Two New Sciences on Superphysics

Small Scale Versus Large Scale

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

You Venetians display constant activity in your famous arsenal. It is a great way to learn about mechanics.

Ropes

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

Question 1: How are fibres 3 cubits long so tightly bound together in a rope 100 cubits long that great force is required to break it?

Gauge Block Wringing

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

I will talk about the breaking strength of other materials which, unlike ropes and most woods, do not have a filamentous structure.

Water Pressure

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

I will tell you:

The Cause of Solidity

Mon, 01 Jan 0001 00:00:00 +0000

Sagredo

On what depends the resistance to breaking, other than that of void?

Polygons

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

Within a finite extent is it possible to discover an infinite number of vacua?

Water Pressure

Mon, 01 Jan 0001 00:00:00 +0000

Simplicio

You are travelling along toward those vacua advocated by a certain ancient philosopher.

Salviati

Galileo’s antagonist said Galileo “denied Divine Providence”

Infinity and Indivisibility

Mon, 01 Jan 0001 00:00:00 +0000

Sagredo

Give us this geometrical proof that there is always equality between these solids and between their bases.

Salviati

IPC is a right angle. The square of the radius IC is equal to the sum of the squares on the 2 sides IP, PC.

Equivalence Principle

Mon, 01 Jan 0001 00:00:00 +0000

Sagredo

If the preceding be true, it seems to me impossible that an infinite number is greater than another infinite.

Finite and Infinite

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

Between finite and infinite discrete quantities there is a third intermediate term which corresponds to every assigned number.

Rest Versus Motion

Mon, 01 Jan 0001 00:00:00 +0000

Sagredo

Do substances become fluid by being resolved into their infinitely small indivisible components?

Salviati

I take a hard substance such as stone. Then I reduce it through a hammer into powder which are still:

What is Unity?

Mon, 01 Jan 0001 00:00:00 +0000

Sagredo

When we seek the infinite among numbers we find it in unity.

Expansion and Contraction

Mon, 01 Jan 0001 00:00:00 +0000

Simplicio

How would these indivisible quantities help us understand contraction and expansion, avoiding at the same time the vacuum and the penetrability of bodies?

Cylinders

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

We have seen above what relations hold between equal cylinders of different height or length.

What Causes Contraction and Expansion?

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

If contraction and expansion consist in contrary motions, one should find for each great expansion a correspondingly large contraction.

Heavy Bodies

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

We should distinguish between heavy bodies in motion and the same bodies at rest.

Descending Speeds

Mon, 01 Jan 0001 00:00:00 +0000

Sagredo

Bodies of different weights do not move in one and the same medium with velocities proportional to their weights.

Lead Versus Harmony

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

I agree. In very long distances, the lead might cover 100 miles while the bladder was traversing 1 mile.

How to determine the specific gravity of air

Mon, 01 Jan 0001 00:00:00 +0000

Sagredo

How do we determine the specific gravity of air with reference to water and hence with reference to other heavy substances?

Simplicio

But if we find that air has levity instead of gravity what then shall we say of the foregoing discussion which, in other respects, is very clever?

Salviati

It was empty, vain, and trifling.

Compressed air

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

Compressed air weighs as much as the sand. It loses this weight when once allowed to escape as uncompressed air.

Pendulums

Mon, 01 Jan 0001 00:00:00 +0000

Sagredo

In the case of the pendulums, that each of them traverses now an arc of 60 degrees, now one of fifty, or thirty or ten or eight or four or two, etc.

Sounds

Mon, 01 Jan 0001 00:00:00 +0000

Aristotle has discussed accoustical questions.

Sagredo

I take pleasure in every kind of musical instrument and have paid considerable attention to harmony. But I have never been able to fully understand why some combinations of tones are more pleasing than others, or why certain combinations not only fail to please but are even highly offensive.

Harmonies

Mon, 01 Jan 0001 00:00:00 +0000

Sagredo

I have been perplexed about these different harmonies.

The resistance of solids

Thu, 25 Sep 2025 00:00:00 +0000

Sagredo

You advanced a principle for the resistance which all solids offer to fracture and depended on a certain cement which held the parts glued together so that they would yield and separate only under considerable pull [potente attrazzione].

Propositions 1-2

Thu, 25 Sep 2025 00:00:00 +0000

Proposition 1

A prism or solid cylinder of glass, steel, wood or other breakable material which is capable of sustaining a very heavy weight when applied longitudinally is easily broken by the transverse application of a weight which may be much smaller in proportion as the length of the cylinder exceeds its thickness.

Small Scale Versus Large Scale

Thu, 25 Sep 2025 00:00:00 +0000

Corollary

The resistance [strength] of a prism or cylinder of constant length varies in the sesquialteral ratio of its volume.

This is evident because the volume of a prism or cylinder of constant altitude varies directly as the area of its base, i. e., as the square of a side or diameter of this base; but, as just demonstrated, the resistance [strength] varies as the cube of this same side or diameter. Hence the resistance varies in the sesquialteral ratio of the volume—consequently also of the weight—of the solid itself.

Cylinders and Prisms

Thu, 25 Sep 2025 00:00:00 +0000

Proposition 5

Prisms and cylinders which differ in both length and thickness offer resistances to fracture [i. e., can support at their ends loads] which are directly proportional to the cubes of the diameters of their bases and inversely proportional to their lengths.

Propositions 8

Thu, 25 Sep 2025 00:00:00 +0000

Proposition 8

Given a cylinder or prism of the greatest length consistent with its not breaking under its own weight; and having given a greater length, to find the diameter of another cylinder or prism of this greater length which shall be the only and largest one capable of withstanding its own weight.

