To the English gentrie, and all others studious of the mathematicks which shall bee readers hereof. The just apologie of Wil: Oughtred, against the slaunderous insimulations of Richard Delamain, in a pamphlet called Grammelogia, or the mathematicall ring, or mirisica logarithmorum projectio circularis.

TO THE ENGLISH GENTRIE, and all others ſtudious of the MATHEMATICKS, which ſhall bee Readers hereof. The juſt Apologie of WIL: OVGHTRED, againſt the ſlaunderous inſimulations of RICHARD DELAMAIN, in a Pamphlet called Grammelogia, or the Mathematicall Ring, or Mirifica logarithmorum projectio circularis.

HOnourable, and much honoured Gentlemen, I was of late at my comming up to London, for the performance of mine ordinary ſervice in the houſe of my moſt Honourable Lord the Earle of Arundell and Surrey, and Earle Marſhall of England, by many of my loving friends preſented with a moſt idle and ſcandalous Pamphlet written againſt me by Richard Delamaine, who profeſſeth himſelfe a Teacher of the Mathematickes about the City: Wherein I am brought before you upon the Scaffold, and with all the petulancies of a vexed mind and diſtempered paſſion, inſimulated and charged with, I know not what, injuries he pretendeth I ſhould have done unto him (your noble ſelves alſo by him ingaged therein, and incenſed againſt me) and at laſt, as if quite caſt, I am ſchooled by him with a long Lecture or Common place againſt Slaunder and Detraction. I did much wonder at it, to ſee my ſelfe ſo baſely and impudently abuſed by one whom I never had wronged, but had done very many courteſies for, giving him acceſſe to my chamber in Arundell Houſe day by day, teaching and inſtructing him in that facultie he profeſſeth: not onely ſatisfying his ſcruples in thoſe things he partly knew: but even laying the very foundation of diverſe parts, whereof hee was utterly ignorant. And I did not ſo much marvell to ſee him ſo bold with me a poore man, but duſt and aſhes; as I was amazed to ſee him ſo fearefully (yet without feare) to play with Almighty God, hypocritically and againſt his owne conſcience in things apparantly falſe, invoking and challenging his all-knowing teſtimony: and in the middeſt of his moſt unmannerly raylings, in his booke; and his ſlaunderous back-biting and depraving me, by audacious intruding himſelfe upon my moſt honourable favours with falſe complaints, utterly to overthrow and diſcredite me; in a perſonated admonition againſt ſuch uncharitable calumniations, to pronounce judgement againſt him ſelfe. But of theſe things we ſhall, God willing, ſee more in good time. I borrowed and peruſed that worthleſle Pamphlet, and in reading it (I beſhrew him for making me caſt away ſo much of that little time is remayning to my declined yeares) I met with ſuch a patchery and confuſion of disjoynted ſtuffe, that I was ſtriken with a new wonder, that any man ſhould be ſo ſimple, as to ſhame himſelfe to the world with ſuch a hotch-potch.

In the two firſt pages, (for ſo he afterward calleth them) are two Schemes of his Inſtrument. In the fourth page is his Epiſtle to the Kings Majeſtie. In the 5, 6, 7, are verſes to his great commendation. In the 8 to the end of 21, he hath an Epiſtle opprobrious againſt me, moſt plainely ſtill pointing me out, that he needeth not to name me: and therein moſt learnedly diſputeth with me his jealous oppoſite and the ſuppoſed, and aſſumed author, and divulg • r, and what not, in ſixe whole leaves, a queſtion about the aſſes ſhadow, I ſhould have ſayd, whether the ring, or the Index at the center, bee the better? that word BETTER cruelly wrings him. What, ſuch a compariſon of BETTER? ſuch a comparative aſperſion of BETTER? Too great, and too looſe an aſperſion: An unſavory report indeed: which ſavours of too high a conceipt of the one, and too great a detraction from the other: Endeavouring, what in him lyeth, to annihilate and beate downe the way, which I write upon, and to glory in the rayſing up of his ſuppoſed owne: thereby not onely poſſeſsing men with an untruth, but making ME alſo ignorant in MY choyce, that I ſhould leave unto the world the weakeſt and imperfecteſt part of the projection of the Logarithmes, and leave the beſt for another to write upon. I never thought, when I firſt writ upon this my invention or my name ſo to come to the worlds rumour: which may teach ME and others carefulneſſe hereafter (yea and fit it ſhould) how and what WE publiſh to the world: ſeeing there are ſuch carpers and maligners, ſuch buſy-bodies, who marre what others make: ſuch who have ſtings like Bees, and arrowes to ſhoote: ſharp-witted Critickes, Diogenes like ſnarling, who while they will needes have many callings, neglect their owne. Good Sir be pacifyed: who troubleth your patience? I, whom you make your adverſary (a better friend then you deſerve) never, I aſſure you, delivered that comparative attribution: I diſclaime it utterly: I never made compariſons with you: you muſt ſeeke you ſome other antagoniſt. And now what is become of your angry queſtion of BETTER? it had been much better, and more for your honeſty, to have held your peace.

But we will goe on in your Pamphlet. Next followeth a ſecond Epiſtle to the Reader, Pag: 22, 23, Then the projecting and dividing the circles of the Ring, from pag: 24, till the end of 43. Wherein you pleaſe your ſelfe much with a portentuous invention of your great Cylinder, for a ſtudy (he that will be at the charge (ſubaudi) were a great foole) of a yard diameter: which brave conceipt doth ſo elate, or rather eſterate you, that in the very next leaf you muſt needs give me a laſh: very wiſely unveyling a great ſecret about the circle of equall parts. After this, twenty two whole leafes being already paſt, you beginne in pag: 1, with your Pamphlet printed 1630; worthy indeed for the learnedneſſe of it to be enrolled in this diſorderly band. And then in token of triumph, pag: 24, you ſet up a banner of other encomiaſticall verſes.

