A comment on proofs of Nanson's formula with a new proof

In terms of the three typical proofs for the Nanson’s formula nowadays in literatures, the paper evaluates the three proofs with their characteristics from a point of view of both mathematical deduction and limpiditazation of mechanical concepts, pointing out respectively for each proof the advantages and disadvantages together with the spots where improvements for the proofs may be made. Accordingly, the paper puts forward an improved and comprehensible proof for the formula. Also, the paper proposes an argumentation that a proof for a mechanical problem should reflect the intrinsic law of mechanics.