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I have been told always that $F$ is directly proportional to acceleration.

My question is that for finding such a relationship there should be source that produces desired force and in which the force can be adjusted i.e. Twice, thrice and more. But the problem is initially before the discovery of laws of motion how can one say that a force is twice the other, how can he even judge the relationship between two forces without knowing the quantitative definition of force?

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    $\begingroup$ Duplicate of physics.stackexchange.com/q/2644 $\endgroup$
    – Kyle Kanos
    Commented Nov 13, 2013 at 15:53
  • $\begingroup$ @kyle kanos that question does not answers the question above $\endgroup$
    – user28804
    Commented Nov 13, 2013 at 15:57
  • $\begingroup$ It does as stated from the title of this question. $\endgroup$
    – Ignacio Vergara Kausel
    Commented Nov 13, 2013 at 16:17
  • $\begingroup$ Another possible duplicate: physics.stackexchange.com/q/70186/2451 $\endgroup$
    – Qmechanic ♦
    Commented Nov 13, 2013 at 16:22
  • $\begingroup$ @user28804: I disagree. Lubos's answer provides the answer to your question in his last 3 paragraphs. Please read it again. $\endgroup$
    – Kyle Kanos
    Commented Nov 13, 2013 at 16:33

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how can he even judge the relationship between two forces without knowing the quantitative defination of force ??

One can't. The concept "Force" is an abstraction from observation and must be well defined before quantitative relationships (once, twice, thrice, etc.) can be established.

But this was Newton's accomplishment, correctly recognizing and defining (net) force as that which acts to change an object's momentum (an abstraction which also must be correctly recognized and defined).

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  • $\begingroup$ can you tell what did newton used as a source of constant force for studying hi relationships ?? $\endgroup$
    – user28804
    Commented Nov 14, 2013 at 11:19

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