Euclid — "Let it be granted that a straight line may be drawn from any one point to any ot…"
Let it be granted that a straight line may be drawn from any one point to any other point.
Get This Quote & Author's Image Illustrated On:
Click any product to generate a realistic preview. Up to 3 at a time.
* Initial load can take up to 90 seconds — revising the preview in another color is nearly instant.
Kitchen
Apparel
Other
More from Euclid
"If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be e…"
"What do I gain by learning these things?"
"Trilateral figures are those contained by three straight lines, quadrilateral those contained by four, and multilateral those contained by more than four straight lines."
"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 …"
"If a straight line be cut into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts together with the square on the line between the points of section is equal…"
Verification
Confirmed
Found in 2 providers: grok,gemini
2 sources checked
Understanding this quote
What it means
Two points always define a straight line between them — accept this as given. Euclid isn't proving this; he's declaring it a foundational rule, a postulate. Modern geometry, engineering, and physics still operate on this assumption. It means space is uniform: no matter where two points exist, a direct path connects them. This simple grant launches the entire logical edifice of geometry from one unquestionable starting rule.
Relevance to Euclid
Euclid's entire achievement in Elements rests on five postulates — minimal assumptions he asked readers to grant without proof. This first postulate reflects his axiomatic philosophy: build irrefutable logical chains from the fewest possible starting truths. As a teacher at Alexandria's Mouseion, he believed mathematics required rigorous foundations, not intuition. His character was methodical and precise — this postulate captures that perfectly, asking one obvious concession before constructing 465 theorems atop it.
The era
Around 300 BCE in Alexandria, Egypt, Greek thinkers were systematizing all knowledge under Ptolemy I's patronage. Plato's influence had established that truth comes through reason, not observation alone. Before Euclid, geometric facts were scattered and assumed informally. His era demanded formal demonstration — but demonstration requires starting somewhere. This postulate answered that challenge: declare obvious first principles, then derive everything else through pure logic, a revolutionary move in an age building civilization on reason.
AI-generated insights based on extensive research and information for context. Factual errors? Email [email protected].