See apotome in All languages combined, or Wiktionary
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The mathematical sense is attested in Euclid's Elements (Book X, proposition 73, et seq.).", "forms": [ { "form": "apotomes", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "apotome (plural apotomes)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "_dis1": "0 0 0", "word": "binomial" }, { "_dis1": "0 0 0", "word": "limma" } ], "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Geometry", "orig": "en:Geometry", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "45 41 14", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "50 41 9", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "45 41 14", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "44 41 16", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "36 37 27", "kind": "other", "name": "Terms with Ancient Greek translations", "parents": [], "source": "w+disamb" }, { "_dis": "46 38 16", "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w+disamb" } ], "examples": [ { "ref": "2012, Jade Roskam, “Book X of The Elements: Ordering Irrationals”, in Bharath Sriraman, editor, Crossroads in the History of Mathematics and Mathematics Education, Information Age Publishing, page 210:", "text": "Yet it is not until Book X that the properties of such a line (with greater length is an apotome and lesser length a first apotome) are explained and not until Book XIII that this type of line is applied, which will be discussed in more detail later.[…]The likewise is true of apotomes (X. 97).", "type": "quote" }, { "text": "2014, Jacques Sesiano (translator), Liber Mahameleth, Part Two: Translation, Glossary, [12th c, Anonymous (possibly John of Seville), Liber Mahameleth], Springer, page 767,\nIf some number and the root of the root of a number are multiplied by the corresponding apotome, the result will be an apotome." } ], "glosses": [ "The difference between two quantities or lengths commensurable only in power, as between 1 and the square root of 2, or between the diagonal and side of a square." ], "id": "en-apotome-en-noun-5Eu9BLpo", "links": [ [ "mathematics", "mathematics" ], [ "geometry", "geometry" ], [ "difference", "difference" ], [ "commensurable", "commensurable" ], [ "power", "power" ], [ "square root", "square root" ], [ "diagonal", "diagonal" ], [ "side", "side" ], [ "square", "square" ] ], "raw_glosses": [ "(mathematics, geometry) The difference between two quantities or lengths commensurable only in power, as between 1 and the square root of 2, or between the diagonal and side of a square." ], "topics": [ "geometry", "mathematics", "sciences" ], "translations": [ { "_dis1": "79 18 3", "code": "grc", "lang": "Ancient Greek", "roman": "apotomḗ", "sense": "difference between two quantities commensurable only in power", "tags": [ "feminine" ], "word": "ἀποτομή" }, { "_dis1": "79 18 3", "code": "pt", "lang": "Portuguese", "sense": "difference between two quantities commensurable only in power", "tags": [ "masculine" ], "word": "apótomo" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Music", "orig": "en:Music", "parents": [ "Art", "Sound", "Culture", "Energy", "Society", "Nature", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "45 41 14", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "50 41 9", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "45 41 14", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "44 41 16", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "36 37 27", "kind": "other", "name": "Terms with Ancient Greek translations", "parents": [], "source": "w+disamb" }, { "_dis": "46 38 16", "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w+disamb" } ], "examples": [ { "text": "1813, Music, article in John Mason Good, Olinthus Gregory, Newton Bosworth, Pantologia: A New Cyclopaedia, Volume 8: MID—OZO, unnumbered page,\nThis semitone was termed by the Pythagoreans apotome, and the diatonic semitone was termed limma. They contended, that the apotome, or distance from B flat to B natural, was larger than the limma, or distance from A to B flat." }, { "ref": "1820, Proclus, translated by Thomas Taylor, The Commentaries of Proclus on the Timæus of Plato, Volume 2, Facsimile edition, published 1967, pages 66–67:", "text": "For the ratio of the excess of the apotome, above that which is truly a semitone, and which cannot be obtained in numbers, is thus called. This then is demonstrated. To what has been said however, it must be added, that we have called the ratio of d b a semitone, not that a sesquioctave is divided into two equal ratios; for no superparticular ratio is capable of being so divided; but because the followers of Aristoxenus assume a semitone after two sesquioctaves, the ratio of a semitone is assumed, as we have said, according to their position, in order to discover what the ratio is of the comma and apotome to the ratio of the leimma.", "type": "quote" }, { "ref": "1984, Mark Lindley, Lutes, Viols, Temperaments, Cambridge University Press, page 9:", "text": "The traditional term, from ancient Greek theory, for the diatonic pythagorean semitone is 'limma'; and for the larger, chromatic semitone, ‘apotome’.