a – e c d - b - h

h is the center of the world.

o – m – n – p - S q r

Here there are two poles, of which the first is m, the second is n; the arms of the first are m p and m o, the arms of the second are n p and n o. And the pole m is above q, the point of contact, and is a pole above the center of the world; this is called a pole perpendicular to the center of the world. And the pole n is the pole of the balance p m o, which balance is oblique in its position, because upon that center it continually exchanges the inequality of its arms, now to the right and now to the left.

The heavy body that descends obliquely weighs so much more, or less, upon the place from which it moves, as it is slower or faster.

The heavy body that descends straight down weighs only toward the center of the elements. But the heavy body that descends obliquely divides its natural gravity between the straight motion toward the center of the world and also the oblique motion; but the more toward the center of the world, the nearer such motion is to the straight line than to the horizontal, and the less toward the center of the world, the nearer such motion is toward the center of the world.

a - b

a b is the middle line that divides the weight equally.

c - m f K – i a l – h d g – b – e -

e is the center of the world.
The oscillation of that balance will be briefer in its time the smaller the thickness of its pole.

o – m – q p n – a

a is the center of the world.
The lower weight n is more distant from the central line m a of the balance n p q; that is, the arm n p is made longer than the opposite arm p q.

Air and water and earth are continually changeable in their levity and gravity through the heat of the sun, which by heating lightens that part of the element nearest to it, and does the contrary in the opposite part of those elements.
The balance made from the circumference of the wheel upon its pole does not have equal opposite weights that oscillate between themselves, as does the balance made of a beam.

c b a - o d

The heavy body d is whole throughout the whole cord a d and is whole in every part of it. It follows that it is whole at the upper end of that cord. Therefore the balance will stand in the position of equality, because the weights are given equal to one another, and so the balance comes to rest at an equal distance from the center of the elements.

a e — c — b d

The interrupted impetus is that which, in the oscillating arms of the balance, dies in one arm and is reborn in the other, or rather passes from one arm to the other; and this impetus is never reborn of the magnitude of its antecedent. The oscillation of the arms of the balance does not die of itself immediately, because it has as much of motion as it has of weight, and as much of weight as it has of motion.

K - f e – g – h d c – b n a - b

b, center of the world.

The nearer this center of the sphere is to the center of the world, the more the space c d will exceed the space d h, and never will those spaces, that is those arms of the balance, be equal to one another.

c f are two equal weights, situated equally distant from the central line K b and equidistant from the center of the greatest circle; but because the contact n of the greatest circle upon the plane a b is nearer to the center of the weight c than...

f — h d c — b

c — b — a

The oscillation is made according to the length of the beam of the balance. If the center of the balance is concentric with the center of the world b, then the weights of the balance a b will come to rest without oscillation at whatever degree of obliquity one wishes.