Simple inequality.

Multiple: 2:1 double, 3:1 triple, 4:1 quadruple.

Superparticular: 3:2 sesquialtera (1 and 1/², 4:3 sesquitertia (1 and 1/³, 5:4 sesquiquarta (1 and 1/⁴, 6:5 sesquiquinta (1 and 1/⁵.

Superpartient: 5:3 superbipartient (1 and 2/³, 8:5 supertripartient (1 and 3/⁵, 9:5 superquadripartient (1 and 4/⁵, 11:6 superquinquepartient (1 and 5/⁶.

Superparticular sesquialtera proportion, where the greater contains the smaller once and a half.

Composite inequality.

Multiple-superparticular: 5:2 double-sesquialtera (2 and 1/², 7:3 double-sesquitertia (2 and 1/³, 13:4 triple-sesquiquarta (3 and 1/⁴.

Division of the greater inequality, which is of two kinds, namely simple and composite. The simple has three members, and the composite has two members. The three of the simple are these: multiple, superparticular, superpartient. The multiple is when the greater term contains the smaller exactly several times, as 1 to 2, 8 to 4, 6 to 2; whence if the greater term contains the smaller exactly twice, this will have a species of the multiple called double, as 1 to 2; and if that greater contains the smaller exactly three times, this will be called triple, as 6 to 2; and if it contains it four times, it is called quadruple; and if five, quintuple.

1:2 double; 2:6 triple.

The superparticular is when the greater contains the smaller an exact number of times, plus some aliquot (multiplicative) part, as 2 is an aliquot part of 6, and 4 of 12. The non-aliquot (aggregative) part will be 2 with 5. And if the aliquot part is exactly half the smaller term, the proportion is called sesquialtera; and if that aliquot is 1/3 of the smaller term, it is called sesquitertia; and if the aliquot part is a quarter of the smaller, it is called sesquiquarta; and if it is the fifth, sesquiquinta.

The simple superpartient is when the greater term contains the smaller once and a non-aliquot part composed of aliquot parts, as the proportion from 5 to 3, where 5 contains 3 once, and also 2, which is not an aliquot part of 3, though it be composed of two aliquot parts of 3, that is two units.

Levity desires to stand as far as it can, circularly, from gravity.

Gravity, force, and material motion together with percussion are four accidental powers, with which all the evident works of mortals have their being and their death.

Gravity is a certain accidental power which is created by motion and infused into one element drawn or pushed into another; and this gravity has as much life as that element labours to return to its homeland.

There is yet another.

Gravity is an invisible power which by accidental motion is created, and infused into bodies that are removed from their natural place.

Between gravity and levity I know no other difference than in their creation and privation, because gravity uses its birth and death by lines opposite to those of levity, since the motions of their birth and death are opposite.

Gravity is a certain invisible power which is created by accidental motion, and is infused into bodies standing outside their natural place. This in all its powers is like levity, its contrary.

The invisible gravity is a certain accidental power, which is created by motion and infused into bodies standing outside their natural place.

Gravity and levity are two elements transmuted one into the other. These two powers are so alike in every office, except in the motions of their creation and privation, that they are almost to be named one and the same.