Let me now ſee whither we are come: and we had need looke about us: for here is a vaſt hiatus, a huge Gulfe. And upon an inſtant from pag: 24 we are hurryed to pag: 53: Where tenthly we have a third Epiſtle to the Reader, that promiſeth him wonders in Aſtronomie, Horolography, in plaine triangles, applyed to dimenſions, Navigation, Fortification, &c. marry this &c. was well put in: but it had done paſſing well two lines before. Yet you have provided well enough for all that: you have left a great lacuna, that what you have no skill in now, peradventure you may hereafter picke out of the labours of ſome other: and then challenge it as comming within your intentions: and thence ſupply your vacuum.

After all this he rambleth backe againe, by way of introduction: of the examination of the graduation of the circles of the ring: which may ſerve as an inducement and furtherance to the learner, to fit and acquaint him. What, are we no farther yet? we have fairely rowled Syſiphus ſtone: but to make amends, we have a few ſcrambling uſes in Aſtronomie, in Dyalling in plaine triangles, from pag: 56 to 67. And then the Flag of encomiaſtical verſes, of p. 24, is again gloriouſly diſplayed in pag: 68. Fy upon foolery! Fy upon vaine-glory! Fy upon ſuch miſerable penury of matter! Now make roome: Here comes a new projection of circles enlarged, either by a moveable and fixed circle, or by a ſingle projection with an Index at the peripheria, or center: for here is plenty and variety. A wondrous ſecret it is, that a man may divide either one circle, or elſe foure, or ten circles, or as many as one will, into 1000 equall parts. But here our Vnvayler hath a worſe rub in his way. As ſpite would have it, this was firſt hit upon by one Thomas Browne a Ioyner: yet not one word of Browne: onely I am a beame in his eye. And herein lyeth a myſtery of his skill: He holdeth it no maſtery to joyne forces with a Ioyner: but by ſetting on a bold face, if with petulant inſolencies hee ſhall dare mee; hee thinketh the attempt will bee more glorious. Wherein I thanke him for putting a little difference in his eſtimation for matter of art betweene me and a Ioyner. And yet there is another matter in it too. Browne hath done it in a Serpentine line; and he in juſt circles: the very names of circle and Serpentine (though the things themſelves are the ſame: the ſerpentine revolution being but two true ſemicircles deſcribed on ſeverall centers) may to the ignorant (for ſuch they are that Delamaine muſt perſwade) ſeeme to intimate things different in nature: and ſo make good his claime againſt Browne. This part he cuts off ſhort in two leafes onely; reſerving all the reſt, that ought to be ſpoken thereof (which he will find harder then he conceiveth) to his large intentions.

But now (vvoe is me therfore) my puniſhment is at hand. All the reſt of this worthy Pamphlet, which is thirteene leafes (except the laſt page onely, vvhich is alſo an Epiſtle to the Reader, the very ſame promiſing one, which was before in pag: 22, the former) is a moſt vile, unmannerly, and barbarous invective againſt me: full of untruths, full of malice, full of ſcandall, full of hypocriſy. In pag: 73 I am argued of ſpreading unſavoury rumours: who (God knowes) have ſcarce ſo much as thought upon him, till this ſcandalous Pamphlet came to my hands: and of ignorance of his intentions; whereas it partly hath, and ſhall better appeare, that I know his intentions well enough. Then followeth pag: 74, a fourth Epiſtle to the Reader, ſhort, but very quick: that the world hath bin abuſed, as well as himſelfe, with a falſe rumour rayſed by ſome rude & ignorant tongue: by their malicious phantaſie: and that he (good ſoule) did not intend to take this courſe, but ſought peace, and his right by a private and friendly way: but fayling of it, his good intentions ſcorned and ſlighted, maketh the enſuing diſcourſe his plea.

Noble Gentlemen, excuſe I pray you my moſt juſt indignation. While he was ridiculous and vaine in his opprobries, I dallyed with him: now this ſo deepe taxing me of want of charity, in refuſing peace ſought, and proſecuting contention and diſcord, contrary to my Chriſtian duty, pierceth to the quicke: which only ſcandal-full calummation had it not been, I had ſcarce vouchſafed an anſwer to all the reſt. Impudent and impure mouth, for ever be thou ſtopped, that delighteſt in ſlaunder, and with lyes cutteſt like a ſharpe razor! When didſt thou ever ſeeke peace of me, and I refuſed it? when did I not but moſt mildly and modeſtly behave my ſelfe unto thee? returning thee good words fo • ill: which my Chriſtian humility thou haſt, it ſeemeth in thy price interpreted abjectneſſe, and growne thereby more importunate and unreaſonable. What have I done? what have I ſpoken at all, with which thou canſt juſtly charge me of wrong? how many wayes haſt thou moſt intollerably provoked me; by raylings to my face, and threatning thou wouldſt overtop me, by letters into the countrey; and all to urge me to impatient ſpeeches, that thou mighteſt get occaſion of a ſute at law, as thy ſelfe acknowledgedſt, to have a perſonall action at the Kings bench Barre againſt me? When I was from London, thou madeſt enquiry after me and my comming up, in a diſtempered and threatning manner. When I came to London, thou ſoughteſt me out, and openly in the audience of divers witneſſes reviledſt me about my book & inſtrumēt called The circles of proportion (which yet I ſet not out, nor ever ſought to make one penny benefit by) while I onely ſtood ſilent and amazed to ſee thy audaciouſneſſe and deſperate conſcience: till at laſt extreamely provoked with thy braving reproaches I onely ſayd, what ſtrange impudence is this? You know that I know what is in you, and that you have no skill in diverſe arts, which in your table you profeſſe: or if you have any, you may thanke me for it: and that you have and might have made better uſe and benefit of my friendſhip, then by theſe challenges you are ever like to get. And you anſwerd, then belike I haue all I ſhal have. And I ſaid, unleſſe you can better deſerve it. Afterward when I was in the countrey above a quarter of a yeare together, in deriſion of my calling you ſent ſome Porter dreſſed up like a wandring Miniſter, with a ſcandalous letter, full of injurious expoſtulations of wronging you in print, which I never did: of ſtealing your invention, which is as falſe: of traducing the dead: of intruding my ſelfe into your calling: and neglecting mine owne: and ſuch like peaceable ſtuffe, which letter I would not keepe, leſt by it I might hereafter be provoked againſt you: but cloſing it up againe, delivered it to the Porter, willing him to returne it backe into your hands, and bid you peruſe it with a better mind. And when afterward I ſent up to you a Canon of ſines, tangents, and ſecants, which I had borrowed, you asked if I had not alſo ſent ſome ſcornefull anſwer to your letter. After this (diſpairing to get any advantage out of my words) you ſhameleſſely exclaimed upon me to my Lord Marſhall, and to my Lord of London, and to as many of the Nobility, Gentrie, and Clergie, as you thought I was known to; that ſo by depriving me of my friends and hopes, you might procure my utter undoing. Is this your Chriſtianity? Is this a private and a friendly way? is this to ſeeke peace? are theſe your good intentions? which becauſe you had not your wicked purpoſe in, you hold as ſlighted and ſcorned: and God grant that they may be ever ſo ſlighted and ſcorned, that is fruſtrated of their divelliſh intentions and deſignes, as many as have evill will againſt the innocent. Thus have you ſeene in him (honoured Gentlemen) the lively character of a querulous, clamorous, injurious, ill natured man: that like an angry curre can together bite and whine: crying out upon wrong, when hee himſelfe is the onely wrong-doer.

