Metrica

book by Heron of Alexandria

Written by

The Information Architects of Encyclopaedia Britannica

Last updated

June 30, 2026

Quick Summary

Metrica is a significant work by the Greek mathematician and inventor Heron of Alexandria, who flourished around 62 CE. This text is a compilation of geometric formulas and rules for calculating areas and volumes of various plane and solid figures, drawing from diverse sources.12

A key contribution within Metrica is the expression of a triangle's area using its side lengths. This method, now known as Heron's formula, involves calculating half the perimeter (the semi-perimeter) and applying arithmetic operations. The formula is:13

Area = (\sqrt{s(s-a)(s-b)(s-c)})

where a, b, and c are the lengths of the triangle's sides, and s is the semi-perimeter ((s = \frac{a+b+c}{2})). This approach emphasizes measurement and arithmetic rather than purely geometric constructions. While credited to Heron, some researchers suggest the formula may have originated with Archimedes.32

Summary created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

6 Britannica Sources

Ask Britannica AI about this topic

Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.

Heron of Alexandria
Heron’s most important geometric work, Metrica, was lost until 1896. It is a compendium, in three books, of geometric rules and formulas that Heron gathered from a variety of sources, some of them going back to ancient Babylon, on areas and volumes of plane and solid figures. Book I enumerates…
Read More
Heron’s most important geometric work, Metrica, was lost until 1896. It is a compendium, in three books, of geometric rules and formulas that Heron gathered from a variety of sources, some of them going back to ancient Babylon, on areas and volumes of plane and solid figures. Book I enumerates…
Read More