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{"author":null,"backreferences":[{"context_html":"<p>On another principle, 120 is a triangular<a class=\"fnanchor pginternal\" href=\"#Footnote_1039\" id=\"FNanchor_1039\">[1039]</a> number, and consists of\r\nthe equality<a class=\"fnanchor pginternal\" href=\"#Footnote_1040\" id=\"FNanchor_1040\">[1040]</a> of the number 64, [which consists of<span class=\"pagenum\" id=\"Page_353\">[353]</span> eight of the\r\nodd numbers beginning with unity],<a class=\"fnanchor pginternal\" href=\"#Footnote_1041\" id=\"FNanchor_1041\">[1041]</a> the addition of which (1, 3,\r\n5, 7, 9, 11, 13, 15) in succession generates squares;<a class=\"fnanchor pginternal\" href=\"#Footnote_1042\" id=\"FNanchor_1042\">[1042]</a> and of the\r\ninequality of the number 56, consisting of seven of the even numbers\r\nbeginning with 2 (2, 4, 6, 8, 10, 12, 14), which produce the numbers\r\nthat are not squares.<a class=\"fnanchor pginternal\" href=\"#Footnote_1043\" id=\"FNanchor_1043\">[1043]</a></p>","headings":["THE WRITINGS OF CLEMENT OF ALEXANDRIA.","BOOK VI.","CHAPTER XI. THE MYSTICAL MEANINGS IN THE PROPORTIONS OF NUMBERS, GEOMETRICAL RATIOS, AND MUSIC."],"marker_anchor":"FNanchor_1039","paragraph_id":"pg73020-paragraph-757"}],"canonical_references":[],"date_end":null,"date_start":null,"deduplication_fingerprint":"936e7ff88c20ab288be95b7675460381c6531553c787da1b041a62d40ee0c159","edition_title":"The writings of Clement of Alexandria, Vol. 2 (of 2)","edition_translators":["William Wilson"],"edition_year":1869,"explicit_reference_candidates":[],"headings":[],"id":"pg73020-Footnote_1039","license_url":"https://www.gutenberg.org/policy/license.html","public_import_allowed":false,"record_kind":"original-editor-translator-note","review_required":["work and recension attribution","original-work chronology","Bible reference numbering and citation kind","English edition rights and attribution"],"review_status":"needs_review","rights_evidence":"Project Gutenberg metadata: Public domain in the USA. Existing 1869 English translation; translator died 1875. Electronic transcription subject to Project Gutenberg reuse terms.","source_anchor":"Footnote_1039","source_ebook":73020,"source_html":"<div class=\"footnote\">\n<p><a class=\"label pginternal\" href=\"#FNanchor_1039\" id=\"Footnote_1039\">[1039]</a> “Triangular numbers are those which can be disposed\r\nin a triangle, as 3 <img alt=\"\" id=\"img_images_i_p352.jpg\" src=\"images/i_p352.jpg\" style=\"height:.5em; padding:0 0em 0 0em;\"/>\r\n, 6 <img alt=\"\" id=\"img_images_i_p352a.jpg\" src=\"images/i_p352a.jpg\" style=\"height:1em; padding:0 0em 0 0em;\"/>\r\n, etc., being represented\r\nby the formula <img alt=\"\" id=\"img_images_i_p352b.jpg\" src=\"images/i_p352b.jpg\" style=\"height:2em; padding:0 0em 0 0em;\"/>\r\n (Liddel and Scott’s\r\n<i>Lexicon</i>). Each side of the triangle of course contains an equal\r\nnumber of units, the sum of which amounts to the number.</p>\n</div>","source_sha256":"c35077683d75abe553cc6ef5d3ef5a1a978f07dfbcf4bad5c3d56302ad03dc19","source_url":"https://www.gutenberg.org/cache/epub/73020/pg73020-images.html#Footnote_1039","text_sha256":"fa0ba575651dd1273b0b6c1398f4a68835f2c5908ae06340c8dac6ea750ab0aa","verified":false,"work_id":null}references: [] | work_id: | origin: existing-private-derived-record | source: https://www.gutenberg.org/cache/epub/73020/pg73020-images.html#Footnote_1039