Euclid — "To draw a straight line at right angles to a given straight line from a given po…"
To draw a straight line at right angles to a given straight line from a given point on it.
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More from Euclid
"A surface is that which has length and breadth only."
"If four magnitudes be proportional, the rectangle contained by the extremes is equal to the rectangle contained by the means."
"A straight line is that which lies evenly between its extreme points."
"A straight line is a line which lies evenly with the points on itself."
"A plane surface is a surface which lies evenly with the straight lines on itself."
Verification
Unverifiable
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Understanding this quote
What it means
From any point on a line, you can always construct a perfect perpendicular — a line at exactly 90 degrees. This captures something fundamental: perpendicularity is not an approximation or a convention, but a precise, reproducible geometric truth that anyone, anywhere, can construct with only a straightedge and compass.
Relevance to Euclid
This is literally Euclid's Postulate-derived Proposition 11 from Elements. It embodies his entire philosophy: build complex truths from minimal, self-evident rules. Euclid didn't discover perpendiculars — he proved they could always be constructed rigorously, reflecting his obsession with logical certainty over intuition.
The era
Around 300 BCE Alexandria, Greek thinkers were systematizing knowledge under Ptolemy I's patronage. Land surveying, architecture, and astronomy all demanded precise angle measurement. Formalizing perpendicular construction gave builders and scholars a provable, repeatable standard — transforming practical craft into deductive science during a pivotal intellectual flourishing.
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