De Divina Proportione

Luca Pacioli's De Divina Proportione, printed by Paganino Paganini in Venice in 1509, is the primary text that gave the golden ratio its enduring name divine proportion, illustrated with polyhedra drawings, including the stella octangula, attributed to Leonardo da Vinci, who was Pacioli's collaborator and friend in Milan at the time of composition. Its strength as a source is that it is the original primary document, not a later paraphrase, and its authorship and illustration are independently corroborated by Leonardo's own notebooks and by the documented Pacioli-Leonardo collaboration. Its limit is that Pacioli's treatise mixes genuine geometric content with numerological and theological claims about the ratio's supposed divine significance that are Pacioli's own Renaissance era argument rather than settled mathematics, so a claim treating the divine proportion's cosmic significance as established fact should be read as reporting Pacioli's argument, not confirming it.