But reaſon is wee ſhould heare his plea: in which hee ſtill playeth his owne part, that is of ſcurrility, calumniation, out-facing, and hypocriſy. A pittifull caſe it was indeede that the world ſhould ſpie out his vanity in aſſuming to himſelfe the firſt diſcovery of the Horizontall projection and circles of proportion: It was a malevolous diſpoſition of envious detractours: famouſing ſome, and infaming others: which did not a little diſturbe the quiet and peace, which formerly hee enjoyed: when in his greedy hopes hee had ſwallowed downe the golden baite of vaine-glory, and of a large fee out of every Inſtrument the workeman ſhould ſell. But alſo ſlacked his intentions: or elſe there had beene yet greater helpe for ſuch as affect Mathematicall (he would have ſaid Manuall or Inſtrumentall) practices: Not out of mercenary reſpect, nor interlaced (O ſtay there: tell the very plaine truth: and ſay, Not without mercenary reſpect: interlaced) with deluſions & humbaſt ſtuff by way of illuſtration, if not confuſion: Had he not bin prevented by ſome others, whoſe callings might have invited them to ſpend their houres better: and which have work enough at home: whoſe ambition to bee ſomebody hath incited him forward to deliver ſome ſuppoſed new ſtuffe, or ſcrambling pieces, if not confuſed fragments of his owne, or ſome others to a publicke view, in obſcure and various phraſes: a thing ſuppoſed to be forged of ſundry heads, rather then one alone: ſeeing there is ſuch roving from the text: onely ſo farre to be truſted, as is agreeable to the text and doctrinall methode: amongſt whom to blow ſome ſmoke thereto, there was ſome groſſe one, ſeeing the matter is ſo common; for to a finer element perhaps his capacity could not aſſent, or aſcend: Yet there was ſome honeſty ſhowne not to take the crop, but the gleanings, holding it eaſyer to follow a beaten path, then to hazard a diſcovery. A blind guide, and a Parats ſpeech are not much different: the one walkes he knowes not whither, and the other ſpeakes he knoweth not what: and ſuch are all precepts in arts, which leade, and make men ſpeake without demonſtration: which doe not onely protract the ſtudious, and fruſtrate the affectionate, but maketh an ingenious ſpirit (who is ever more rationall then practicall) to contemne ſuch circumlocutions, and laugh in private, if not in publicke, at the learned ſtile of ſome Authours making themſelves by their obſcure kind of writing ſeemingly famous, ſticke not to calumniate othe • s to make them infamous: It is an ancient Proverbe among us, Good wine needeth no buſh: But the wine muſt not be faſt lockt up then, that none can come by it, if ſo it wants both buſh and key. Excellently ſcolded: even ſo I have ſometimes at a publicke Conduit heard a Tankard-woman in her furious and rayling fit; till ſhe hath runne her ſelfe quite out of breath, and ſenſe. But Richard Delamain, are you ſo mad upon the fruſtrated prey of your vain-glory and lucre, that neither the ſacredneſſe of my function, nor the reverence of mine age, nor my many good deſerts, nor my innocencie of any ill demerite, nor your knowledge of ſom • skill I have in thoſe ſciences, can eſcape the deriſion of your ſardonicall laughter, nor the wound of your virulent tongue? You are not in this fell paſſion to be reaſoned with. Onely I will ſoberly tell you that William Forſter, whom you call a Parrat ſpeaking he cannot tell what, is a farre more grounded Artiſt in all parts of the Mathematicks then is R. D: and better knoweth what belongeth to demonſtration then R. D. doth: as may ſoone bee tryed And as for my Clavis Mathematica, at which you make your ſelfe ſo merry, though I doate not, as you doe, upon mine owne (for I ſuppoſe you will not lay claime to that too) yet I confeſſe I like it the better, becauſe it pleaſeth not your palate, to which nothing can ſavour, that is learned and Analyticall: but onely the ſuperficiall ſcumme and froth of Inſtrumentall trickes and practices. It is you ſay hard and ſhort: Did any man, I pray you, ever make a key, but of hard matter, and portable for the ſmallneſſe? and yet it openeth an entrance into the moſt magnificent ſtructures. I ſee you, and ſuch as you are, looked for an Epitome: you were deceived: It is the way of rationall Scientialliſts, not of ground-creeping Methodicks. Hee that deſireth therein any reſolution, to him I have in the Epiſtle, for the honour of my moſt illuſtrious Lord, in whoſe ſervice and family I penned it, moſt freely profered my ſelfe gentle and curteous. He that liketh it not, may let it alone. But to him that can rightly uſe that key, it will unlocke the hardeſt myſteries of thoſe Sciences, and of the writers thereof; as is not unknowne to many, who to their great contentment have beene and are verſed therein.

