Understanding Ultimate Ratio of Equality

[adiputra]

hi,
1)can anyone help me to understand ultimate ratio of equality? (from this extract)

Cor. Hence if two quantities of any kind are any how divided into an equal number of parts, and those parts, when their number is augmented, and their magnitude diminished in infinitum, have a given ratio one to the other, the first to the first, the second to the second, and so on in order, the whole, quantities will be one to the other in that same given ratio. For if, in the figures of this Lemma, the parallelograms are taken one to the other in the ratio of the parts, the sum of the parts will always be as the sum of the parallelograms; and therefore supposing the number of the parallelograms and parts to be augmented, and their magnitudes diminished in infinitum, those sums will be in the ultimate ratio of the parallelogram in the one figure to the correspondent parallelogram in the other; that is (by the supposition), in the ultimate ratio of any part of the one quantity to the correspondent part of the other.

2)if you are throwing a ball in a space and under equation F=ma, will the ball keep accelerating or it will accelerate for a momentary?



(sorry my english is very poor)

 

[dicerandom]

For (1) it would help to have the lemma and the pictures if you could.

For (2) you should take a closer look at the equation F=ma. What is necessary to cause an acceleration? How do you apply such a thing?

 

[quicknote]

I can help you understand the concept of ultimate ratio of equality. This concept is based on the idea that if two quantities are divided into equal parts and those parts have a given ratio to each other, then the whole quantities will also have that same ratio. This can be seen in the example of parallelograms, where the sum of the parts is always in the same ratio as the sum of the parallelograms. This ratio remains the same even when the number of parts and parallelograms is increased infinitely and their sizes are decreased infinitely.

Regarding your second question, if you are throwing a ball in a space under the equation F=ma, the ball will continue to accelerate as long as there is a force acting on it. Once the force is removed, the ball will either continue moving at a constant velocity or decelerate depending on the external forces acting on it. It will not accelerate for a momentary, but rather for as long as there is a force acting on it. I hope this helps clarify your understanding.