Mechanical elements.

The descent of the beam raised obliquely by one of its ends is necessarily made more along an arc than along a chord.

But if that descent is constrained to occur along the chord, then the beam, being made the hypotenuse of the right angle, will be as much more powerful at one end than at the other as the sides of its rectangle are longer, one than the other.

When the beam is made the hypotenuse of a right angle whose other two sides are equal, then equal weights attached at the ends will make equal resistance to one another; and if they are unequal, the greater weight will move the lesser.

But if the sides of the right angle are unequal, then equal weights set at the opposite ends of the hypotenuse will give motion to that hypotenuse; and if they are unequal, the lesser weight placed on the shorter side of the right angle will move the greater one placed on the longer side.

That end of the hypotenuse will be of greater resistance which is nearer to the right angle of its rectangle. And that part of the hypotenuse resists less which is farther from the right angle. There are two varieties of wheels that can touch with their circles, namely equal to one another, or one greater than the other.

Here the lines n o and m p are drawn for the adversary, that is, for his arguments. The heavy body placed upon the contact of the circles of two wheels discharges onto their poles, passing to them along the lines that extend between those poles and the point of contact made by the weight upon those wheels. Among wheels that touch with their circles, the one of smaller circle will take more of the weight placed upon their contacts.

Where the descent is easier, the ascent will be proportionally more difficult.

Among the lines that divide with equal distance from the central line and converge to the center of the world, the one that is longer will be less oblique.

The central line of the heavy body that rests on the circle of the wheel runs straight to the center of the world; and equal weights placed at equal distances from the center of that wheel will make equal resistances to one another.

But if the weight has another support opposite the wheel, then the power of the heavy body abandons the central line of the world and presses only upon the center of that wheel, and weights very unequal, at equal distances from the center, will make equal resistances among themselves.

It is impossible that any power pressing perpendicularly from the circle toward the center of the wheel should ever make that wheel turn.

The contact of two circles lies on the straight line terminated at their centers. Every straight line that extends between the center and the circumference cuts that circumference at equal angles.

The power of that heavy body which rests on the circle of the wheel is always directed straight to the center of the world.

And equal weights placed at equal distances from the central line of that wheel will make equal resistances among themselves.

This power, with its descent, pushes b c laterally upon the center of the wheels.

The power of that heavy body is always directed straight to the center of the world, the body that rests upon the circle of the wheel, which is suspended by a single support.

The power of that heavy body that rests upon the circle of the wheel will always be directed straight to the center of the world.

Every heavy body directs its power to the center of the world, the body that is suspended by a single support.

The power of every heavy body is always directed straight to the center of the world.

And that heavy body becomes faster which descends along a straighter line.

And that one will be slower which moves along a more oblique line.

Its natural motion is not oblique, and whoever makes it oblique loads it with as much weight as that body is retarded from its motion.