My calling miniſtreth to R. D. a diverſe and contrary matter, both of mirth and ſcandall. His mirth I willingly leave unto him, as not unbefitting the reſt of his good manners: for hypocriſy and prophaneneſſe may well ſymbolize together. His ſcandall, being taken at the good gifts of God, cannot alſo but bee moſt unjuſt. For it is not without impiety to be affirmed, that any part of good literature is alien and abhorrent from the calling of a Divine: but that in all ages many of the moſt eminent in the ſublimity of Theologie, have beene alſo converſant in the ſtudy of the Mathematicks; moſt profitably making them to ſerve and ancillate to their higheſt contemplations: and they that have wanted ſuch helpe, have heartily wiſhed for it, and found in themſelves the defect. And that in no other thing, after his ſacred word, Almighty God (who creating all things in number, weight, and meaſure, doth moſt exactly Geometrize) hath left more expreſſe p • ints of his heavenly & infallible truth, then in theſe Sciences: in which onely the mind and underſtanding of a man can find ſecure reſt and ſure footing; all other knowledges being involved with a thicke miſt of ignorance and obſcurity. Beſides, that the exerciſe of theſe Arts accuſtomed to the certainty of demonſtration, quickeneth the underſtanding, rouſing it up from a laſie and drowſie indormition and ſervile aſſent to dialecticall and conjecturall probabilities and ſpurring it forward, and ſupplying it with meanes, unto the accurate inveſtigation of true and undeceivable principles. Now tell me R. D. are theſe ſtudies worthy of a Divine, or no? Indeed to know no more thereof then you know, that is to play with Inſtruments as a child doth with babies, or a Juggler (though the word trouble you) with his trinkets, is unworthy of a Divine, yea of a rationall man: worthy onely of ſome rude and reaſonleſſe dulman.

But he upb •• ideth me for taking libertie enough to the leſſe of time: and neglecting my calling. I muſt confeſſe this ſcandall cutteth deepe: and hath w • th the • , to whom I am not knowne, wrought me much prejudice and diſ • dvant • ge in anſwering whereof I muſt crave your patience in all humble modeſty, to make a briefe recitall of the courſe of my poore laborious and painfull life.

Next after E • ton ſchoole, I was bred up in Cambridge in Kings Colledge: of which ſociety I was a member about eleven or twelve ye • res: wherein how I behaved my ſelfe, going hand in hand with the reſt of my r • nke in the ordinary Academicall ſtudies and exerciſes, and with what approbation, is well knowne and remembred by many: the time which over and above thoſe uſuall ſtudies I employed upon the Mathematicall ſciences, I redeemed night by night from my naturall ſleep, defrauding my body, and inuring it to watching, cold, and labour, while moſt others tooke their reſt. Neither did I therein ſeek only my private content, but the benefit of many: and by inciting, aſſiſting, and inſtructing others, brought many into the love and ſtudy of thoſe Arts, not only in our own, but in ſome other Colledges alſo: which ſome at this time (men far better then my ſelfe in learning, degree, and preferment) will moſt lovingly acknowledge. Ever ſince my departure from the Vniverſity, which is about thirty yeares, I have lived neere to the Towne of Guildford in Surrey: where, whether I have taken ſo much liberty to the l • ſſe of time, and the neglect of my calling, the whole Countrey thereabout, both Gentry and others, to whom I am full well knowne, will quickely informe him; my houſe being not paſt three and twenty miles from London: and yet I ſo hid my ſelfe at home, that I ſeldomly travelled ſo farre as London once in a yeare. Indeed the life and mind of man cannot endure without ſome interchangeableneſſe of recreation, and pawſes from the intenſive actions of our ſeverall callings: and every man is drawne with his owne delight. My recreations have been diverſity of ſtudies: and as oft as I was toyled with the labour of my owne profeſſion, I have allayed that tediouſneſſe by walking in the pleaſant and more then Elyſian fields of the diverſe and various parts of humane learning, and not of the Mathematics onely. In all which knowledges if I have attained to no more ripeneſſe and perfection, then to be reputed, and dared out by Richard Delamain with ſuch contemptuous challenges, as a match ſcarce equall for him, it is ſurely a great meaneneſſe and defect of naturall gifts in mee (wherein I have juſt cauſe to be, and indeed am, humbled) and not altogether ſo much my loſſe of time.

About five yeares ſince, the Earle of Arundell my moſt honourable Lord in a time of his private retiring to his houſe in the countrey, then at Weſt Horſley, foure ſmall miles from me (though ſince he hath a houſe in Aldebury the pariſ • where I live) hearing of me (by what meanes I know not) was pleaſed to ſend for me: and afterward at London to appoint mee a Chamber in his owne houſe: where, at ſuch times, and in ſuch manner as it ſeemed him good to imploy me, and when I might not inconveniently be ſpared from my charge, I have been moſt ready to preſent my ſelfe in all humble and affectionate ſervice: I hope alſo without the offence of God, the tranſgreſſion of the good Lawes of this Land, neglect of my calling, or the deſerved ſcandall of any good man. And R. D. too, (if hee had ſo much grace or wit) may taxe himſelfe of malapert ſawſineſſe to call in queſtion the priviledges and wills of Noblemen, the diſpenſations of the Lawes, and the conſciences of others, by ſuch uncharitable and ſcandalous cenſures. But hee and his like muſt be ſuffered to preſcribe lawes for others, and not ſo much as keepe good manners themſelves.

And although I am no mercenary man, nor make profeſſion to teach any one in theſe arts for gaine and recompence, but as I ſerve at the Altar, ſo I live onely of the Altar: yet in thoſe interims that I am at London in my Lords ſervice, I have been ſtill much freque • ted both by Natives and Strangers, for my reſolution and inſtruction in many difficult poynts of Art; and have moſt freely and lovingly imparted my ſelfe and my skill, ſuch as I had, to their contentments, and much honourable acknowledgement of their obligation to my Lord for bringing mee to London, hath beene teſtifyed by many. Of which my liberallity and unwearyed readineſſe to doe good to all, ſcarce any one can give more ample teſtimony then R D. himſelfe can: would he be but pleaſed to allay the flame of this his hot and eager contention, blowne up onely with the full bellowes of intended glory and gaine; and to ſpeake the truth. Yea neither is hee ſo unkind: but ſome furtherance from mee in triviall matters hee doth and ſhall acknowledge freely. This were an honeſt profeſſion if it were with gratitude, and for love of the truth, and not to aſſert a greater untruth: See his cunning: thus he argues: I had not in the Horizontall Inſtrument the leaſt touch of furtherance from him or any man breathing, either by tranſcript or verball direction: for if I had, it may be preſumed, I ſhould as ingenuouſly have confeſſed it, as I doe freely acknowledge his furtherance in ſome other things. A fine piece of Sophiſtry that Ariſtotle never taught; by confeſſing a truth to aver • e a lye. And marke how caut • lous and ſubterfugious (though he jeſt at the words) his acknowledgement is: other triviall matters. What doe you here acknowledge, when you reſerve power to deny every particular thing? Well, wee will take what you pleaſe to beſtow. they were triviall matters. Such a learned Authour as you are, to be furthered in triviall matters? If you need ſuch furtherance in triviall, we ſhall ſuſpect you in greater. Becauſe you ſcorne to mention ſuch triviall things, I will helpe you out with them: they were the firſt elements of Aſtronomie concerning the ſecond motions of the fixed ſtarres, and of the Sunne and Moone: they were the firſt elements of Conics, to delineate thoſe ſections: they were the firſt elements of Optics, Catoptrics, and Dioptrics: of all which you knew nothing at all. And diverſe things alſo which you profeſſe, whereof you knew very little. I recite not theſe things for exprobration: but that you may a little remember your ſelfe.

