must be distributed in the conclusion which was not distributed in one of the premises; (5) from negative premises nothing can be inferred; (6) if one premise be negative, the conclusion must be negative, and vice versa — followed by two rules Jevons explicitly calls "subordinate," "deduced" from the first six: (7) from two particular premises no conclusion can be drawn; (8) if one premise be particular, the conclusion must be particular.

This is the same structure claim-aikins-1902-ch16-footnote-quotes-jevons-eight-syllogism-rules-verbatim-then-rejects-them describes Aikins reproducing verbatim in his Chapter XVI footnote, "The rules, as stated by Jevons, are as follows": eight numbered rules covering the same three-term/three-proposition requirement, middle-term distribution, conclusion distribution, and negative/particular premises, with the last two explicitly marked "subordinate rules" "deduced" from the first six — matching Jevons's own framing rule for rule, in the same order.

This resolves question-verify-aikins-1902-jevons-source-edition-for-conversion-and-syllogism-rules for the syllogism-rules half of that question. See claim-jevons-elementary-lessons-lesson-x-source-of-aikins-conversion-rule-citations for the companion match on the conversion-rule side, and claim-jevons-elementary-lessons-1881-printing-toc-confirms-stable-pagination-since-1870 for the independent pagination check.