The Reformed Library Keeper, Essay 1
AN Idea of Mathematics written by Mr Joh. Pell to Samuel Hartlib.
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 attend thoſe ſtudies, it is no marvail if they make no great progreſs in them. To remedie which, I conceiv theſe means not to bee amiſs.
1. To write a Conſiliarius Mathematicus, (ſo I call it) anſwering to theſe 3 queſtions:
Q. 1. What fruit or profit ariſeth from the ſtudie of Mathematics?
Q. 2. What helps are there for the attaining this profitable knowledg?
Q. 3▪ What order is to bee obſerved in uſing theſe helps?
To this purpoſe it ſhould contain
1. A plain and popular diſcourſ of the extent of the Mathematics, with the profit that redound's, firſt to the Student himſelf, and then to the Countrie wherein there are manie ſuch grounded Artiſts.
2. A Catalogue of Mathematicians and their works in this order:
1. A Synopſis of all the ſeveral kinds of Mathematical writings, either extant in print, or acceſſible Manuſcripts in publick Libraries, with ſeveral numbers ſet to everie kinde.
2. A Chronical Catalogue of all Mathematician's names that ever were of note, according to the order of the years when they lived, with the year when anie of their works were firſt printed,
3. A Catalogue of the writings themſelvs, in the order of years in which they vvere printed in anie language: And this I vvould contrive thus: Firſt, the year of our Lord, and then the names of all the Mathematical Books Printed that year in anie Countrie or Language, after the uſual manner of Catalogues: but
1. Adding the volume, that is, not onelyonly what fold [40. 80. &c.] but alſo the number of leavs, that wee may eſtimate the bulk of the Book.
2. Prefixing before the title the year to vvhichwhich you muſt look back to know either vvhen it vvas vvritten, or vvhen it vvas laſt before Printed, in that or any other Language.
3. Setting in the margent, after the Title.
1. The year vvherein it vvas the next time Printed.
2. The number of reference to the Synopſis in the firſt page; By vvhichwhich 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 everie kinde; In vvhat order, and how to read them, What to obſerv, what to beware of in ſom 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 mankinde. 2. of that more refined pleaſure of hunting out hidden truths, vvraſtling vvith difficult Problemes, and getting the victorie; and ſo much the rather, becauſ 3. of the great facilitie that is novv in that ſtudie, by reaſon of the many helps to ſpare much labor, time and coſt, vvhichwhich our forefathers vvere forced to ſpend. Secondly, To all thoſe who have underſtanding to eſtimate the worth of theſe ſtudies, and wealth vvherewith to purchaſe themſelvs laſting honor by the vviſe 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 vvhichwhich their Genius lead's them. Eſpecially, To all Princes and Estates, vvhom it concern's to take a courſ, 1. that their dominions may bee better furniſhed vvith this ſort of ſtudents. 2. That the vvaie may bee made leſs laborious and coſtlie, 3. That Mathematica ingenia may bee diſcovered and aſſiſted.
To vvhichwhich end it vvould bee good.
2. to erect a Publick Librarie, containing all thoſe Books, and one inſtrument of everie ſort that hath been invented, vvith ſufficient revenue,
1. To buy one copie of all thoſe that ſhall bee Printed yearly in other Countries. and
2. To maintain a Librarie-keeper of great judgment, to whom it may belong †
1. To peruſe all Books of ſuch ſubjects, to bee Printed within that Countrie, and 1. Suppreſs vvhatſoëver is not according to Art, that Learners bee not abuſed, and 2. Admoniſh the Writers, if they bring nothing but ſtale ſtuff.
2. Upon his credit to approv excellent inventions, and unpartially to commend the inventors to the rewarders.
3. To receiv, record and place one Printed copie of everie Book ſo peruſed, ſent into the Librarie, vvell bound at the Autor's or Book-ſeller's charge.
4. To reſolv anie ſtudent that enquire's about anie Probleme, vvhether it have been don already or no, fearing leſt hee ſhould actum agere, and therefore perhaps ſuppreſſing ſom invention vvhichwhich hee hath light upon, but doubts it is old and to bee found in ſom of the Books of that Librarie.