\nThe oldest extant fretting formula, that of the ninth-century theorist Al-Kindi for the ud (the Arabic lute), is pythagorean. It calls for five frets, to make the following succession of semitones down from nut: limma, apotome, limma, apotome', limma.", "type": "quote" } ], "glosses": [ "The remaining part of a whole tone after a minor second has been deducted from it; an augmented unison. Most commonly used to refer to the Pythagorean chromatic semitone, which has a ratio of 2187/2048." ], "id": "en-apotome-en-noun-YMWJFVbb", "links": [ [ "music", "music" ], [ "tone", "tone" ], [ "minor second", "minor second" ], [ "deduct", "deduct" ], [ "augmented unison", "augmented unison" ] ], "raw_glosses": [ "(music) The remaining part of a whole tone after a minor second has been deducted from it; an augmented unison. Most commonly used to refer to the Pythagorean chromatic semitone, which has a ratio of 2187/2048." ], "topics": [ "entertainment", "lifestyle", "music" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Zoology", "orig": "en:Zoology", "parents": [ "Biology", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "45 41 14", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "45 41 14", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "44 41 16", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "36 37 27", "kind": "other", "name": "Terms with Ancient Greek translations", "parents": [], "source": "w+disamb" }, { "_dis": "46 38 16", "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w+disamb" } ], "examples": [ { "ref": "1964, Proceedings of the Zoological Society of London, Zoological Society of London, page 287:", "text": "The bands pass inside the margins of the apotome as they approach its constriction and form two pigmented areas broadly based on the frontal sutures and becoming dispersed towards the mid-line.", "type": "quote" }, { "ref": "2008, John L. Capinera, Encyclopedia of Entomology, →ISBN, page 3766:", "text": "In generalized Diplura, Archaeognatha and some Thysanura, five parts or apotomes are distinguished, which from the anterior to the posterior part are: the presternum, the basisternum, the furcasternum, the spinasternum and the poststernum.", "type": "quote" } ], "glosses": [ "A distinct division of an insect which is divided from the other divisions by a pinch point." ], "id": "en-apotome-en-noun-6~FVz6gR", "links": [ [ "zoology", "zoology" ] ], "raw_glosses": [ "(zoology) A distinct division of an insect which is divided from the other divisions by a pinch point." ], "topics": [ "biology", "natural-sciences", "zoology" ] } ], "sounds": [ { "ipa": "/əˈpɒtəmi/" }, { "audio": "LL-Q1860 (eng)-Flame, not lame-apotome.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/3/35/LL-Q1860_%28eng%29-Flame%2C_not_lame-apotome.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-apotome.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/3/35/LL-Q1860_%28eng%29-Flame%2C_not_lame-apotome.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-apotome.wav.ogg" }, { "rhymes": "-ɒtəmi" } ], "wikipedia": [ "Apotome", "Euclid's Elements", "Pythagoreanism#Music" ], "word": "apotome" }
{ "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English terms borrowed from Ancient Greek", "English terms derived from Ancient Greek", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Rhymes:English/ɒtəmi", "Rhymes:English/ɒtəmi/4 syllables", "Terms with Ancient Greek translations", "Terms with Portuguese translations" ], "derived": [ { "word": "Pythagorean apotome" } ], "etymology_templates": [ { "args": { "1": "en", "2": "grc", "3": "ἀποτομή", "4": "", "5": "cutting off" }, "expansion": "Ancient Greek ἀποτομή (apotomḗ, “cutting off”)", "name": "bor" } ], "etymology_text": "Borrowing from Ancient Greek ἀποτομή (apotomḗ, “cutting off”). The musical sense originates from the Pythagorean tradition. The mathematical sense is attested in Euclid's Elements (Book X, proposition 73, et seq.).", "forms": [ { "form": "apotomes", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "apotome (plural apotomes)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "binomial" }, { "word": "limma" } ], "senses": [ { "categories": [ "English terms with quotations", "en:Geometry", "en:Mathematics" ], "examples": [ { "ref": "2012, Jade Roskam, “Book X of The Elements: Ordering Irrationals”, in Bharath Sriraman, editor, Crossroads in the History of Mathematics and Mathematics Education, Information Age Publishing, page 210:", "text": "Yet it is not until Book X that the properties of such a line (with greater length is an apotome and lesser length a first apotome) are explained and not until Book XIII that this type of line is applied, which will be discussed in more detail later.