Postulate 1 ‘[It is possible] to draw a straight line from any point to any point’.
Postulate 2 ‘[It is possible] to produce a finite straight line continuously in a straight line’.
Postulate 3 ‘[It is possible] to describe a circle with any centre and diameter’.
Euclid’s theorems are still true and his methods are still admired. For millenia his books have been studied and referenced, though they are no longer used as a school text-book.53 He entitled his principal work Elements, and it was intended to be a foundational work in the subject, a starting point. The same Greek word (stoikheia) also means the letters in the alphabet, and Euclid’s elements are to geometry what letters are to language: the building blocks or basic components.
Plato considered geometry and number as the most reduced and essential, and therefore the ideal, philosophical language. But it is only by virtue of functioning at a certain ‘level’ of reality that geometry and number can become a vehicle for philosophic contemplation. Greek philosophy defined this notion of levels, so useful in our thinking, distinguishing the ‘typal‘ and the ‘archtypal‘. Following the indication given by Egyptian wall reliefs, which are laid out in three registers, an upper, a middle and a lower, we can define a third level, the ‘ectypal‘, situated between the archtypal and typal.
To see how these operate, let us take an example of a tangible thing, such as the bridle of a horse. This bridal can have a number of forms, materials, sizes, colours, uses, all of which are bridals. The bridal considered in this way, is typal; it is existing, diverse and variable. But on another level there is the idea or the form of the bridal, the guiding model of all bridals. This is an unmanifest, pure, formal idea and its level is ectypal. But yet above this there is an archtypal level which is that of the principal or power-activity, that is a process which the ectypal form and typal example of the bridal only represent. The archtypal is concerned with universal processes or dynamic patterns which can be considered independently of any structure or material form
Three Greek columns; Ionic, Corinthian and Doric made up of the capital, shaft and base. Of the three columns found in Greece, Doric columns are the simplest. They have a capital (the top, or crown) made of a circle topped by a square. The shaft (the tall part of the column) is plain and has 20 sides.
There is no base in the Doric order. The Doric order is very plain, but powerful-looking in its design. Doric, like most Greek styles, works well horizontally on buildings, that’s why it was so good with the long rectangular buildings made by the Greeks. The area above the column, called the frieze [pronounced “freeze”], had simple patterns.
Above the columns are the metopes and triglyphs. The metope [pronounced “met-o-pee”] is a plain, smooth stone section between triglyphs. Sometimes the metopes had statues of heroes or gods on them. The triglyphs are a pattern of 3 vertical lines between the metopes.