"quod erat demonstrandum" meaning in Latin

{
  "etymology_templates": [
    {
      "args": {
        "1": "la",
        "2": "grc",
        "3": "ὅπερ ἔδει δεῖξαι",
        "4": "",
        "lit": "(that) which was to be demonstrated"
      },
      "expansion": "Calque of Ancient Greek ὅπερ ἔδει δεῖξαι (hóper édei deîxai, literally “(that) which was to be demonstrated”)",
      "name": "cal"
    }
  ],
  "etymology_text": "Calque of Ancient Greek ὅπερ ἔδει δεῖξαι (hóper édei deîxai, literally “(that) which was to be demonstrated”).",
  "forms": [
    {
      "form": "quod erat dēmōnstrandum",
      "tags": [
        "canonical"
      ]
    },
    {
      "form": "quae erant dēmōnstranda",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "la",
        "2": "phrase",
        "3": "plural",
        "4": "quae erant dēmōnstranda",
        "head": "quod erat dēmōnstrandum"
      },
      "expansion": "quod erat dēmōnstrandum (plural quae erant dēmōnstranda)",
      "name": "head"
    }
  ],
  "lang": "Latin",
  "lang_code": "la",
  "pos": "phrase",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "Latin entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 5 entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "la",
          "name": "Mathematics",
          "orig": "la:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "q. e. d."
        },
        {
          "word": "Q. E. D."
        },
        {
          "word": "QED"
        }
      ],
      "glosses": [
        "which was to be proved; which was to be demonstrated."
      ],
      "id": "en-quod_erat_demonstrandum-la-phrase-xinhYqd3"
    }
  ],
  "sounds": [
    {
      "ipa": "/ˈkʷo.de.rat.deː.monsˈtran.dum/",
      "tags": [
        "Classical-Latin"
      ]
    },
    {
      "ipa": "[ˈkʷɔd̪ɛräd̪ːeːmõːs̠ˈt̪rän̪d̪ʊ̃ˑ]",
      "tags": [
        "Classical-Latin"
      ]
    },
    {
      "ipa": "/kwod ˈe.rat de.monˈstran.dum/",
      "note": "modern Italianate Ecclesiastical"
    },
    {
      "ipa": "[kwɔd̪ ˈɛːrät̪ d̪emonˈst̪rän̪d̪um]",
      "note": "modern Italianate Ecclesiastical"
    }
  ],
  "word": "quod erat demonstrandum"
}

{
  "derived": [
    {
      "word": "q. e. d."
    },
    {
      "word": "Q. E. D."
    },
    {
      "word": "QED"
    }
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "la",
        "2": "grc",
        "3": "ὅπερ ἔδει δεῖξαι",
        "4": "",
        "lit": "(that) which was to be demonstrated"
      },
      "expansion": "Calque of Ancient Greek ὅπερ ἔδει δεῖξαι (hóper édei deîxai, literally “(that) which was to be demonstrated”)",
      "name": "cal"
    }
  ],
  "etymology_text": "Calque of Ancient Greek ὅπερ ἔδει δεῖξαι (hóper édei deîxai, literally “(that) which was to be demonstrated”).",
  "forms": [
    {
      "form": "quod erat dēmōnstrandum",
      "tags": [
        "canonical"
      ]
    },
    {
      "form": "quae erant dēmōnstranda",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "la",
        "2": "phrase",
        "3": "plural",
        "4": "quae erant dēmōnstranda",
        "head": "quod erat dēmōnstrandum"
      },
      "expansion": "quod erat dēmōnstrandum (plural quae erant dēmōnstranda)",
      "name": "head"
    }
  ],
  "lang": "Latin",
  "lang_code": "la",
  "pos": "phrase",
  "senses": [
    {
      "categories": [
        "Latin 7-syllable words",
        "Latin entries with incorrect language header",
        "Latin lemmas",
        "Latin multiword terms",
        "Latin phrases",
        "Latin terms calqued from Ancient Greek",
        "Latin terms derived from Ancient Greek",
        "Latin terms with Ecclesiastical IPA pronunciation only",
        "Latin terms with IPA pronunciation",
        "Pages with 5 entries",
        "Pages with entries",
        "la:Mathematics"
      ],
      "glosses": [
        "which was to be proved; which was to be demonstrated."
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ˈkʷo.de.rat.deː.monsˈtran.dum/",
      "tags": [
        "Classical-Latin"
      ]
    },
    {
      "ipa": "[ˈkʷɔd̪ɛräd̪ːeːmõːs̠ˈt̪rän̪d̪ʊ̃ˑ]",
      "tags": [
        "Classical-Latin"
      ]
    },
    {
      "ipa": "/kwod ˈe.rat de.monˈstran.dum/",
      "note": "modern Italianate Ecclesiastical"
    },
    {
      "ipa": "[kwɔd̪ ˈɛːrät̪ d̪emonˈst̪rän̪d̪um]",
      "note": "modern Italianate Ecclesiastical"
    }
  ],
  "word": "quod erat demonstrandum"
}