Dusty Phrases

Hi! Welcome to “Dusty Phrases.” You will find below an ancient phrase in one language or another, along with its English translation. You may also find the power to inspire your friends or provoke dread among your enemies.

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Greek:

εὕρηκα!
Heúrēka!

English:

I have found it!

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You have likely heard or read the English version of the word, Eureka. The Greek is a transliteration of an exclamation attributed to Ancient Greek mathematician and inventor Archimedes. (More on him, via Wiki)

The exclamation “Eureka!” is attributed to the ancient Greek scholar Archimedes. He reportedly proclaimed “Eureka! Eureka!” after he had stepped into a bath and noticed that the water level rose, whereupon he suddenly understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. (This relation is not what is known as Archimedes’ principle—that deals with the upthrust experienced by a body immersed in a fluid.) He then realized that the volume of irregular objects could be measured with precision, a previously intractable problem. He is said to have been so eager to share his discovery that he leapt out of his bathtub and ran naked through the streets of Syracuse.

Archimedes’ insight led to the solution of a problem posed by Hiero of Syracuse, on how to assess the purity of an irregular golden votive crown; he had given his goldsmith the pure gold to be used, and correctly suspected he had been cheated by the goldsmith removing gold and adding the same weight of silver. Equipment for weighing objects with a fair amount of precision already existed, and now that Archimedes could also measure volume, their ratio would give the object’s density, an important indicator of purity (as gold is nearly twice as dense as silver and therefore has significantly greater weight for the same volume).

This story first appeared in written form in Vitruvius‘s books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, on the grounds that the votive crown was a fine item, thus an impure crown would displace water only minutely, compared to a pure one. Precise means needed to measure this minute difference was not available at the time. For the problem posed to Archimedes, though, there is a simple method which requires no precision equipment: using a balance, compare the weight of the crown against pure gold. While they are still suspended from the arms of the balance, simultaneously submerge the crown and the gold in water. If the volumes are the same, the balance remains in equilibrium, meaning that their densities are the same and therefore the crown must be pure gold. But if the density of the crown is less (due to being alloyed with another metal like silver), increased buoyancy of the crown results in imbalance. Galileo Galilei himself weighed in on the controversy, suggesting a design for a hydrostatic balance that could be used to compare the dry weight of an object with the weight of the same object submerged in water.