I have, I hope, even now cleared my calling, and claime that I may make to theſe arts of Mathematics, ſo far forth as I uſe them I may therefore with better manners aske you, how you obtayned that calling and profeſsion: for you challenge both names to your ſelfe. What Vniverſity, what degree, what court of faculties, what other lawfull way, conferred it upon you? I beleeve you can anſwer me never a word: but will be horribly to ſeeke in your plea. Well, I will ſtand your friend once more, and helpe you out, and derive you a faire title to the inheritance of a vulgar Teacher. When you had learned to reade, you went to the Writing ſchoole: and can in deed if you liſt write a faire hand. Then you learned over your accidence: Afterwards, I heard you ſay, you went into France (it may be to the Iſle Iernſey) where your name got the French garbe: but little or nothing of the tongue brought you home with you. Next you tooke the degree of a Iuſtices Clearke, or a Doctours of Phyſick, or both: to make Warrants or Mittimus, or it may be Recipe's, provided they were not in Latine, or in French. From thence you were advanced to keepe a Writing ſchoole in Drury lane: and ſo had opportunity to heare the Lectures at Greſham Colledge: and to have the benefit of conference with learned men. When you now thought you could cant in the Inſtrumentary idiome, you requeſted Iohn Thomſon the maker of Mathematic Inſtruments in Hoſier lane, to helpe you to ſome Schollers. And is not this a faire pretence to the Mathematics: which you doubt not to call Our noble profeſsion, and our profeſsion of ſo noble a Science?

But leſt I may ſeem to make good that crime of Detraction wherewith he doth charge me, by detracting from him both French and Latine, contrary to the faſhion of his name, and the many ſhreds and thrummes of Latine he doth ſo artificially weave into the web of his Pamphlet, I will without any ſlander tell you a true ſtory. Betweene foure and five yeares agoe, a young Dutch Gentleman whoſe name was Dunheft comming into this Land, ſo journed in a friends houſe of mine in London: and becauſe the Gentleman addicted himſelfe to the warres, hee was deſirous to have the helpe of ſome learned Teacher of the Mathematics. My friend thinking Richard Delamain to be ſuch an one, ſent for him; to whom the Gentleman ſpake (I cannot ſay ſignifyed) his deſire in Latine: but our learned Profeſſor ſtared him in the face as if he wondred, but anſwered him not: which the Gentleman perceiving ſpake in French: but that was more ſtrange: the Gentleman therefore making uſe of ſuch little Engliſh as he had gotten, asked him, cannot you ſpeak Latine? No. Can you not ſpeake French? No. How ſhall I then that underſtand not Engliſh learne of you? And ſo our grand Maſter went away as wiſe as he came without his Scholler. which great misfortune of that poore young man to loſe ſuch learned fundamentall Mathematicall Doctrine may be a faire warning for all Gentlemen ſtrangers to get them an Engliſh tongue in their heads, and that quickly: or elſe they are not like to have their ſight holpen by this our great oculiſt and unvayler of the ſubject Richard Delamain. But here by the way ſome malevolous Detractor may ſpightfully collect, that if our Profeſſors Latine, and French, and Greeke be but meere contrefaict, which yet he doth ſo ventilate for his glory: his Mathematics may well be ſuſpected to be of the ſame ſtuffe.

God knowes how unwillingly and with how grieved a mind I write theſe things, or ſo much as put pen to paper againſt him: But moſt indignous and inſufferable are the abuſes offered by him to me, his ſcandalls, calumniations, bravings, and outfacings, and all mixed with more then Thraſonicall arrogancy, throughout his whole Pamphlet: which that hee may bee ſure to ſcatter every where, he ſendeth up and downe to his acquaintance by halfe doſens: and therewith all a letter, wherein he both requeſteth to have them diſperſed, and nameth to whom: and alſo bitterly inveigheth againſt me, and threatneth me. ſome of which letters have bin ſhewed to me: and it may be I ſhall prevaile to have them produced. Beſides in his daily talke to every man he baſely traduceth me, and gloryeth in reading unto them his Pamphlet, and his letter which he ſent me into the Countrey, marveilouſly pleaſing himſelfe at the ſport he maketh with his ſcoffes and jeſts, acting them with his hands and the geſture of his body, and ſaying here I come over him finely, here I give him a laſh, here I ſcourge him, with other ſuch like contemptuous ſpeeches. And alſo ſendeth to me ſometimes threatning, ſometimes ſcornefull meſſages: challenging, and even daring me to make him an anſwer. What ſhould I, what can I doe in this caſe? If I let him alone in all theſe his deſpightfull and in humane injuries; all men may ſcorne me, and the very boyes in the ſtreet point at me; and he (as hitherto he hath done) by my patience and meekeneſſe grow into a higher degree of pride and inſolencie, and be more obfirmed. I ſpeake unfeignedly, that in my heart I pitty him: and wiſh him not the leaſt hurt: for he needeth it not: but this he needeth, to repent, and be humbled, that he may know himſelfe, and his friends. I could have written much more, and more ſharpely: but leſſe then I have done, and with greater mildneſſe (conſidering the haynouſneſſe of his injuries, not only in print reviling and diſgracing me publikely, but alſo by ſecret ſlanders and malicious clamourings labouring utterly to diſcredite and undoe me) I could not write.

