sesquialterate

• sesqui-alterate

From Latin sesquialter (“one and a half times”) +‎ -ate (adjective-forming suffix), from sesqui- (“a half and a”) +‎ alter (“another, a second”).

• IPA^(key): /sɛskwɪˈaltərət/

sesquialterate (not comparable)

1. (mathematics, archaic) In a ratio of 3 to 2 or 1½ times to 1.

   Synonyms: sesquialteral, sesquialter, sesquialteran, sescuple

   • 1818, Iamblichus, translated by Thomas Taylor, Life of Pythagoras‎^[1], page 328:

     […] the ratio of 3 to 2, which is sesquialter, forms the symphony diapente […]

   • 1859, Frances Power Cobbe, An Essay on Intuitive Morals: Being an Attempt to Popularize Ethical Science, page 84:

     People ignorant of geometry did not know the sesquialterate ratio of the sphere, cylinder, and cone, and therefor no man could know it […]

   • 1888, Sir Isaac Newton, Portsmouth Collection of Books and Papers Written or Belonging to Sir Isaac Newton (page xviii)

     from Kepler's Rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centers of their orbs I deduced […]

   9 and 6 are in a sesquialterate ratio.

• sesquialter

• “sesquialterate, adj.”, in OED Online ⁠, Oxford: Oxford University Press, 2022.