incommensurable

From Middle French incommensurable, from Medieval Latin incommensurabilis.

Its full etymology is equivalent to that of in- + commensurable.

• (Received Pronunciation) IPA^(key): /ɪnkəˈmɛnʃ(ə)ɹəbəl/, /ɪnkəˈmɛnsjʊəɹəbəl/
• (General American) IPA^(key): /ɪn.kəˈmɛnt͡ʃ.ɹə.bəl/, /ɪn.kəˈmɛn(t).sə.ɹə.bəl/, /ɪn.kəˈmɛn(t).sə.ɹə.bəl/

incommensurable (comparative more incommensurable, superlative most incommensurable)

1. (mathematics, of two real numbers) having a ratio that is not expressible as a fraction of two integers.

   The side and diagonal of a square are incommensurable with each other; the diameter and circumference of a circle are incommensurable.

2. (mathematics, of two integers) having no common integer divisor except 1.
3. Not able to be measured by the same standards as another term in the context.

The term contrasts with unmeasurable and immeasurable in that both mean "not able to be measured at all", with the latter generally being because of some infinite quality of the thing being described.

• incommensurate

incommensurable (plural incommensurables)

1. An incommensurable value or quantity; an irrational number.
   • 1946, Bertrand Russell, chapter 3, in History of Western Philosophy:

     Unfortunately for Pythagoras, his theorem led at once to the discovery of incommensurables, which appeared to disprove his whole philosophy.

• “incommensurable”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
• “incommensurable”, in The Century Dictionary […], New York, N.Y.: The Century Co., 1911, →OCLC.
• “incommensurable”, in OneLook Dictionary Search.

Borrowed from Late Latin incommēnsūrābilis.

• IPA^(key): /ɛ̃.kɔ.mɑ̃.sy.ʁabl/

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incommensurable (plural incommensurables)

1. (mathematics) incommensurable
2. immeasurable

   Synonym: immense

• incommensurablement

• “incommensurable”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.