ultimate ratio การใช้

Essentially, the ultimate ratio is the ratio as the increments vanish into nothingness.
Importantly, Newton explained the existence of the ultimate ratio by appealing to motion;
The ultimate ratio of yacht speed to wind speed therefore also gives rise to Beta by inverse cosine . e . g . speed-sailing at twice the windspeed corresponds to a 30 degrees apparent wind angle i . e . Beta = 30 degrees.
This revised calculus of ratios continued to be developed and was maturely stated in the 1676 text " De Quadratura Curvarum " where Newton came to define the present day derivative as the ultimate ratio of change, which he defined as the ratio between evanescent increments ( the ratio of fluxions ) purely at the moment in question.
:" When we have grasped the spirit of the infinitesimal method, and have verified the exactness of its results either by the geometrical method of prime and ultimate ratios, or by the analytical method of derived functions, we may employ infinitely small quantities as a sure and valuable means of shortening and simplifying our proofs ."