[…]The likewise is true of apotomes (X. 97).", "type": "quote" }, { "text": "2014, Jacques Sesiano (translator), Liber Mahameleth, Part Two: Translation, Glossary, [12th c, Anonymous (possibly John of Seville), Liber Mahameleth], Springer, page 767,\nIf some number and the root of the root of a number are multiplied by the corresponding apotome, the result will be an apotome." } ], "glosses": [ "The difference between two quantities or lengths commensurable only in power, as between 1 and the square root of 2, or between the diagonal and side of a square." ], "links": [ [ "mathematics", "mathematics" ], [ "geometry", "geometry" ], [ "difference", "difference" ], [ "commensurable", "commensurable" ], [ "power", "power" ], [ "square root", "square root" ], [ "diagonal", "diagonal" ], [ "side", "side" ], [ "square", "square" ] ], "raw_glosses": [ "(mathematics, geometry) The difference between two quantities or lengths commensurable only in power, as between 1 and the square root of 2, or between the diagonal and side of a square." ], "topics": [ "geometry", "mathematics", "sciences" ] }, { "categories": [ "English terms with quotations", "Quotation templates to be cleaned", "en:Music" ], "examples": [ { "text": "1813, Music, article in John Mason Good, Olinthus Gregory, Newton Bosworth, Pantologia: A New Cyclopaedia, Volume 8: MID—OZO, unnumbered page,\nThis semitone was termed by the Pythagoreans apotome, and the diatonic semitone was termed limma. They contended, that the apotome, or distance from B flat to B natural, was larger than the limma, or distance from A to B flat." }, { "ref": "1820, Proclus, translated by Thomas Taylor, The Commentaries of Proclus on the Timæus of Plato, Volume 2, Facsimile edition, published 1967, pages 66–67:", "text": "For the ratio of the excess of the apotome, above that which is truly a semitone, and which cannot be obtained in numbers, is thus called. This then is demonstrated. To what has been said however, it must be added, that we have called the ratio of d b a semitone, not that a sesquioctave is divided into two equal ratios; for no superparticular ratio is capable of being so divided; but because the followers of Aristoxenus assume a semitone after two sesquioctaves, the ratio of a semitone is assumed, as we have said, according to their position, in order to discover what the ratio is of the comma and apotome to the ratio of the leimma.", "type": "quote" }, { "ref": "1984, Mark Lindley, Lutes, Viols, Temperaments, Cambridge University Press, page 9:", "text": "The traditional term, from ancient Greek theory, for the diatonic pythagorean semitone is 'limma'; and for the larger, chromatic semitone, ‘apotome’.\nThe oldest extant fretting formula, that of the ninth-century theorist Al-Kindi for the ud (the Arabic lute), is pythagorean. It calls for five frets, to make the following succession of semitones down from nut: limma, apotome, limma, apotome', limma.", "type": "quote" } ], "glosses": [ "The remaining part of a whole tone after a minor second has been deducted from it; an augmented unison. Most commonly used to refer to the Pythagorean chromatic semitone, which has a ratio of 2187/2048." ], "links": [ [ "music", "music" ], [ "tone", "tone" ], [ "minor second", "minor second" ], [ "deduct", "deduct" ], [ "augmented unison", "augmented unison" ] ], "raw_glosses": [ "(music) The remaining part of a whole tone after a minor second has been deducted from it; an augmented unison. Most commonly used to refer to the Pythagorean chromatic semitone, which has a ratio of 2187/2048." ], "topics": [ "entertainment", "lifestyle", "music" ] }, { "categories": [ "English terms with quotations", "Quotation templates to be cleaned", "en:Zoology" ], "examples": [ { "ref": "1964, Proceedings of the Zoological Society of London, Zoological Society of London, page 287:", "text": "The bands pass inside the margins of the apotome as they approach its constriction and form two pigmented areas broadly based on the frontal sutures and becoming dispersed towards the mid-line.", "type": "quote" }, { "ref": "2008, John L. Capinera, Encyclopedia of Entomology, →ISBN, page 3766:", "text": "In generalized Diplura, Archaeognatha and some Thysanura, five parts or apotomes are distinguished, which from the anterior to the posterior part are: the presternum, the basisternum, the furcasternum, the spinasternum and the poststernum.", "type": "quote" } ], "glosses": [ "A distinct division of an insect which is divided from the other divisions by a pinch point." ], "links": [ [ "zoology", "zoology" ] ], "raw_glosses": [ "(zoology) A distinct division of an insect which is divided from the other divisions by a pinch point." ], "topics": [ "biology", "natural-sciences", "zoology" ] } ], "sounds": [ { "ipa": "/əˈpɒtəmi/" }, { "audio": "LL-Q1860 (eng)-Flame, not lame-apotome.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/3/35/LL-Q1860_%28eng%29-Flame%2C_not_lame-apotome.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-apotome.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/3/35/LL-Q1860_%28eng%29-Flame%2C_not_lame-apotome.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-apotome.wav.ogg" }, { "rhymes": "-ɒtəmi" } ], "translations": [ { "code": "grc", "lang": "Ancient Greek", "roman": "apotomḗ", "sense": "difference between two quantities commensurable only in power", "tags": [ "feminine" ], "word": "ἀποτομή" }, { "code": "pt", "lang": "Portuguese", "sense": "difference between two quantities commensurable only in power", "tags": [ "masculine" ], "word": "apótomo" } ], "wikipedia": [ "Apotome", "Euclid's Elements", "Pythagoreanism#Music" ], "word": "apotome" }
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