The triangles already belonged to a satire of unlimited emancipation
Somebody wrote a work called "The Loves of the Triangles";
The title belongs to a collaborative parody published in three installments of the Tory Anti-Jacobin in 1798. The inspected witness is Tristanne Connolly's 2025 Romantic Circles transcription of the original issues 23, 24 and 26, which records variants from the 1799 collections. Its introduction identifies Gifford, Canning, Ellis and Frere as involved while warning that particular contributions are difficult to assign securely. The poem parodies the erotic scientific personification of Erasmus Darwin's botanical poetry: its mock argument includes a marriage of Euclid and Algebra and a Rectangle in love with three Curves. See the edition, introduction and opening argument, PDF pp. 1–5.
An especially apt coincidence lies in the prose introduction, where the fictitious author Higgins treats established institutions as restraints on natural human agency and imagines humanity expanding beyond its existing condition. Chesterton's joke thus names a work whose own satire had connected extravagant emancipation with geometrical absurdity. He expressly says he has never read it, so this contextual fit should not be turned into an influence claim. His immediate use of its title is different: even affection for a triangle would presuppose the identity supplied by its three sides.
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