Multiply with or by? (2025)

Hi, before I came across the text below, I had thought we couldn't use "with" with "multiply" -for example, not "multiply two with four" but "multiply two by four".

"Let us therefore multiply body A, proportional to 1, with its speed, proportional to 2; the product or quantity of motion will be proportional to 2. On the other hand,let us multiply body B, proportional to 4, with its speed, proportional to 1; the product or quantity of motion will be proportional to 4"

It's from Leibniz's discourse on metaphysics and the original text is French.

The context is somewhat obscure - the idea of multiplying a "body" by a speed is a strange concept - I suspect that there might be a mistake in the translation.

In a usual context, e.g. "multiply two by four", by is correct. However, although it is usual to multiply by a number, it is also possible to multiply with a noun, i.e. one that references a number, where "with" has the meaning of "by the use of", e.g. "Multiply A by B and then multiply the answer with the answer from your earlier result."

NB
Please note that Leibniz is a proper noun/name, and therefore must be capitalised.

cheerfulscience said:

"Let us therefore multiply body A, proportional to 1, with its speed, proportional to 2; the product or quantity of motion will be proportional to 2. On the other hand,let us multiply body B, proportional to 4, with its speed, proportional to 1; the product or quantity of motion will be proportional to 4"

Click to expand...

There is no "metaphysical" meaning for "multiply".

This quote seems to refer to physics. The words "body" and "quantity of motion" are bad translations. Most likely "body" should be "mass", and "quantify of motion" should be "kinetic energy". Whatever the correct words are, the translator should have used exact physics technical terms, not general English rough translations.

Since it's a bad translation, we should ignore it when considering whether "with" is acceptable with "multiply".

Use "by" . Using "with" is much less common, and is much easier to use incorrectly.

Note: the phrase "a 1-bit value" means "zero or one". So here "multiple by" really means "choose the number or zero". It is a binary choice, not an actual multiplication.

dojibear said:

Note: the phrase "a 1-bit value" means "zero or one". So here "multiple by" really means "choose the number or zero". It is a binary choice, not an actual multiplication.

Click to expand...

Firstly, thanks, I will use "by".
Secondly, I know exactly what multiplication by 1-bit value means technically. The thing is, I have an operation that is multiplication from algorithm point of view. It just so happens that I can reduce the multiplier to one bit. And of course, the implementation of the multiplication becomes very simple. However, it is not as simple as you think because I am dealing with complex values. Anyway, I was just wondering how to call this simplified operation.

Malakias said:

However, it is not as simple as you think because I am dealing with complex values.

Click to expand...

I vaguely remember the definition of "multiplication" for complex values. It's a different operation. I don't remember what terminology is used in mathematics for this operation. My comment about "by/with" was for general English: the multiplication of scalars. No imaginary numbers. No vectors. No complex numbers.

dojibear said:

I vaguely remember the definition of "multiplication" for complex values. It's a different operation. I don't remember what terminology is used in mathematics for this operation. My comment about "by/with" was for general English: the multiplication of scalars. No imaginary numbers. No vectors. No complex numbers.

Click to expand...

It doesn't matter if they are complex numbers. It's the same remembering that i- squared is equal to minus one. Multiplication is always'by'.