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Isaac Newton, Leonhard Euler and *F* = *ma*

In Newton's time, the terms

*acceleration*and*second derivative*did not exist, so he could not have written*F*=*ma*but unscientifically credited to Newton. Euler directly and independently gave various equations of force*F*=*ma*/2 or*F*=*ma*/*n*in 1736,*F*= 2*ma*in 1750 (the coefficient 2 depended on the unity of measure),*F*=*ma*/2*g*in 1765 and*F*=*ma*in 1775 in different ways. Further,*F*=*ma*is used to derive the rest mass energy equation (*E*_{0}=*m*_{0}*c*^{2}), but if*F*= 2*ma*,*F*=*ma*/2, and*F*=*ma*/2*g*are used then equations for rest mass energy become*E*_{0}= 2*m*_{0}*c*^{2},*E*_{0}=*m*_{0}*c*^{2}/2, and*E*_{0}=*m*_{0}*c*^{2}/2*g*. The situation is similar to kinetic energy. The equation for Principia's Law II is*F*=*k*(*v−u*), which is not discussed at all. Newton gave a velocity dependent force and Euler an acceleration dependent force. If the magnitudes of equations of force*F*=*ma*and*F*= 2*ma*are equal then it implies 1 = 2, which is not true. Euler used two primary or fundamental units*L*(length) and*F*(force), hence the coefficient is 2. The systems of primary units*L*(length),*F*(force),*T*(time) and*L*(length),*m*(mass),*T*(time) were introduced in the following century. Thus equation*F*=*ma*may be understood as a postulate. The terms “motion” and “quantity of motion,” are required to be properly understood as defined in the*Principia.*Further the terms “alteration” and “rate of change of” are entirely different. In highly specialized literature it is mentioned that Euler invented*F*=*ma*(48 years after death of Newton), but in the standard literature or textbooks level physics Newton is the originator of*F*=*ma*. The debate concerning various aspects of*F*=*ma*is wide open and will reveal new facts in science.
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**Keywords:**
Euler;
F = ma;
Newton

**Document Type:** Research Article

**Affiliations:**
Fundamental Physics Society, His Mercy Enclave, Post Box 107 GPO, Shimla 171001, HP, India

Publication date: 16 September 2014

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