SIR:  
THe sum of what I have heretofore written or spoken to you, concerning the advancement of the mathematics, is this: As long as men want will, wit, means or leisure to atter●● those studies, it is no marvel if they make no great progress in them. To remedy which, I conceive these means not to be amiss.  
1. To writ a Consiliarius Mathematicus,( so I call it) answering to these 3. questions: 

Q. 1. What fruit or profit ariseth from the study of Mathematics?  
Q. 2. What helps are there for the attaining this profitable knowledge?  
Q. 3. What order is to be observed in using these helps?    
To this purpose it should contain 

1. A plain and popular discourse of the extent of the Mathematics, with the profit that redounds, first to the Student himself, and then to the Country wherein there are many such grounded Artists.  
2. A catalogue of Mathematicians and their works in this order: 

1. A Synopsis of all the several kindes of mathematical writings, either extant in print, or accessible Manuscripts in public Libraries, with several numbers set to every kind.  
2. A Chronicall catalogue of all Mathematicians names that ever were of note, according to the order of the yeares when they lived, with the year when any of their works were first printed.  
3. A catalogue of the writings themselves, in the order of yeares in which they were printed in any language: And this I would contrive thus: First, the year of our Lord, and then the names of all the mathematical books printed that year in any country or language, after the usual manner of Catalogs; but 

1. adding the volume, that is, not onely what fold[ 4o. 8o. &c.] but also the number of leaves, that we may estimate the bulk of the book.  
2. praefixing before the title, the year to which you must look back to know either when it was written, or when it was last before printed, in that or any other language.  
3. setting in the margin, after the title, 

1. the year wherein it was the next time printed:  
2. the number of reference to the Synopsis in the first page.; By which numbers one may presently run over all the books of one sort, of this or that particular subject.        
3. A counsel directing a student to the best books in every kind; In what order, and how to read them, What to observe, what to beware of in some Mathematicasters, how to proceed and keep all.  
4. A Paraenesis, First, To all those who have means and leisure, and a wit not unapt for these studies, to set upon them in regard 1. of their profitableness to the student, and to mankind, and 2. of that more refined pleasure of hunting out hidden truths, wrestling with difficult problems, and getting the victory; and so much the rather, because 3. of the great facility that is now in that study, by reason of the many helps to spare much labour, time and cost, which our forefathers were forced to spend. Secondly, To all those who have understanding to estimate the worth of these studies, and wealth wherewith to purchase to themselves lasting honour by the wise dispensing of it, to take more notice of this sort of students, and to encourage them, setting apart the choicest of them, to perfect the inventions, to which their Genius leads them: Especially, To all Princes and Estates, whom it concerns to take a course 1. that their dominions may be better furnished with this sort of students, 2. that the way may be made less laborious and costly, 3. that Mathematica ingenia may be discovered and assisted.    
To which end it would be good  
2. To erect a Public Library, containing all those books, and one instrument of every sort that hath been invented, with efficient revenue, 1. to buy one copy of all those that shall be printed yearly in other countries.  
and 2. to maintain a Library keeper of great judgement, to whom it may belong† 

1. to peruse all books of such subjects, to be printed within that country, and 1. suppress whatsoever is not according to Art, that Learners be not abused, and 2. admonish the writers, if they bring nothing but stale stuff.  
2. 〈…〉 credit to approve excellent inventions, and unpartially to commend the inventors to the rewarders.  
3. to ●eceive, record and place one printed copy of every book so perused, sent into the Library, well bound at the Authors or booksellers charge.  
4. to resolve any student that inquires about any problem▪ ●hether it have been done already or no, fearing lest he should actum agere, and therefore perhaps suppressing ●o●● 〈◇〉 ention which he hath light upon, but doubts it is old and to be found in some of the books of that Library.  
5. to receive, &c. all such Manuscripts as shall be brought thit●er by way of gift, Legacy, or the like.  
6. to maintain correspondence with such as himself in other countries, to know what is printed there.  
7. to take notice of all his countrymen that are fit to be teachers, &c.  
8. to keep a catalogue of all such workmen as are able and fit to be employed in making mathematical instruments and representations, working upon wood, magnets, metals, glass, &c.  
9. to give testimonial, after examination, to all sorts of practisers, as Pilots, Masters, Landmeters, accountants, &c. of their s●●culative ability and practical dexterity, that those that have occasion to use such men, be not abused by unable undertakers, to their exceeding great damage. 

By the catalogue, men might be informed, in that multitude of books, with which the world is now pestered, what the names are of those books that tend to this study onely.  
In the Library, they might find the books themselves, read them, and if they liked them, know whither to sand to buy them, Besides, any, whether foreigners on others, might have recourse thither, and learn what helps that country would afford them in these studies.    
And this is the best course that I can think on for the making use of such helps as we have already. If men desire better helps, let them employ fit Artists    
3. To writ and publish these three new Treatises:† 