The Inſtruments I doe not value or weigh one ſingle penny. If I had been ambitious of praiſe, or had thought them (or better then they) worthy, at which to have taken my riſe, out of my ſecure and quiet obſcuritie, to mount up into glory, and the knowledge of men: I could have done it many yeares before this pretender knew any thing at all in theſe faculties. And when at William Forſters requeſt I was contented to give way that he might publiſh them, I had not the leaſt thought to be ſeene or acknowleded by them: but only to gratify and doe ſome good to Elias Allen, whom he very ſpitefully, yet more fooliſhly (contrary to the generall repute had of him in this and other lands) termeth an unexpert Workeman. Now judge, I beſeech you, had it not beene extreame ſimpleneſſe in me, to ſtand by, and hold the candle; while a vaineglorious braggard, who had by mine, and Elias Allens meanes gotten the overture of thoſe Inſtruments, ſhould ſo perk up himſelfe in ſtolne feathers, and audaciouſly out face me in mine owne: and make Elias Allen his farmer for my free gift, not to worke, but at his devotion, and for his profit? Might not I then juſtly have beene laughed at, and ſtiled the Bawde and Pandar of the vaine-glory, and ſhamefull lucre of Delamain?

But he pleadeth hard for them, you will ſay: and I have not yet anſwered his allegations. Neither indeed will I at all: there is in them no ſhew of argument; but onely preſumptions, braggings, bravings, outfacings, beggings of credit, ſcoffings at me, and reproachings. Will any Reader but an affectionate one (and affectionate he had need to be and partiall) be perſwaded with ſuch pittifull ſtuffe? Honoured, and moſt worthy Gentlemen, I will lay downe thoſe two Inſtruments, the Horizontall, and the circles of proportion at your feet: and onely in the plaine word of an honeſt Chriſtian man, without any one braving lye, open to you the very truth of both, which I doubt not but you will acknowledge together with me: and when I have ſpoken, if you ſhall be pleaſed to adjudge, and beſtow them upon him; let him take them with all my heart, and make his beſt of them.

Of the Horizontall Inſtrument.

LOng agoe, when I was a young ſtudent of the Mathematicall Sciences, I tryed many wayes and devices to fit my ſelfe with ſome good Diall or Inſtrument portable for my pocket, to finde the houre, and try other concluſions by. and accordingly framed for that my purpoſe both Quadrants, & Rings, and Cylinders, and many other compoſures. Yet not to my full content and ſatisfaction: for either they performed but little, or els were patched up with a diverſity of lines by an unnaturall and forced contexture. At laſt I conſidering that all manner of queſtions concerning the firſt motions were performed moſt properly by the Globe it ſelfe rectifyed to the preſent elevation, by the helpe of a moveable Azumith: I projected the Globe upon the plaine of the Horizon, and applyed to it at the center, which was therein the Zenith, an Index with projected degrees, for the moveable Azumith. in which projection I firſt found what I had before with much ſtudie and paines in vaine ſought for. And becauſe I ſeldomely came to London, where I might have the helpe of large Compaſſes, and other Inſtruments, for drawing the arches of very big circles: I was forced to betake my ſelfe to ſuch ſhift, as Art would afford me: and invented many Theoremes, problemes, and practices (ſuch as no man before, that ever I could find, had delivered) for the finding out of the interſections, and all and every points of all thoſe circles, by which I might draw the ſame, and divide them being drawne. Which rules I have yet in my paper booke, carrying their antiquity in their very ſhew: and are acknowledged by this challenger to have beene ſeene by him. And though I invented them being young, yet they will paſſe the skill of his glorioſity, but even fitly to apply them to uſe, much more to demonſtrate them.

About thirty yeares ſince I preſented one of them drawne with min • owne hand to the truely reverend Prelate Doctour Bylſon Biſhop of Wincheſter, by whom I was made presbyter.

About five and twenty yeares agoe I beſtowed one upon a noble Ladie, the wife of a worthy and learned Knight, then abiding neere the place where I live, but ſince dwelling in Worceſterſhire; which Lady with ingeniouſneſſe and ſolertie more then foeminine tooke delight in the ſpeculation and uſe of the Globe. And for her I writ many notes upon my Inſtrument, the very ſame almoſt word for word, which many yeares after I ſent in a letter to Elias Allen; and are they which Delamain acknowledgeth to have ſeene, but ſlighteth. I remember I did upon that Inſtrument tricke out in colours and mettall, the coate armes of both thoſe families joyned in pale, the draught of which armes I yet have together with thoſe rules. And I doubt not but that noble Lady doth as yet keepe that little Inſtrument; and will be pleaſed for the vindication of my credite to produce the ſame.

In the Spring 1618 I being at London went to ſee my honoured friend Maſter Henry Briggs at Greſham Colledge: who then brought me acquainted with Maſter Gunter lately choſen Aſtronomie reader there, and was at that time in Doctour Brooks his chamber. With whom falling into ſpeech about his quadrant, I ſhewed him my Horizontall Inſtrument: He viewed it very heedfully: and queſtioned about the projecture and uſe thereof, often ſaying theſe words, it is a very good one. And not long after he delivered to Maſter Briggs to be ſent to me mine owne Inſtrument printed off from one cut in braſſe: which afterwards I underſtood he preſented to the right Honourable the Earle of Bridgewater, and in his booke of the Sector printed ſixe yeares after, among other projections ſetteth down this: herein ingenuous that he did not challenge it to himſelfe (as our challenger doth) but not ingenuouſly enough acknowledging from whom he had it. But ſuch is the providence of God, I kept that very letter of Maſter Briggs wherein he ſent me that print from Maſter Gunter, dated from Greſham Colledge 2 Iun. 1618: and the poſtſcript 4 Iune: and which came to my hands Iune 10. In which letter are theſe wordes Maſter Gunter doth here ſend you the print of a Horizontall Diall of his drawing after your Inſtrument. This very letter hath beene left by me in the hands of Elias Allen above theſe two yeares to be ſeene of any one that will require it. Yea and our challenger himſelfe in his Epiſtle to the Reader before his booke of the Horizontall quadrant doth acknowledge the ſight of this letter, and ſetteth downe the very words. Which maketh me wonder at the ſtupidity of his audaciouſneſſe, ſo without all ſhame and ſenſe contradicting himſelfe. Vnleſſe he thinke to have this evaſion, that I deviſed the projection, but knew not the uſe of it when I had done. I preethee R. D. why did I ſhew it to Maſter Gunter then? was it only for the pictures ſake? And what did he like it for? becauſe it was ſo fairely lineated? Or was it not for the excellent and copious uſe it hath above any other Inſtrument of that nature? But heare his plea, or rather his play and jugling with God and man, and his owne conſcience: The extendure of Gods hand in his donations is manifold, and where his ſpirit pleaſeth to breath there is a doore opened: they poſſeſſe the world with a contrary opinion, thereby wronging God in his diſpenſation, and man in his reputation. Gentlemen, doth not your haire ſtand an end with horrour at ſuch prophane hypocriſy? for ſhame repent. but why doe I call for ſhame where is none?

