Triangle

Hellenic religion

• Triangle appears in Hellenic religion.

  Pausanias notes triangular grounds and pediment speech among sanctuary forms. A named triangle form in that periegesis, not three as the number already met and not a tetrahedron solid dump.

  from Pausanias · Description of Greece, c. 150–180 CE

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• Equilateral is used in Triangle.

  Heath’s Euclid Book I seats the equilateral triangle among the opening constructed figures — all sides equal — in the plane-geometry handbook. A named equilateral species of triangle in that Elements speech, not isosceles alone and not a bare three-side dump.

  from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908

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• Isosceles is used in Triangle.

  Heath’s Euclid Book I defines the isosceles triangle as the figure with two equal sides and proves its base-angle equality. A named isosceles species in that handbook, not equilateral as all-three equal and not scalene.

  from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908

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• Scalene is used in Triangle.

  Heath’s Euclid Book I defines the scalene triangle as the figure with three unequal sides among the triangle species. A named scalene species in that handbook, not isosceles and not a modern inequality dump alone.

  from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908

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• Acute triangle is used in Triangle.

  Heath’s Euclid Book I classifies triangles by angles and works with acute-angled cases among ordinary plane figures. A named acute-triangle species in that handbook, not the right-angled Pythagorean seat and not obtuse.

  from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908

  used in · sourced · documented

• Obtuse triangle is used in Triangle.

  Heath’s Euclid Book I classifies obtuse-angled triangles among the angle species of plane triangles. A named obtuse-triangle species in that handbook, not right-triangle I.47 and not acute.

  from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908

  used in · sourced · documented

• Triangle represents Trinity.

  In Twining’s Symbols and Emblems, the triangle is shown among emblems of the Trinity — the triangle represents that Trinity figure.

  from Louisa Twining · Symbols and Emblems of Early and Mediaeval Christian Art, 1852 (new ed. 1885)

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• Triangle is historically related to Square.

  In Ure’s Dictionary of Arts, Manufactures, and Mines, triangular grooves made use of for square iron have for their profile an isosceles triangle slightly obtuse — the triangle shapes that square bar.

  from Andrew Ure · Dictionary of Arts, Manufactures, and Mines, 1839 (and later PD editions)

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• Fillet is associated with Triangle.

  In Ure’s Dictionary of Arts, Manufactures, and Mines, rolling grooves are round, triangular, rectangular, or fillet form — fillet-form sits with that triangular groove class.

  from Andrew Ure · Dictionary of Arts, Manufactures, and Mines, 1839 (and later PD editions)

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• Pentagon is associated with Triangle.

  In Ure’s Dictionary, diamond brilliant cutting modifies the octahedron into faces that include a pentagon and two triangles — pentagon and triangle mark that brilliant face set.

  from Andrew Ure · Dictionary of Arts, Manufactures, and Mines, 1839 (and later PD editions)

  associated with · sourced · documented