34.Nothing,I say,can be plainer to any impartial reader than that,by the evanescence of augments in the above-cited passage,Sir Isaac means their being actually reduced to nothing.But,to put it out of all doubt that this is the truth,and to convince even you,who shew so little disposition to be convinced,I desire you to look into his"Analysis per Aequationes Infinitas''(p.20),where,in his preparation for demonstrating the first rule for the squaring of simple curves,you will find that,on a parallel occasion,speaking of an augment which is supposed to vanish,he interprets the word evanescere by esse nihil .Nothing can be plainer than this,which at once destroys your defence.And yet,plain as it is,I despair of making you acknowledge it;though I am sure you feel it,and the reader if he useth his eyes must see it.The words evanescere sive esse nihil do (to use your own expression)stare us in the face.Lo!This is what you call (p.56)"so great,so unaccountable,so horrid,so truly Boeotian a blunder,''that according to you,it was not possible Sir Isaac Newton could be guilty of it.For the future,I advise you to be more sparing of hard words;since,as you incautiously deal them about,they may chance to light on your friends as well as your adversaries.As for my part,I shall not retaliate.It is sufficient to say you are mistaken.But I can easily pardon your mistakes.
Though,indeed,you tell me,on this very occasion,that I must expect no quarter from Sir Isaac's followers.And I tell you that I neither expect nor desire any.My aim is truth.My reasons I have given.Confute them,if you can.But think not to overbear me either with authorities or harsh words.The latter will recoil upon yourselves.The former,in a matter of science,are of no weight with indifferent readers;and,as for bigots,I am not concerned about what they say or think.
35.In the next place you proceed to declaim upon the following passage,taken from the seventeenth section of the'Analyst.'
"Considering the various arts and devices used by the great author of the fluxionary method;in how many lights he placeth his fluxions;and in what different way he attempts to demonstrate the same point:one would be inclined to think he was himself suspicious of the justness of his own demonstrations.''This passage you complain of as very hard usage of Sir Isaac Newton.You declaim copiously,and endeavour to show that placing the same point in various lights is of great use to explain it;which you illustrate with much rhetoric.But the fault of that passage is not the hard usage it contains:but,on the contrary,that it is too modest,and not so full and expressive of my sense as perhaps it should have been.
Would you like it better if I should say -"The various inconsistent accounts which this great author gives of his momentums and his fluxions may convince every intelligent reader that he had no clear and steady notions of them,without which there can be no demonstration?''I own frankly that I see no clearness or consistence in them.You tell me,indeed,in Miltonic verse,that the fault is in my own eyes,"So thick a drop serene has quench'd their orbs,Or dim suffusion veil'd.''At the same time you acknowledge yourself obliged for those various lights which have enabled you to understand his doctrine.But as for me,who do not understand it,you insult me,saying:"For God's sake,what is it you are offended at,who do not still understand him?''May not I answer,that I am offended for this very reason -because I cannot understand him or make sense of what he says?You say to me that I am all in the dark.
I acknowledge it,and entreat you who see so clearly to help me out.
36.You Sir,with the bright eyes,be pleased to tell me,whether Sir Isaac's momentum be a finite quantity,or an infinitesimal,or a mere limit?If you say a finite quantity:be pleased to reconcile this with what he saith in the scholium of the second lemma of the first section of the first book of his Principles:Cave intelligas quantitates magnitudine determinatas,sed cogita semper diminuendas sine limite .
If you say,an infinitesimal:reconcile this with what is said in his'Introduction to the Quadratures':Volui ostendere quod in methodo fluxionum non opus sit figuras infinite parvas in geometriam introducere .If you should say,it is a mere limit;be pleased to reconcile this with what we find in the first case of the second lemma in the second book of his Principles:Ubi de lateribus A et B deerant momentorum dimidia,&c.,where the moments are supposed to be divided.I should be very glad a person of such a luminous intellect would be so good as to explain whether by fluxions we are to understand the nascent or evanescent quantities themselves,or their motions,or their velocities,or simply their proportions:and,having interpreted them in what sense you will,that you would then condescend to explain the doctrine of second,third,and fourth fluxions,and shew it to be consistent with common sense if you can.You seem to be very sanguine when you express yourself in the following terms:"I do assure you,Sir,from my own experience,and that of many others whom I could name,that the doctrine may be clearly conceived and distinctly comprehended''(p.
31).And it may be uncivil not to believe what you so solemnly affirm,from your own experience.But I must needs own I should be better satisfied of this,if,instead of entertaining us with your rhetoric,you would vouchsafe to reconcile those difficulties,and explain those obscure points above mentioned.if either you,or any one of those many whom you could name will but explain to others what you so clearly conceive yourselves,I give you my word that several will be obliged to you who,I may venture to say,understand those matters no more than myself.But,if I am not mistaken,you and your friends will modestly decline this task.