5. To receiv,† &c. all ſuch Manuſcripts as ſhall bee brought thither by vvaie of gift, Legacie or the like.
6. To maintain correſpondence vvith ſuch as himſelf in other Countries, to know vvhat is Printed there.
7. To take notice of all his Countrimen that are fit to bee Teachers, &c.
8. To keep a Catalogue of all ſuch vvorkmen as are able and fit to bee imploied in making Mathematical Inſtruments and repreſentations, vvorking upon Wood, Magnets, Metals, Glaſs, &c.
9. To give teſtimonial, after examination, to all ſorts of practiſers, as Pilots, Maſters, Landmeters, Accomptants, &c. of their ſpeculative abilitie and practical dexteritie, that thoſe that have occaſion to uſe ſuch men, bee not abuſed by unable undertakers, to their exceeding great damage.
By the Catalogue, men might bee informed, in that multitude of Books, vvith vvhichwhich the vvorld is novv peſtered, vvhat the names are of thoſe Books that tend to this ſtudie onelyonly.
In the Librarie, they might finde the Books themſelvs, read them, and if they liked them, knovv vvhither to ſend to buy them: Beſides, anie, vvhether forreiners or others, might have recourſ thither, and learn vvhat helps that Countrie would afford them in theſe ſtudies.
And this is the beſt courſ that I can think on for the making uſe of ſuch helps as wee have already. If men deſire better helps, let them emploie fit Artiſts.
3. To vvrite and publiſh theſe three new Treatiſes: 3†
1. Pandectae Mathematicae, Comprehending as Clearly, Orderly, and Thrftily, and Ingenuouſly as may bee, vvhatſoëver may bee gathered out of all thoſe Mathematical Books and Inventions that vvere before us, or that may bee inferred as Conſectaries thereon; citing, at the end of everie period or Propoſition, the ancienteſt Autor in vvhichwhich it is found, and branding all later vvriters if they bee taken ſtealing, or borrovving vvithout acknovvledgment, or [vvhichwhich is vvorſ] expreſly arrogating to themſelvs anie other man's inventions. This vvould bring that great Librarie into far leſs room, to the ſaving of more labor, time and coſt, to all after-ſtudents, than men can yet vvell imagine. But becauſ this alſo vvould bee too great and cumberſom to carrie about us, Let there bee compoſed
2. Comes Mathematicus, 4 †Comprehending in a pocket-Book, [and therefore as briefly as may bee] the uſefulleſt Tables and the Precepts for their uſe, in ſolving all Problemes, vvhether purely Mathematical, or applied to ſuch practices as men's various occaſions may require.
And laſtly, that in this kinde of Learning alſo, vvee bee no longer tied to Books, Let there bee compoſed
3. Mathematicus foreign,5 or An inſtruction, ſhevving hovv anie Mathematician that vvill take the pains, may prepare himſelf, ſo, as that hee may, though hee bee utterly deſtitute of Books or Inſtruments, reſolv anie Mathematical Probleme as exactly as if hee had a complete Librarie by him.
And this is the Idéa, vvhichwhich I have long framed to my ſelf, according to my faſhion, vvith vvhom this paſſeth for an undoubted truth, that the ſureſt vvaie to com to all poſſible excellencie in anie thing, is to propoſe to our ſelvs the perfecteſt Idéa's that vvee can imagine, then to ſeek the means tending thereto, as rationally as may bee, and to proſecute it vvith indefatigable diligence; yet, if the Idéa prove too high for us, to reſt our ſelvs content vvith approximation.
As for this preſent Idéa, I am ſo far from counting it meerly-impoſſible, that I ſee not vvhy it might not bee performed by one man, vvithout anie aſſiſtants, provided that hee vvere neither diſtracted vvith cares for his maintenance, nor diverted by other emploiments.
The excellencie of this vvork, make's me vviſh mine ovvn Nation the honor of firſt undertaking and perfecting this deſign, And I conceiv I have ſom reaſon to hope that it vvill bee ſo. For, though I knovv fevv or none that are both able and vvilling to promote deſigns of this nature, yet can I not therefore bee perſvvaded that this Kingdom is ſo deſtitute of learned Nobilitie and Gentrie, that there can bee found none to countenance and advance this part of Learning, even in this vvaie, if they could ſee it poſſible and likely to bee effected.