About two yeares after I had ſhewed that my Inſtrument to Maſter Gunter, I beſtowed the very ſame individuall one upon a young Gentleman, now a Baron, my very honourable and moſt intire friend, a man full of vertue, full of learning, full of all goodneſſe, and true nobility, whoſe only defect and fault is an unquenchable thirſt after knowledge and good literature; who hath yet the very ſame in his cuſtody: and is at this preſent in London: whoſe honourable word and teſtimony will confirme that he him ſelfe ſo many yeares agoe knew the uſes of that Inſtrument: and yet our chalenger never unvayled it to him: nor dareth preſcribe for ſo long time.

In Michaelmas Terme 1627 I came to London, and Elias Allen having beene ſworne his Majeſties ſervant, had a purpoſe to preſent his Majeſty with ſome New-yeares gift: and requeſted me to deviſe ſome pretty Inſtrument for him. I anſwered, that I have heard his Majeſty delighted much in the great concave Dyall at White-hall: and what fitter Inſtrument could hee have then my Horizontall, which was the very ſame repreſented in flat? and that I would upon the backeſide ſet the theorics of the Sun and Moone. And ſo by helpe of both ſides Eclipſes might be calculated with great facility. He liked it well. The Horizontall ſide was begunne by my direction. I was not long at home, but Maſter Allen being at a ſtand in his worke, ſent to me for helpe. I writ him a large letter two ſheets of paper long: wherein I taught him the uſes of the Inſtrument eſpecially the Horizontall: and afteward the fabric or delineation of it: and how to find the ſemidiameters and centers of the ſeverall circles both great and leſſer, and the way to divide them. Which letter Maſter Allen yet keepeth: and is the ſame I ſpake of before: and which Delamain confeſſeth he ſaw.

Obſerve here I pray you, the ſubject even by his owne confeſſion was unvayled before he medled with it. And I would to God Maſter Allen had in good time finiſhed up that Inſtrument: I wiſh it for the challengers ſake: it might have ſaved him from a great deale of ſinne and ſhame. But hereby we may diſcover his worthy intentions, whereof he braggeth ſo much: Hee ſeeing Maſter Allen to neglect it, and my ſelfe not to make any great account of it, tooke it up as a wayft or ſtray: and had a purpoſe long agoe to have famouſed himſelfe thereby: firſt calling it the Grammelogia: And then had hee been pittifully to ſeek of a new name for the Circles of Proportion, an Inſtrument not yet in retum natura with him: for now his Greek Nomenclator, and oracle the Schoole-maſter of Saint Clements was defected by death. Yet the name Grammelogia would ſerve as well for the other Inſtrument, as ſoone as he had heard of it, although by a ſpightfull accident he (being not yet aſcended to the height of a profligated ſhamelesneſſe) was hindred in the production of that his firſt plagiarious birth.

For ſome good tract of time after this, when I was now in my Lords ſervice, and Delamain frequented my chamber: One day after he was gone downe: another man came up and told me, that Delamain was in Maſter Allens ſhop ſhowing unto diverſe a little Inſtrument in braſſe of a triangular or rather harpe-like forme, with which he could performe all the queſtions of the Globe for any part of the world, and make Dialls, and deſcribe Countries, and carry Mines under the earth as farre as betweene Temple barre and Weſtminſter, and ſuch like wonders, which I knew impoſſible for and ſuch Inſtrument to performe. I ſaid ſurely he miſtooke: for bu • now he went hence: and had neither then, nor at any other time, ever ſpoken of any ſuch matter: which I was ſure he would have done, had he any ſuch thing in his mind: But he ſtill affirming it I had a great deſire my ſelf to be a witneſſe of that wonder. I came to Elias Allens ſhop; but he was gone. I told Elias Allen what I had heard: and ſaid I would goe to his houſe, and ſee it. I came to his houſe pretending ſome other occaſion. He ſhewed me a great quadrant of Gemma Friſius he had begunne: and after that a quarter of the Analemma: which I viewing told him that the Meridians were falſely drawne. Indeed ſaid he I cannot make them anſwer to any Center. Whereat I ſmiling ſayd, it is no marvell, for they are not arches of Circles: and ſhewed him the reaſon why they could not be. What are they then ſaid he? They are Ellipſes ſaid I. Ellipſes ſaid he, what is that? I told him: and diſcourſed of the kinds of Conic ſections, the firſt newes that ever he had heard of any ſuch thing. Well, at laſt I asked him for the ſtrange Inſtrument he had ſhewed: and would not be anſwered but he muſt needs ſhew it me: which with much tergiverſation he did. Tuſh ſaid I, this is nothing but halfe my Horizontall which he alſo acknowledging: I asked who drew it? my ſelfe ſaid he. Is it poſſible ſaid I that you that cannot make the Analemma, ſhould draw this projection? Doe you know the uſe of it? Yes ſaid he: I have written ſome notes of the uſes of it: and ſhewed me ſome papers: which I looking upon ſaw the very notes I had declared in my letter to Maſter Allen: but here and there the words diſguiſed after his owne apprehenſion. I went homeward: and ſeeing Maſter Allen in his ſhop, ſaid to him, I pray anſwer me a queſtion, but anſwer me truely▪ he perceiving what I meant to aske, prevented me with theſe words, indeed I did: he had the letter of me a whole fortnight, almoſt as ſoone as you ſent it: and I beleeve he writ it out: for the ſummer following, unknowne to me, he got my ſervant to make it for him: for which I was angry. The reſt of this buſineſſe let Maſter Allen himſelfe tell you.

