De divina proportione

work by Pacioli

Also known as: “Divine Proportion”

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Last updated

July 16, 2026

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Luca Pacioli, a mathematician and Franciscan friar during the Italian Renaissance, authored De divina proportione (1509), which explored the golden ratio. This mathematical concept, often represented by the Greek letter phi ((\phi)), is an irrational number approximately equal to 1.618. It is defined by dividing a line segment into two unequal parts such that the ratio of the whole segment to the longer part is equal to the ratio of the longer part to the shorter. Pacioli's work, illustrated by Leonardo da Vinci, celebrated the ratio's perceived harmony. The golden ratio has roots in ancient Greek mathematics, with Euclid describing it in his Elements.1

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golden ratio
History
mathematician Luca Pacioli published De divina proportione (1509; “Divine Proportion”), a treatise that celebrated the ratio’s supposed harmony. The book was illustrated by polymath Leonardo da Vinci, whose works have often been analyzed for evidence of golden ratio proportions. German astronomer–mathematician Johannes Kepler, in Harmonices Mundi (1619; “Harmony of…
Read More
mathematician Luca Pacioli published De divina proportione (1509; “Divine Proportion”), a treatise that celebrated the ratio’s supposed harmony. The book was illustrated by polymath Leonardo da Vinci, whose works have often been analyzed for evidence of golden ratio proportions. German astronomer–mathematician Johannes Kepler, in Harmonices Mundi (1619; “Harmony of…
Read More