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 His work remains unpublished until 1685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)