Definizioni.23 | Postulati.5 | Nozioni comuni.5

Per Euclide, "linea" e' in generale curva, cioe' il concetto di linea include le linee curve, per questo poi specifica le "linee rette".

"Linee rette" sono i "segmenti (di retta)" della terminologia attuale, non sono linee rette infinite, come oggi intese dalla terminologia attuale.

- point is that which has no part. >>>
- line is breadthless length.
- ends of a line are points.
- straight line is a line which lies evenly with the points on itself.
- surface is that which has length and breadth only.
- edges of a surface are lines.
- plane surface is a surface which lies evenly with the straight lines on itself.

- plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
- Rectilinear angle. And when the lines containing the angle are straight, the angle is called rectilinear.
- Right angle. When a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
- obtuse angle is an angle greater than a right angle.
- acute angle is an angle less than a right angle.

- boundary is that which is an extremity of anything.
- figure is that which is contained by any boundary or boundaries.

- circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another.
- And the point is called the center of the circle.
- diameter of the circle is any straight line drawn through the center and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle.
- semicircle is the figure contained by the diameter and the circumference cut off by it. And the center of the semicircle is the same as that of the circle.

- Rectilinear figures are those which are contained by straight
lines,
- trilateral figures being those contained by three,
- quadrilateral those contained by four, and
- multilateral those contained by more than four straight
lines.

- trilateral figures
- equilateral triangle 3 sides equal
- isosceles triangle 2 sides alone equal
- scalene triangle 3 sides unequal.

- trilateral figures, further
- right-angled triangle has a right angle
- obtuse-angled triangle has an obtuse angle
- acute-angled triangle has its 3 angles
acute.

- quadrilateral figures
- square is both equilateral and right-angled
- oblong is right-angled but not equilateral
- rhombus is equilateral but not right-angled
- rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled.
- trapezia quadrilaterals other than these.

- Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.

- Euclide.
- mathcs.clarku.edu/~djoyce/java/elements/bookI/bookI
- Euclide. Definizioni angolo. Commento di Proclo.
- https://www.maths.tcd.ie/~dwilkins/Euclid/