nemo's notebook
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Elements of Euclid: Book 1

  • Definitions
  • Postulates
  • Common Notions
  • Proposition 1: To construct an equilateral triangle on a given finite straight line.
  • Proposition 2: From a given point, to draw a straight line equal to a given finite straight line.
  • Proposition 3: To cut off from the greater of two given unequal straight lines a straight line equal to the less.
  • Proposition 4: If two triangles have two sides of the one respectively equal to two sides of the other, and the angles contained by those equal sides also equal; then their bases or their sides are also equal: and the remaining and their remaining angles opposite to equal sides are respectively equal: and the triangles are equal in every respect.
  • Proposition 5: In isosceles triangles the angles at the base are equal to one another, and, if the equal straight lines be produced further, the angles under the base will be equal to one another.
  • Proposition 6: If in a triangle two angles be equal to one another, the sides which subtend the equal angles will also be equal to one another.
  • Proposition 7: Given two straight lines constructed on a straight line (from its extremities) and meeting in a point, there cannot be constructed on the same straight line (from its extremities), and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively, namely each to that which has the same extremity with it.
  • Proposition 8: If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they will also have the angles equal which are contained by the equal straight lines.
  • Proposition 9: To bisect a given rectilineal angle.
  • Proposition 10: To bisect a given finite straight line.
  • Proposition 11: To draw a straight line at right angles to a given straight line from a given point on it.
  • Proposition 12: To a given infinite straight line, from a given point which is not on it, to draw a perpendicular straight line.
  • Proposition 13: If a straight line set up on a straight line make angles, it will make either two right angles or angles equal to two right angles.
  • Proposition 14: If with any straight line, and at a point on it, two straight lines not lying on the same side make the adjacent angles equal to two right angles, the two straight lines will be in a straight line with one another.