THe summe of what I have heretofore written or spoken to you, concerning the advancement of the Mathematickes, is this: As long as men want will, wit, meanes or leisure to atter [...] those studies, it is no marvaile if they make no great progresse in them. To remedy which, I conceive these meanes not to be amisse.

1. To write 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 helpes are there for the attaining this profitable knowledge?
• Q. 3. What order is to be observed in using these helpes?

To this purpose it should containe

• 1. A plaine and popular discourse of the extent of the Mathematics, with the profit that redounds, first to the Student him­selfe, and then to the Country wherein there are many such grounded Artists.
• 2. A Catalog of Mathematicians and their workes in this order:
  • 1. A Synopsis of all the severall kindes of Mathematicall writings, either extant in print, or accessible Manu­scripts in public Libraries, with severall numbers set to every kinde.
  • 2. A Chronicall Catalog of all Mathematicians names that ever were of note, according to the order of the yeares when they lived, with the yeare when any of their workes were first printed.
  • 3. A Catalog 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 yeere of our Lord, and then the names of all the Mathematicall bookes printed that yeare in any country or language, after the usuall manner of Catalogs; but
    • 1. adding the volume, that is, not onely what fold [4^o. 8^o. &c.] but also the number of leaves, that we may estimate the bulke of the booke.
    • 2. praefixing before the title, the yeare to which you must looke backe to know either when it was written, or when it was last before printed, in that or any other language.
    • 3. setting in the margent, after the title,
      • 1. the yeare 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 runne over all the bookes of one sort, of this or that particular subject.
• 3. A Counsell directing a student to the best bookes in every kinde; In what order, and how to reade them, What to observe, what to beware of in some Mathematicasters, how to proceed and keepe all.
• 4. A Paraenesis, First, To all those who have meanes and leisure, and a wit not unapt for these studies, to set upon them in re­gard 1. of their profitablenesse to the student, and to mankinde, and 2. of that more refined pleasure of hunting out hidden truths, wrastling with difficult Problemes, 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 helpes 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 concernes to take a course 1. that their dominions may be better furnished with this sort of students, 2. that the way may be made lesse 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 bookes, and one instrument of every sort that hath beene invented, with efficient revenue, 1. to buy one copy of all those that shall be printed yearly in other countries.

and 2. to maintaine 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. suppresse whatsoever is not according to Art, that Learners be not abused, and 2. admonish the writers, if they bring nothing but stale stuffe.
• 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 booke so perused, sent into the Library, well bound at the Au­thors or Book-sellers charge.
• 4. to resolve any student that enquires about any Probleme▪ [...]hether it have beene done already or no, fearing lest hee 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 bookes 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 maintaine correspondence with such as himselfe in other countries, to know what is printed there.
• 7. to take notice of all his countrimen that are fit to be teachers, &c.
• 8. to keepe a Catalog of all such workmen as are able and fit to be imployed in making Mathematicall instruments and representations, working upon wood, magnets, metalls, glasse, &c.
• 9. to give testimoniall, after examination, to all sorts of practisers, as Pilots, Masters, Landmeters, Accomptants, &c. of their s [...]culative ability and practicall dexterity, that those that have occasion to use such men, be not abused by unable undertakers, to their exceeding great damage.
  • By the Catalog, men might be informed, in that multitude of bookes, with which the world is now pestered, what the names are of those bookes that tend to this study onely.
  • In the Library, they might finde the bookes themselves, reade them, and if they liked them, know whither to send to buy them, Besides, any, whether forreiners on others, might have recourse thither, and learne what helps that country would afford them in these studies.
• And this is the best course that I can thinke on for the making use of such helpes as we have already. If men desire better helpes, let them employ fit Artists

3. To write and publish these three new Treatises: †

• 1. Pandectae Mathematicae, Comprehending as cleerly, orderly, thriftily, and ingenuously as may be, whatsoever may be gathered out of all those Mathematicall bookes 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] expresly arrogating to themselves any other mans inventions. This would bring that [...] Library into farre lesse roome, 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 Problemes, whether purely-Mathematicall, or applied to such practices as mens various occasions may require.
• And lastly, that in this kinde of Learning also, we be no longer tyed to bookes, Let there be composed
• 3. Mathematicus [...], or An instruction, shewing how any Mathematician that will take the paines, may prepare himselfe, so, as that he may, though he be utterly destitute of bookes or instruments, resolve any Marhematicall Pro­bleme as exactly as if he had a complete Library by him.

