Euclid — "Let the following be postulated:"
Let the following be postulated:
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More from Euclid
"A figure is that which is contained by any boundary or boundaries."
"Let it be granted that all right angles are equal to one another."
"The extremities of a line are points."
"A 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."
"A straight line is a line which lies evenly with the points on itself."
Verification
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Understanding this quote
What it means
This phrase invites the reader to accept a small set of foundational assumptions without proof. Everything that follows will be logically derived from these starting points. In modern terms, it is like declaring the ground rules before a game begins. No hidden premises, no sleight of hand — just a transparent declaration: here is what we agree to believe, and from it we will build everything else through pure reasoning alone.
Relevance to Euclid
Euclid worked at Alexandria's Library around 300 BCE, synthesizing centuries of scattered Greek geometry into one coherent system. His defining intellectual trait was methodological discipline: he chose only five postulates, the minimum needed, then derived all of plane geometry by logic alone. This phrase reflects his character precisely: honest about assumptions, relentless in deduction. His Elements remained the primary geometry textbook for over two thousand years because of this transparent rigor.
The era
In 300 BCE Alexandria, the intellectual heirs of Plato and Aristotle demanded that knowledge rest on demonstrable logic rather than tradition or divine authority. Hellenistic culture had unified the Mediterranean world, enabling unprecedented exchange of ideas. Yet much knowledge remained tangled with mythology and rhetoric. Euclid's radical move was transparency: declare every assumption openly before deducing consequences. This separated proven truth from assumed truth at a moment when that distinction was philosophically urgent.
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