# Understanding Newton's Principia: "Measure of the Same

• johann1301
In summary, Newton defines the quantity of matter as the measure of the same, arising from its density and bulk conjunctly.
johann1301
"Measure of the same"

From Newtons Principia:

"THE QUANTITY OF MATTER IS THE MEASURE OF THE SAME, ARISING FROM ITS DENSITY AND BULK CONJUNCTLY."

What does he mean when he says "is the measure of the same"?

This phrase is used many times in his other definitions as well:

"THE QUANTITY OF MOTION IS THE MEASURE OF THE SAME, ARISING FROM THE VELOCITY AND QUANTITY OF MATTER CONJUNCTLY."

Or;

"THE ACCELERATIVE QUANTITY OF A CENTRIPETAL FORCE IS THE MEASURE OF THE SAME, PROPORTIONAL TO THE VELOCITY WHICH IT GENERATES IN A GIVEN TIME."

English is not my first language, perhaps the reason to my confusion.

I think it's referring to something in the previous sentence.

The first definition in this topic, is altso the first definition mentioned in Principia. The only thing written before it is this;

"THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY.

DEFINITIONS.

DEFINITION 1."

It is merely the title of the book and two subtitles before the first definition.

I don't see how it can be referring to something in the previous sentence.

johann1301 said:
From Newtons Principia:

"THE QUANTITY OF MATTER IS THE MEASURE OF THE SAME, ARISING FROM ITS DENSITY AND BULK CONJUNCTLY."

What does he mean when he says "is the measure of the same"?

"the same" would refer to "quantity of matter". I read "measure of" to make it clear that it is a numeric quantity. What he calls "quantity of matter" is what we would call "mass". What he calls "bulk" is what we would call "volume". What he is saying is, more briefly:

mass = density χ volume

Thank you for that clarification!

johann1301 said:
Thank you for that clarification!
Newton's time's English is very old fashioned(About 400 years old)
So don't bother about that so much.Stick with the modern language.

The old English construct was, for example, "the weight of a ship is the measure of the same", and over time the "the" was dropped out so that a modern, grammatically normal version would be "the weight of a ship is the measure of same", but even that sounds very archaic to modern ears.

Replacing "measure of the same" with modern English phrasing would give something like:

"The quantity of matter arises from its density and bulk conjointly."

The English version that I've seen uses the word "conjointly" instead of "conjunctly", which I don't think is a proper English word. And "conjointly" is rather old-fashioned.

As you may be aware, this is someone else's translation of Newton's original Latin:

"Quantitas Materiæ est mensura ejusdem orta ex illius Densitate & Magnitudine conjunctim."

http://www.gutenberg.org/files/28233/28233-h/28233-h.htm

"Ejusdem" = "of it" and "ex illius" = "from its". A literal (ungrammatical) translation would be:
"Quantity of matter" is, the measurement of it comes from its density and size together.

Note that the OP's quote is from the translation by Andrew Motte in 1729. It isn't 21st century English!

"Which is the measure of the same," simply means that to arrive at a quantity for the thing in question constitutes having measured the thing in question, be it quantity of matter (mass), quantity of motion (momentum), quantity of acceleration (due to gravity, g), etc. (No particular units are stipulated. In those days everyone used whatever units they liked best for the job at hand.)

It might be best to paraphrase the first definition, for example, as, "the quantity, or measure, of matter is arrived at by multiplying the density times the bulk."

When Newton says two things work "conjunctly" he is indicating they are multiplied.

"the same" clearly refers to MATTER, not to the "quantity of matter".

You may have different types of "measures", suitable to various stuff, one such type of measure being called "the quantity" of the particular type of stuff.

Essentially, Newton defines a particular mathematizable property of matter (the product of density and volume (asssumed to be numbers), calling that the "quantity of matter"), without bothering about other types properties, mathematizable or not, Matter may have.

Thus, "measure of blah-blah" is "classification criterion" in general, "quantity of blah-blah.." a particular type of measure, to be defined after "the same,..."

That's at least how I read it.

Last edited:
arildno said:
"the same" clearly refers to MATTER, not to the "quantity of matter".

I agree

Arildnoization of Newton!

Arildnoization of Newton:

The quantity of matter is that particular property of matter which is defined as the product of two other properties of matter, namely the product of the density and the volume.

## 1. What is Newton's Principia and why is it important?

Newton's Principia is a book written by Sir Isaac Newton that outlines his three laws of motion and the law of universal gravitation. It is considered one of the most influential scientific works in history and laid the foundation for modern physics.

## 2. What does "Measure of the Same" mean in Newton's Principia?

"Measure of the Same" refers to Newton's second law of motion, which states that the rate of change of an object's momentum is directly proportional to the force applied to it. In other words, the force and acceleration of an object are directly related.

## 3. How did Newton come up with the concept of "Measure of the Same"?

Newton observed that objects of different masses fell to the ground at the same rate, regardless of their weight. He also studied the motion of objects on inclined planes and found that the acceleration of an object is directly proportional to the force applied to it. These observations led him to formulate his second law of motion.

## 4. What are the practical applications of "Measure of the Same" in everyday life?

The concept of "Measure of the Same" is used in many practical applications, such as understanding the motion of objects in sports, designing vehicles, and calculating the forces involved in structures and buildings. It is also essential in understanding the principles of flight and the operation of machines.

## 5. How does "Measure of the Same" relate to the law of conservation of momentum?

The law of conservation of momentum states that the total momentum of a system remains constant unless acted upon by external forces. "Measure of the Same" is directly related to this law, as it explains how forces affect the change in momentum of an object, which ultimately affects the momentum of the entire system.

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