Explanation of the triangular pyramid

and of its gravity

All triangles, whether equilateral or with unequal sides, have their center of weight center of gravity The point where the weight of an object is perfectly balanced in all directions. on that line which is drawn from the angle to the middle of the opposite base, which is distant from the base by a third of its length. And the same occurs in every pyramid, which have their center of weight on the line that falls from the angle Here referring to the apex or top point of the pyramid. onto the center of the base, and it is distant from that base by the fourth part of that line.

A horizontal row of five geometrical and mechanical diagrams. From left to right: 1) A cone with a vertical line descending from the apex to the center of the base, ending in a small circular weight. 2) A zig-zag line connecting three circular weights. 3) A rhombus (two triangles joined at the base) with circular weights at each vertex. 4) A pyramid shown in profile with a central vertical axis line. 5) A mechanical device consisting of a rectangular block with a curved upright arm supporting a weight at its tip.

Every weight that hangs by an oblique slanted or non-vertical line pulls toward the perpendicular of its suspension. Therefore, the weight of the pyramid b a c pulls toward the perpendicular a d. Since the entire weight of the pyramid is concentrated in that point which is the center of its gravity. Therefore, by drawing the line e f through the center of the pyramid g h i parallel to the base h i, this line e f intersects the line a d at point l, which is the center of gravity of that pyramid. Thus, that point is the terminus of all the gravity of the pyramid, and that point is what pulls toward the perpendicular of its suspension.

If a pyramid were made of water or another liquid substance, its center of weight would be at the sixth degree The author specifies a "sixth degree" here, though standard Euclidean and Archimedean geometry—and indeed other notes by this author—usually place a pyramid's center of gravity at one-fourth of its height. This may represent an experimental variation or a specific system of measurement. of its height, and if it were made of lead original: "pionbo" it would be in the same degree, and so with every other heavy matter. Since gravity is nothing other than a desire to flee inequality A poetic Renaissance way of describing the physical drive toward equilibrium and balance.. And because the pyramid is unequal, it moves by its gravity toward the center of the world The "center of the world" refers to the center of the Earth, which in the science of the time was believed to be the natural destination for all heavy objects seeking rest., and because the center of the world is equal in every part, it stops when it has reached its center, for there is no reason that would move it further in one direction than another.

Technical vocabulary: pyramid (piramide), center of gravity (cientro della gravità), weight (peso), line (linia), perpendicular (perpendiculare), inequality (disugualità), sixth degree (sesto grado), lead (pionbo)