As for the Librarie and Catalogue, 1.2there can bee no doubt but they may eaſily bee had, if Monie bee not vvanting. Nor is it unlikelie that divers of this Nation (if they be ſet apart for it) are able to compoſe the other 3. new Treatiſes; For though I knovv no ſuch, yet I perſvvade my ſelf there may bee found amongſt us men able to encounter all the difficulties, and to endure all the labor, that they muſt needs meet vvith in the raiſing of ſo great a Fabrick. And I the rather believ that there are many ſuch, becauſ for mine own part, notvvithſtanding the vvant of Counſel and helps in that ſtudie, and the innumerable diverſions and diſtractions that I have had, I am nevertheleſs com to ſuch a confidence of my underſtanding the depth of that ſtudie, that, vvere I to pen thoſe Pandects, 3.I ſhould laie heavier Lavvs upon my ſelf, than I have alreadie mentioned; namely, Firſt to laie dovvn ſuch an exact Method or deſcription of the proceſs of Man's reaſon in inventions, that afterward it ſhould bee imputed meerly to my negligence and diſobedience to my ovvn Lavvs, [and not to their inſufficiencie] if, from my firſt grounds, ſeeds, or principles, I did not, in an orderlie vvaie, according to that preſcribed Method, deduce, not onelyonly all that ever is to bee found in our Anteceſſor's vvritings, and vvhatſoëver they may ſeem to have thought on, but alſo all the Mathematical inventions, Theoremes, Problems and Precepts, that it is poſsible for the vvorking vvits of our ſucceſſors to light upon, and that in one certain, unchanged order, from the firſt ſeeds of Mathematics, to their higheſt and nobleſt applications, as vvell as to the meaneſt and moſt ordinarie. Not ſetting them dovvn at random as they com in my head, as thoſe before us have don, ſo that they ſeem to have light upon their Problems and the ſolutions of them by chance, not to have found them by one perpetual, conſtant, invariable proceſs of Art. Yet ſuch an Art may men invent, if they accuſtom themſelvs, as I have long don, to conſider, not onelyonly the uſefulneſs of men's vvorks, and the meaning and truth of their vvritings, but alſo how it came to paſs that they fell upon ſuch thoughts, and that they propoſed to themſelvs ſuch ends, or found out ſuch means for them.
Were theſe Pandects thus made and finiſhed, I ſuppoſe it is manifeſt, that by their orderlie, rational and uniform compleatneſs, above all that hath been hitherto vvritten, they vvould ſpare after-ſtudents much labor and time that is novv ſpent in ſeeking out of Books, and diſorderlie reading them, and ſtruggling vvith their cloudie expreſſions, unapt repreſentations, different Methods, confuſions, tautologies, impertinencies, falſhoods by paralogiſms and pſeudographemes, uncertainties becauſ of inſufficient demonſtrations, &c. beſides much coſt alſo, novv throvvn avvaie upon the multitude of Books, the greater part vvhereof they had perhaps been better never to have ſeen.
And it may be ſom vvould like the Method of that vvork ſo vvell, as to extend it farther, and applie it to other ſtudies; in ſpeculation imitating this my vvarineſs, that no falſhood bee admitted, and no truth omitted; and for practice enuring themſelvs, anie ſubject beeing propounded, to determine the number of all the Problemes that can bee conceived concerning it, and anie Probleme beeing propounded, demonſtratively to ſhevv either all the means of it's ſolution, or the impoſſibilitie of it: and if ſo, then vvhether it bee not yet, or not at all poſſible.
Men vvould eaſilie ſee hovv to contract theſe Pandects into a pocket-Book for their ordinarie uſe.4. But ſo to laie them up in their heads,5. as to need no Book at all [according to that deſideratum of mine, to have a Mathematicus foreign] vvill perhaps ſeem utterly impoſſible to moſt: No man, that ever I heard of, having propoſed ſuch a ſcope to himſelf before. But perhaps they vvill conceiv it more poſsible, if it pleaſ them to ſuſpend their judgments, till they have conſidered what means may bee uſed to fortifie the imagination, to prompt the memorie, to regulate our reaſon, and what effects may bee produced by the uniting of theſe means, and the conſtant exerciſing of them.
For mine ovvn part, the conſideration of the incomparable excellencie, unſtained pleaſure, vnvaluable profitableneſs, and undoubted poſſibilitie of this vvhole deſign, hath prevailed ſo far vvith mee, that, notvvithſtanding all the diſcouragements that I have met vvithal, I have don more tovvards it than bare Idéa.