**Early third millenium BCE**

The balance with equal arms is introduced in Mesopotamia and Egypt

**Late fifth century BCE**

First mention of a balance with unequal arms in Greek literature

**Fourth century BCE**

The question of the return of a balance to its original position is raised in the Aristotelian *Mechanical Problems*

**Third century BCE**

The concept of *center of gravity* is introduced in Archimedes' *Equilibrium of Planes* and employed in a proof of the law of the lever

**First century**

The problem of the bent lever is treated in Heron's *Mechanics*

**Early fourth century**

Part of Heron's work is quoted in Pappus' *Collection*

**Before 901**

The law of the lever is proven from Aristotelian dynamic principles in Thābit ibn Qurra's *Book on the Steelyard*

**1048–1116**

Thābit's work is elaborated in Al-Muzaffar al Isfizari's *Guiding the Learned Men in the Art of the Steelyard*

**1121–1122**

Abu al-Fath Khāzini argues for the indifferent equilibrium of a balance in his *Book on the Balance of Wisdom*

**After the late eleventh or early twelfth century**

Manuscripts of the Aristotelian *Mechanical Problems* begin to spread to the Latin West from Byzantine sources

(see section 3.4.2)

**Twelfth century**

A version of Thābit's work, suggesting that the balance returns to its original position, is translated into Latin, probably by Gerard of Cremona, under the title *Liber Karastonis*

**Thirteenth century**

Jordanus de Nemore argues, with the help of the newly introduced concept of *positional heaviness*, that the equilibrated balance returns to its original position in his contributions to the *science of weights*

The work of Archimedes, and in particular the concept of *center of gravity*, becomes known in the Latin Middle Ages through the translations of Willem of Moerbeke

**1452–1519**

In his manuscript notes Leonardo da Vinci argues, using the concept of *center of gravity*, for the indifferent equilibrium of the equilibrated balance

(see section 3.4.2)

**1495–1498**

The first printed edition of the Aristotelian corpus, including the *Mechanical Problems*, is published by Aldo Manuzio

**1533**

Petro Apianus publishes Jordanus' *Liber de Ponderibus* containing the claim that the balance returns to its original position

**1546**

Niccolò Tartaglia publishes his *Quesiti, et inventioni diverse* exploiting the work of Jordanus and defending the claim that the balance returns to its original position

**1548**

Francesco Maurolico defines the concept of *momentum* in his *Archimedis de momentis aequalibus*. His work remains unpublished until 1685

**1550**

Girolamo Cardano proposes various measures of *positional heaviness* and defends the claim that the balance returns to its original position in his *Hieronymi Cardani medici mediolanensis de subtilitate libri XXI*

**1565**

Niccolò Tartaglia publishes an edition of Jordanus' *De ratione ponderis* containing an argument pointing toward a new measure of *positional heaviness*

**1577**

Guidobaldo del Monte argues in his *Mechanicorum Liber*, using the concept of *center of gravity*, that the balance does not return to its original position and claims this insight into its indifferent equilibrium as his own major contribution

**1581**

In the Italian edition of the *Mechanicorum Liber* Guidobaldo del Monte refers to experimental evidence in favor of his claim

DelMonte 1581 (see page

**1585**

Giovanni Battista Benedetti introduces, in his *Diversarum speculationum mathematicarum et physicarum liber*, a “new measure” for the positional effect of a weight or a force and argues for an indifferent equilibrium of the balance under terrestrial circumstances and for the claim that the balance tilts into the vertical if the spherical shape of the earth is taken into account

**1588**

Guidobaldo del Monte insists on a strictly Archimedean approach to the treatment of the balance in his *In duos Archimedis aequeponderantium libros paraphrasis*

**After ca. 1592**

Galileo Galilei takes over Benedetti's measure of positional heaviness and introduces the concept of *momento*. Together with the concept of *center of gravity*, defined in terms of *momento*, this becomes the basis for his treatment of mechanical problems such as the inclined plane

(see his treatise *Le mechaniche* 1890-1909b, written in the 1590s and later published in French as *Les méchaniques* 1634)