Demonstratum

Demonstratum is a Latin term derived from demonstrare, meaning to show or to demonstrate. It is the neuter singular form of the perfect passive participle demonstratus and is usually translated as “that which has been shown” or “demonstrated.” In Latin, demonstratum can function as an adjective or as a substantive referring to the object that has been demonstrated.

In historical and scholarly contexts, demonstratum appears in discussions of demonstration and proof to denote the result established by reasoning. It can refer to the proposition or conclusion that has been proven, though in English-language mathematics and logic the term is uncommon and typically replaced by phrases such as proven proposition or theorem. In Latin logical and mathematical treatises, demonstratum helps distinguish the outcome of a demonstration from the act itself.

In modern scholarship, demonstratum is encountered mainly in studies of Latin terminology, translations of classical texts, or discussions of medieval and early modern logic and mathematics. Its practical meaning aligns with the general notion of a proven statement or established result, but it remains a largely historical or linguistic term rather than a standard term in contemporary practice.

See also: demonstrare; demonstrandum; demonstration; theorem; proof.