''Ex pede Herculem'', "from his foot, e can measure

Hercules Hercules (, ) is the Roman equivalent of the Greek divine hero Heracles, son of Jupiter and the mortal Alcmena. In classical mythology, Hercules is famous for his strength and for his numerous far-ranging adventures. The Romans adapted the ...

", is a maxim of proportionality inspired by an experiment attributed to

Pythagoras Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samian, or simply ; in Ionian Greek; ) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His politi ...

Origin

According to Aulus Gellius' ''Noctes Atticae'':

"The philosopher Pythagoras reasoned sagaciously and acutely in determining and measuring the hero's superiority in size and stature. For since it was generally agreed that Hercules paced off the racecourse of the stadium at Pisae, near the temple of Olympian Zeus, and made it six hundred feet long, and since other courses in the land of Greece, constructed later by other men, were indeed six hundred feet in length, but yet were somewhat shorter than that at Olympia, he readily concluded by a process of comparison that the measured length of Hercules' foot was greater than that of other men in the same proportion as the course at Olympia was longer than the other stadia. Then, having ascertained the size of Hercules' foot, he made a calculation of the bodily height suited to that measure, based upon the natural proportion of all parts of the body, and thus arrived at the logical conclusion that Hercules was as much taller than other men as the race course at Olympia exceeded the others that had been constructed with the same number of feet." (translated by John C. Rolfe of the University of Pennsylvania for the Loeb Classical Library, 1927)

In other words, one can extrapolate the whole from the part. ''Ex ungue leonem'', "from its claw e can knowthe lion," is a similar phrase, noted in ''

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'' 1948. The principle was raised to an axiom of

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...

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, in ''On Growth and Form'', 1917; it has found dependable use in

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, where the measurements of a fossil jawbone or a single

vertebra The spinal column, a defining synapomorphy shared by nearly all vertebrates, Hagfish are believed to have secondarily lost their spinal column is a moderately flexible series of vertebrae (singular vertebra), each constituting a characteristi ...

, offer a close approximation of the size of a long-extinct animal, in cases where comparable animals are already known. The studies of proportionality in biology are pursued in the fields of

morphogenesis Morphogenesis (from the Greek ''morphê'' shape and ''genesis'' creation, literally "the generation of form") is the biological process that causes a cell, tissue or organism to develop its shape. It is one of three fundamental aspects of deve ...

biophysics Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. ...

and biostatistics.

Origin

See also