And this is the Idéa, which I have long framed to my selfe, 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 our selves the [...] we can imagine, then to seeke the meanes tending thereto, as rationally as may be, and to prosecute it with [...] gence; yet, if the Idéa prove too high for us, to rest our selves content with approximation.

As for this present Idéa, I am so farre 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 worke, makes me wish mine owne 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 designes of this nature, yet can I not therefore be persuaded that this Kingdome 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 Catalog, 1.2 there can be no doubt but they may easily be had, if mony 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 my selfe 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 Fabricke. And I the rather beleeve that there are many su [...] because for mine owne part, notwithstanding the want of Counsell and helpes in that study, and the innumerable diversions a [...] distractions that I have had, I am neverthelesse come to such a confidence of my understanding the depth of that study, tha [...] were I to pen those Pandects, 3 I should lay heavier lawes upon my selfe, than I have already mentioned; namely, First to l [...] downe such an exact Method or description of the processe of Mans reason in inventions, that afterward it should be imput [...] meerly to my negligence and disobedience to my owne lawes, [and not to their insufficiency] if, from my first grounds, see [...] or principles, I did not, in an orderly way, according to that praescribed Method, deduce, not onely all that ever is to be fou [...] in our Antecessors writings, and whatsoever they may seeme to have thought on, but also all the Mathematicall invention Theoremes, Problemes and Precepts, that it is possible for the working wits of our successors to light upon, and that in one ce [...]taine, 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 seeme [...] have light upon their Problemes and the solutions of them by chance, not to have found them by one perpetuall, constant, in [...]riable processe of Art. Yet such an Art may men invent, if they accustome themselves, as I have long done, to consider, not one [...] the usefulnesse of mens workes, and the meaning and truth of their writings, but also how it came to passe that they fell upon su [...] thoughts, and that they proposed to themselves such ends, or found out such meanes for them.

Were these Pandects thus made and finished, I suppose it is manifest, that by their orderly, rationall and uniforme co [...] pleatnesse, above all that hath beene hitherto written, they would spare after-students much labour and time that is now spe [...] in seeking out of bookes, and disorderly reading them, and struggling with their cloudy expressions, unapt representations, d [...]ferent Methods, confusions, tautologies, impertinencies, falshoods by paralogismes and pseudographemes, uncertainties b [...] cause of insufficient demonstrations, &c. besides much cost also, now throwne away upon the multitude of bookes, the gre [...]ter part whereof they had perhaps beene better never to have seene.

And it may be some would like the Method of that worke so well, as to extend it farther, and apply it to other studies; [...] speculation imitating this my warinesse, that no falshood be admitted, and no truth omitted; and for practice enuring themselve [...] Any subject being propounded, to determine the number of all the Problemes that can be conceived concerning it, and A [...] Probleme being propounded, demonstratively to shew either all the meanes 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. 4 But so to lay them up in th [...] heads, as to need no booke at all [according to that desideratum of mine, to have a Mathematicus [...]] will perhaps see [...] utterly impossible to most: 5 No man, that ever I heard of, having proposed such a scope to himselfe before. But perha [...] they will conceive it more possible, if it please them to suspend their judgements, till they have considered what meanes [...] be used to fortifie the imagination, to prompt the memory, to regulate our reason, and what effects may be produced by [...] uniting of these meanes, and the constant exercising of them.

For mine owne part, the consideration of the incomparable excellency, unstained pleasure, unvaluable profitablenesse, and [...] doubted possibility of this whole designe, hath prevailed so farre with me, that notwithstanding all the discouragements tha [...] have met withall, I have done more towards it than bare Idéa,.