1. Pandectae Mathematicae, Comprehending as clearly, orderly, thriftily, and ingenuously as may be, whatsoever may be gathered out of all those mathematical books and inventions that were before us, or that may be inferred as Consectaries thereon; citing, at the end of every period or proposition, the ancientest Author in which it is found, and branding all later writers if they be taken stealing, or borrowing without acknowled●●●ent, or[ which is worse] expressly arrogating to themselves any other mans inventions. This would bring that 〈◇〉 Library into far less room, to the saving of more labour, time and cost, to all after-students, than men can yet well Imagine. But because this also would be too great and cumber some to carry about us, Let there be composed  
2. Comes Mathematicus, Comprehending in a pocket-booke,[ and therefore as briefly as may be] the usefullest Tables and the Precepts for their use, in solving all problems, whether purely-Mathematicall, or applied to such practices as mens various occasions may require.  
And lastly, that in this kind of Learning also, we be no longer tied to books, Let there be composed  
3. Mathematicus {αβγδ}, or An instruction, showing how any Mathematician that will take the pains, may prepare himself, so, as that he may, though he be utterly destitute of books or instruments, resolve any Marhematicall problem as exactly as if he had a complete Library by him.    
And this is the Idéa, which I have long framed to myself, according to my fashion, with whom this 〈…〉 ●●ted truth, that the surest way to come to all possible excellency in any thing, is to propose to ourselves the 〈…〉 we can imagine, then to seek the means tending thereto, as rationally as may be, and to prosecute it with 〈…〉 gence; yet, if the Idéa prove too high for us, to rest ourselves content with approximation.  
As for this present Idéa, I am so far from counting it meerely-impossible, that I see not why it might not be performe●… one man, without any assistants, provided that he were neither distracted with cares for his maintenance, nor diverted by o●… employments.  
The excellency of this work, makes me wish mine own nation the honour of first undertaking and perfecting this desig●… And I conceive I have some reason to hope that it will be so. For, though I know few or none that are both able and willing promote designs of this nature, yet can I not therefore be persuaded that this kingdom is so destitute of learned Nob●… and Gentry, that there can be found none to countenance and advance this part of Learning, even in this way, if they co●… see it possible and likely to be effected.  
As for the Library and catalogue, there can be no doubt but they may easily be had, if money be not wanting. Nor is it unlik●… that divers of this nation( if they be set apart for it) are able to compose the other 3. new Treatises; For though I know ●… such, yet I persuade myself there may be found amongst us men able to encounter all the difficulties, and to endure all the ●… bour, that they must needs meet with in the raising of so great a fabric. And I the rather believe that there are many su●… because for mine own part, notwithstanding the want of counsel and helps in that study, and the innumerable diversions a●… distractions that I have had, I am nevertheless come to such a confidence of my understanding the depth of that study, tha●… were I to pen those Pandects, I should lay heavier laws upon myself, than I have already mentioned; namely, First to l●… down such an exact Method or description of the process of Mans reason in inventions, that afterward it should be imput●… merely to my negligence and disobedience to my own laws,[ and not to their insufficiency] if, from my first grounds, see●… or principles, I did not, in an orderly way, according to that prescribed Method, deduce, not onely all that ever is to be fou●… in our Antecessors writings, and whatsoever they may seem to have thought on, but also all the mathematical invention theorems, problems and Precepts, that it is possible for the working wits of our successors to light upon, and that in one ce●… ta'en, unchanged order, from the first seeds of Mathematics, to their highest and noblest applications, as well as to the mean●… and most ordinary. Not setting them down at randon as they come in my head, as those before us have done, so that they seem ●… have light upon their problems and the solutions of them by chance, not to have found them by one perpetual, constant, in●… riable process of Art. Yet such an Art may men invent, if they accustom themselves, as I have long done, to consider, not one●… the usefulness of mens works, and the meaning and truth of their writings, but also how it came to pass that they fell upon su●… thoughts, and that they proposed to themselves such ends, or found out such means for them.  
Were these Pandects thus made and finished, I suppose it is manifest, that by their orderly, rational and uniform co●… pleatnesse, above all that hath been hitherto written, they would spare after-students much labour and time that is now spe●… in seeking out of books, and disorderly reading them, and struggling with their cloudy expressions, unapt representations, d●… ferent Methods, confusions, tautologies, impertinencies, falshoods by paralogisms and pseudographemes, uncertainties b●… cause of insufficient demonstrations, &c. besides much cost also, now thrown away upon the multitude of books, the gre●… ter part whereof they had perhaps been better never to have seen.  
And it may be some would like the Method of that work so well, as to extend it farther, and apply it to other studies; ●… speculation imitating this my wariness, that no falsehood be admitted, and no truth omitted; and for practise enuring themselve●… Any subject being propounded, to determine the number of all the problems that can be conceived concerning it, and A●… problem being propounded, demonstratively to show either all the means of its solution, or the impossibility of it: and if ●… then whether it be not yet, or not at all possible.  
Men would easily see how to contract these Pandects into a pocket-booke for their ordinary use. But so to lay them up in th●… heads, as to need no book at all[ according to that desideratum of mine, to have a Mathematicus {αβγδ}] will perhaps see●… utterly impossible to most: No man, that ever I heard of, having proposed such a scope to himself before. But perha●… they will conceive it more possible, if it please them to suspend their judgements, till they have considered what means ●… be used to fortify the imagination, to prompt the memory, to regulate our reason, and what effects may be produced by ●… uniting of these means, and the constant exercising of them.  
For mine own part, the consideration of the incomparable excellency, unstained pleasure, unvaluable profitableness, and ●… doubted possibility of this whole design, hath prevailed so far with me, that notwithstanding all the discouragements tha●… have met withall, I have done more towards it than bare Idéa,.