# Why is the parallelogram rule for the addition of forces as it is?

1. Mar 1, 2014

### zexott

Why is the parallelogram rule for the addition of forces as it is?
I feel it must have some deep origin and pointing to something fundamental. Though I know this problem may have no answer: God design it as such.
But I wonder how the first person came up with this rule, where does his/her intuition come from?
Are there something that addition of forces simply must obey due to logic itself?
Are there active research going on that is investigating this?

2. Mar 1, 2014

### 256bits

Would you accept vector addition as being the logic?

3. Mar 1, 2014

### bhillyard

It is likely that it arose because, at the time this was being developed, probably at the time of people like Stevens (1548 - 1620) most mathematics was carried out geometrically. So the parallelogram construction was the natural mode of working.

4. Mar 1, 2014

### bhillyard

Whoops, autocorrect jumped in. I mean Stevenus .

5. Mar 1, 2014

Use the Edit button to correct it.

6. Mar 1, 2014

### dauto

All the parallelogram rule does is to enforce that the addition of two vectors actually add their components.

7. Mar 1, 2014

### UltrafastPED

Historically it was an observation about ropes. The rule is equivalent assuming the rule of linear superposition of forces ... that is, application of one force does not interfere with any other. This means that forces form a linear vector space.

The rule dates back to at least the first century BC; it appears in Heron's "Mechanics". But it is probably older.

8. Mar 1, 2014

### zexott

Ah, observation of ropes, that's how their intuition comes. Now it seems conceivable for me. Your information is very detailed and now I guess I can trace it down. Thank you so much! And thank you all for your time and attention!

9. Mar 2, 2014