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  <front>
    <journal-meta>
      <journal-id journal-id-type="issn">2411-3336</journal-id>
      <journal-id journal-id-type="eissn">2541-9404</journal-id>
      <journal-title-group>
        <journal-title xml:lang="ru">Записки Горного института</journal-title>
        <journal-title xml:lang="en">Journal of Mining Institute</journal-title>
      </journal-title-group>
      <publisher>
        <publisher-name xml:lang="ru">Санкт-Петербургский горный университет императрицы Екатерины ΙΙ</publisher-name>
        <publisher-name xml:lang="en">Empress Catherine II Saint Petersburg Mining University</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id custom-type="pmi" pub-id-type="custom">pmi-15122</article-id>
      <article-id pub-id-type="uri">https://pmi.spmi.ru/pmi/article/view/15122</article-id>
      <article-categories>
        <subj-group subj-group-type="section-heading" xml:lang="ru">
          <subject>Статьи</subject>
        </subj-group>
        <subj-group subj-group-type="section-heading" xml:lang="en">
          <subject>Articles</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">Theorem relating to the circle system</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Теорема, относящаяся к системе кругов</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Fedorov</surname>
            <given-names>E. S.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Федоров</surname>
              <given-names>Е. С.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Fedorov</surname>
              <given-names>E. S.</given-names>
            </name>
          </name-alternatives>
          <email>pmi@spmi.ru</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <aff-alternatives id="aff1">
          <aff>
            <institution xml:lang="ru"> (Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en"> (Russia)</institution>
          </aff>
        </aff-alternatives>
      </contrib-group>
      <pub-date pub-type="epub" iso-8601-date="1914-01-01">
        <day>01</day>
        <month>01</month>
        <year>1914</year>
      </pub-date>
      <pub-date date-type="collection">
        <year>1914</year>
      </pub-date>
      <volume>5</volume>
      <issue>1</issue>
      <fpage>17</fpage>
      <lpage>18</lpage>
      <history>
        <date date-type="received" iso-8601-date="1913-07-16">
          <day>16</day>
          <month>07</month>
          <year>1913</year>
        </date>
        <date date-type="accepted" iso-8601-date="1913-09-19">
          <day>19</day>
          <month>09</month>
          <year>1913</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="1914-01-01">
          <day>01</day>
          <month>01</month>
          <year>1914</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>© E. S. Fedorov</copyright-statement>
        <copyright-year>1914</copyright-year>
        <copyright-holder xml:lang="ru">Е. С. Федоров</copyright-holder>
        <copyright-holder xml:lang="en">E. S. Fedorov</copyright-holder>
        <license xlink:href="http://creativecommons.org/licenses/by/4.0">
          <license-p>CC BY 4.0</license-p>
        </license>
      </permissions>
      <self-uri xlink:type="simple" xlink:href="https://pmi.spmi.ru/pmi/article/view/15122">https://pmi.spmi.ru/pmi/article/view/15122</self-uri>
      <abstract xml:lang="ru">
        <p>Эта теорема весьма просто разрешает задачу, которую можно следующим образом формулировать как задачу элементарной геометрии (см. статью). Несмотря на всю простоту решения ее как задачи в системе кругов она едва ли разрешима на основании теорем элементарной геометрии. Понятно, что эту теорему можно непосредственно перенести в систему шаров, заменив в ней слова „круг“ словами ,,шар“. Для доказательства же достаточно принять централь Q R, за ось вращения. Таким образом в самом общем виде разрешается и задача нахождения центров сферотерций шаров, которая раньше была разрешена посредством формул.</p>
      </abstract>
      <abstract xml:lang="en">
        <p>This theorem very simply solves the problem, which can be formulated as follows as a problem of elementary geometry (see article). Despite the simplicity of solving it as a problem in a system of circles, it is hardly solvable on the basis of theorems of elementary geometry. It is clear that this theorem can be directly transferred to the system of spheres by replacing the words “circle” with the words “sphere”. To prove it, it is enough to take the central Q R as the axis of rotation. Thus, in the most general form, the problem of finding the centers of spherotions of sphers, which was previously solved through formulas, is resolved.</p>
      </abstract>
    </article-meta>
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        <label>1</label>
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