Land animals

Thu, 25 Sep 2025 00:00:00 +0000

Simplicio

Land animals should really be called air animals since they live in the air, surrounded by air, and breathe air.

Sagredo

Giant fish, if pulled ashore, would not survive. It would be crushed under its own mass as soon as the connections between the bones gave way.

Salviati

The same thing would happen in a very big ship which floats on the sea without going to pieces under its load of merchandise and armament, but which on dry land and in air would probably fall apart.

Prisms

Thu, 25 Sep 2025 00:00:00 +0000

Sagredo

Since the prism AB grows constantly stronger and more resistant to the pressure of its load at points which are more and more removed from the middle, we could in the case of large heavy beams cut away a considerable portion near the ends which would notably lessen the weight, and which, in the beam work of large rooms, would prove to be of great utility and convenience.

Fig. 32

The Parabola

Thu, 25 Sep 2025 00:00:00 +0000

Sagredo

The circumscribed shape is larger than 1/3 of the rectangle CP. This will not prove so easy.

Salviati

There is nothing very difficult about it.

Change Of Position. [De Motu Locali]

Thu, 25 Sep 2025 00:00:00 +0000

In nature, the oldest topic is motion.

I have noted that the free motion [naturalem motum] of a heavy falling body is continuously accelerated.

But to just what extent this acceleration occurs has not yet been announced.

Movement Speed

Mon, 01 Jan 0001 00:00:00 +0000

Theorem 2, Proposition 2

If a moving particle traverses 2 distances in equal intervals of time, these distances will bear to each other the same ratio as the speeds.

Conversely if the distances are as the speeds then the times are equal.

Freely Falling Bodies

Mon, 01 Jan 0001 00:00:00 +0000

Sagredo

All definitions are arbitrary.

Uniformly Accelerated Motion

Mon, 01 Jan 0001 00:00:00 +0000

Simplicio

I believe that a falling body:

The Motion of a Falling Body

Mon, 01 Jan 0001 00:00:00 +0000

Theorem 2, Proposition 2

The spaces described by a body falling from rest with a uniformly accelerated motion are to each other as the squares of the time-intervals employed in traversing these distances.

Theorem 3

Mon, 01 Jan 0001 00:00:00 +0000

Theorem 3, Proposition 3

If one and the same body, starting from rest, falls along an inclined plane and also along a vertical, each having the same height, the times of descent will be to each other as the lengths of the inclined plane and the vertical.

Theorem 9

Mon, 01 Jan 0001 00:00:00 +0000

Theorem 9, Proposition 9

If from any point on a horizontal line two planes, inclined at any angle, are drawn, and if they are cut by a line which makes with them angles alternately equal to the angles between these planes and the horizontal, then the times required to traverse those portions of the plane cut off by the aforesaid line are equal.

Problem 5-6

Mon, 01 Jan 0001 00:00:00 +0000

Problem 5, Proposition 18

Given the distance through which a body will fall vertically from rest during a given time-interval, and given also a smaller time-interval, it is required to locate another [equal] vertical distance which the body will traverse during this given smaller time-interval.

Theorem 15

Mon, 01 Jan 0001 00:00:00 +0000

Theorem 15, Proposition 24

Given:

2 parallel horizontal planes and a vertical line connecting them
an inclined plane passing through the lower extremity of this vertical line

If a body falls freely along the vertical line and have its motion reflected along the inclined plane, the distance which it will traverse along this plane, during a time equal to that of the vertical fall, is greater than once but less than twice the vertical line.

Theorem 21

Mon, 01 Jan 0001 00:00:00 +0000

Theorem 21, Proposition 32

If in a horizontal line any 2 points are chosen and if through one of these points a line be drawn inclined towards the other.

If from this other point a straight line is drawn to the inclined line in such a direction that it cuts off from the inclined line a portion equal to the distance between the two chosen points on the horizontal line, then the time of descent along the line so drawn is less than along any other straight line drawn from the same point to the same inclined line.

Theorem 22

Mon, 01 Jan 0001 00:00:00 +0000

LEMMA

Let ACIB be the quadrant of a circle. From B draw BE parallel to AC.

Around any point in the line BE draw a circle BOES, touching AB at B and intersecting the circumference of the quadrant at I.

The Motion Of Projectiles

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

Once more, Simplicio is here on time; so let us without delay take up the question of motion. The text of our Author is as follows:

In the preceding pages we have discussed the properties of uniform motion and of motion naturally accelerated along planes of all inclinations. I now propose to set forth those properties which belong to a body whose motion is compounded of two other motions, namely, one uniform and one naturally accelerated.

Motions through the air

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

Air resistance exhibits itself in 2 ways:

Theorem 3

Mon, 01 Jan 0001 00:00:00 +0000

Theorem 3, Proposition 3

Let the motion take place along the line ab, starting from rest at a, and in this line choose any point c.

Let ac represent the time required for the body to fall through the space ac.

Momentum

Mon, 01 Jan 0001 00:00:00 +0000

Salviati

We can only talk about motions and their velocities or momenta [movimenti e lor velocità o impeti] whether uniform or naturally accelerated if we have established a measure for speed and time.

How to Measure Force

Mon, 01 Jan 0001 00:00:00 +0000

PROPOSITION 5. PROBLEM

Having given a parabola, find the point, in its axis extended upwards, from which a particle must fall in order to describe this same parabola.

Let ab be the given parabola, hb its amplitude, and he its axis extended. The problem is to find the point e from which a body must fall in order that, after the momentum which it acquires at a has been diverted into a horizontal direction, it will describe the parabola ab. Draw the horizontal ag, parallel to bh, and having laid off af equal to ah, draw the straight line bf which will be a tangent to the parabola at b, and will intersect the horizontal ag at g: choose e such that ag will be a mean proportional between af and ae.