On weight: the central line of gravity in suspended bodies
Where the angle of two oblique cords falls; the central and intercentric lines defined
Leonardo continues the science of weights, stating that the two oblique cords suspending a body always meet in an angle lying on the body's central line of gravity, and that this meeting angle may fall above, within, or below the weight while remaining of equal validity. He defines the "central concentric line" and the "intercentric line" alike as lines that rise from the centre of the world through the weight's centre and continue straight to infinity. The proof rests on a dotted triangle labelled with the natural centre, the accidental centre and the centre of the world (a b c, e, d, f, g, h). The drawings show bodies hung from forked cords with the angle marked in each of its positions.
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The cords' angle lies on the central line of gravity
Two cords descending obliquely to suspend a body always meet at an angle set on the central line of that body's gravity. Whether the angle falls above, within, or below the weight, the three cases are of one and the same validity because all lie on the same central line.
Definition of the central concentric line
The central concentric line is born from the centre of the world and penetrates the accidental centre of the suspended weight, passing through it in continuous straightness to infinity.
The intercentric line h f proved by triangle
Let the intercentric line be h f, extending from the centre of the earth's natural gravity h to the natural or accidental centre f (or g) of the suspended weight, continuing straight to infinity. This is proved by the fourth proposition, on the proportion of weight to weight and angle to angle among cords of differing lengths.