How Euclid Helped Shape Modern Geometry

Euclid V.24 — Add Matched Magnitudes, Keep the Ratio

Euclid Elements Def III.4 — Equal Distance from a Centre

Euclid Spotted a Giant Structure Hidden in the Dark Universe...

Euclid Found an Entire Galaxy Made of Dark Matter

Euclid Elements Def III.3 — Circles That Touch Without Cutting

95% of the universe has never been seen

Euclid Elements Def III.6 — What Is a Segment of a Circle?

Euclid's Elements III.18 — The Radius to a Tangent Is Perpendicular

Euclid's Book I · Definitions I.15–16 · Circle and Center

Euclid Elements II.14 — Constructing an Equal-Area Square

Euclid Elements Def III.1 — Equal Circles

Euclid's Elements III.33 — Construct a Segment Admitting a Given Angle

Euclid's Elements III.36 — The Tangent Square Equals the Secant Rectangle