Deliver I of the Elements of Euclide

The delivers I of the Éléments of Euclide contains the bases for the continuation of the work:

  • 35 definitions of vocabulary
  • 5 requests (or postulates according to Proclos) more a apocryphal book
  • 5 common concepts (or Axiom S according to Proclus) more four apocryphal books
  • 48 proposals

Here some important points of this book:

  • I-1 Definition of the Elements of Euclide , the point is that of which the part is null

  • Définition I-2 of the Elements of Euclide , a line is a length without width
  • Définition I-3 of the Elements of Euclide , the ends of a line are points
  • Définition I-4 of the Elements of Euclide , the straight line is that which is also placed between its points
  • Définition I-5 of the Elements of Euclide , a surface is what has only one length and width
  • Définition I-6 of the Elements of Euclide , the ends of a surface are , and the line placed at the top is known as perpendicular with that on which it is placed
  • Définition I-11 of the Elements of Euclide , the obtuse angle is that which is larger than a right
  • Définition I-12 of the Elements of Euclide , the acute angle is that which is smaller than a right
  • Définition I-13 of the Elements of Euclide , one calls limit what is the end of something
  • Définition I-14 of the Elements of Euclide , a figure is what is included/understood by only one or several limits
  • Définition I-15 of the Elements of Euclide , a circle is a plane figure included/understood by only one line that circumference is named, all the lines led to the circumference of one of the points placed in this figure being equal between them
  • Définition I-16 of the Elements of Euclide , this point names the center of the circle
  • Définition I-17 of the Elements of Euclide , the diameter of the circle is a line carried out by the center and finished on both sides by the circumference of the circle, the diameter divides the circle in two equal parts
  • Définition I-18 of the elements of Euclide , a half circle is the figure included/understood by the diameter and the portion of the circumference supported by the diameter
  • I-35 Definition of the Elements of Euclide , definition of the parallel straight lines
  • Request 5 of the Elements of Euclide , the postulate of the parallels
  • common Notion 1 of the Elements of Euclide , the sizes form classes of equivalences
  • the Congruence of triangles
    • Proposition I-4 of the Elements of Euclide
    • Proposition I-8 of the Elements of Euclide
    • Proposition I-26 of the Elements of Euclide
  • Proposition I-32 of the Elements of Euclide , nap of measurements of the Angle S of a Triangle
  • Proposition I-46 of the Elements of Euclide , construction of the square
  • Theorem of Pythagore
    • I-47 Proposal of the Elements of Euclide , direct theorem
    • I-48 Proposal of the Elements of Euclide , Reciprocal theorem

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