Data

Euclid. Euclidis Opera Omnia, Volume 6. Menge, Heinrich; Heiberg, J.L, editors. Leipzig: Teubner, 1896.

Open Greek and Latin · CC BY-SA 4.0

Cloned and adapted by Humanitext, with ongoing edits.

This work is a mathematical treatise that explores what it means for geometric elements to be "given" (data) and how their determination leads to the determination of other elements. Through a series of rigorous propositions and proofs, it demonstrates that if certain lengths, angles, areas, ratios, or positions are known, then other related geometric components are also uniquely determined. The discussion begins with foundational definitions and basic properties of lines and angles, gradually moving toward complex relationships in plane figures such as triangles and quadrilaterals. In the latter sections, the work addresses more intricate problems, proving that when the angle between two lines, the area they contain, and the difference of the squares on them are given, the lines themselves can be found. Ultimately, the treatise systematically categorizes the solvability of various geometric problems, establishing a robust framework for geometric analysis.