Well: this might have beene all ſpared, you will ſay: the ſight of that letter and of thoſe uſes is confeſſed: but they were ordinary, meane, and triviall: and he ſlighted them. That my very letter is yet extant at Maſter Allens making appearance to anſwer to the diſgracefull taxations of Richard Delamain. In which letter dated December 3. 1627. you ſhall find theſe uſes following.

1 To find the declination of the Sunne every day. 2 To find the courſe of the Sun; or the parallel which the Sun runneth, or deſcribeth every day. 3 To find the riſing of the Sunne, and his ſetting; and the diurnall arch or length of the day, or of the night. 4 To find the diſtance of the Sunnes riſing and ſetting from the Eaſt and Weſt points, Northward in ſummer or Southward in winter, called the Amplitude Ortive. 5 To find the true place of the Sunne on the Inſtrument at any time of the day. 6 To find the houre of the day. 7 To find the Azumith or verticall circle in which the Sunne is: or the Horizontall diſtance of the Sunne from the Meridian. 8 Againe the Azumith of the Sun being given, to find the altitude of the Sunne, and the houre. 9 To find at what houre the Sunne commeth to be full Eaſt or Weſt every day in ſummer 10 To find the height of the Sunne at high noone every day, and likewiſe at every houre. Whereby is made Maſter Gunters Quadrant, and all other Quadrants of that ſort, deſcribed by Gemma Friſius, Munſter, Clavius, and others: alſo all manner of Rings; Cylinders, and innumerable other Topicall Inſtruments, for the finding out of the houre, and other like concluſions. And likewiſe the reaſon of finding out the houre of the day by a mans ſhadow: or by the ſhadow of any gnomon ſet up perpendicular to the Horizon, or elſe parallel to it. 11 To find out the Meridian line, and the points of the Compaſſe without a needle: yea more exactly then with a needle. 12 To find the declination of any wall. 13 To find at what houre the Sunne commeth unto any wall, or window every •• y in the yeare: as alſo when it leaveth it. 14 To find h • w many, and what houre lines are to bee drawne in every plaine Diali. 15 To find how low the Sun is under the Horizon at any houre of the night: and in what point of the Inſtrument the true place of the Sunne then is. 16 To find in which of the twelve houſes the Sunne is at any time of the d • y or night. 17 To find the length of the crepuſculum or twy-light every day. 18 To find out the houre of the night. 19 To find the ſigne and degree in which the Sunne is every day. 20 To find the declination of the Sunne every day.

But I could beſide theſe adde diverſe other operations to be performed by the Inſtrument as now it is: and many others with ſome additions to the Inſtrument: as namely the degree of the Aequinoctiall in the Meridian at any time: and the degree of the Aequinoctiall in the Horizon Eaſt and Weſt: and the degree of the Zodiac in the Meridian called Cor coeli: and the aſcendent degree thereof called the Horoſcope: and concerning the twelve houſes of the heavens for the erecting of a figure: and concerning the ninetyeth degree of the Ecliptic above the Horizon, and the altitude of it. and I know not what elſe, or rather almoſt any thing elſe.

Theſe are the ordinary, meane, and triviall uſes, which I delivered, and are to be ſeene in my letter. And hath Delamain unvayled any I doe not ſay more (for he runneth diviſion) but other uſes then I have done? Yes marry hath he. for in his booke of his Horizontall quadrant, from pag: 44 to 51, you ſhall find theſe uſes.

Eighth-ly, to find the inequallity of time in aequall moneths, or aequall number of dayes. Ninth-ly, to find the degree of the Aequator in the Horizon by ſuppoſing the degree of the Ecliptic in the Horizon. Tenth-ly, to find the degree of the Ecliptic in the Horizon by ſuppoſing the degree of the Aequator in the Horizon. Eleventh-ly. But if the degree of the Ecliptic in the Horizon were required by knowing the degree of the Ecliptic in the Meridian. Twelf-ly, to find the Horoſcope, or the degree aſcendent, or deſc ••• ent and the Nonageſime degree at any houre. Thirteenth-ly, to find what angle the Ecliptic maketh with the Horizon, or the altitude of the Nonageſime degree of the Ecliptic above the Horizon: and what Azumith it is in at any houre.

O Sir (may Richard Delamain ſay) now I have overtopped you: in theſe things you cannot deny, but that I have unvayled the ſubject to helpe your fight. Not ſo neither: for every worke is aſcribed to him that firſt found it out. Nor is the Authour therfore to be accounted ignorant, or to want fight, though ſome other after him ſhall make ſome addition or acceſſe thereto: ſeeing it is an eaſy matter to adde to an invention once diſcovered. But yet let us ſee what learned and rare uſes thoſe are, which you have unvayled.

The eighth is utterly alien from this Inſtrument: and requireth neceſſarily the knowledge of the true, and proper motion of the Sunne, which this Inſtrument giveth not at all: and of the exact right aſcenſion, which this Inſtrument giveth but at large: and ſo is this uſe of no uſe, but a vaine flouriſh.

The ninth is nothing elſe but to find out the Sunnes oblique •• cention.

The tenth, eleventh, twelfth, and thirteenth (which indeed were excellent uſes, if he could ſhew them) are utterly falſe. In all which you have unvayled nothing but your owne want of skill, and moſt groſſe ignorance of the very ground of this projection. And now have you not very fairely h ••• en my ſight, and the ſight of others, to ſee your raſhneſſe and lacke of art? which all your facing (though your face, if it be poſſible, were harder then it is) will never bee able to make good.

Yet for all this (and now I challenge you) let us ſee the performance of theſe queſtions upon the Horizontall Inſtrument, with what reaſonable addition you can, which ſhall not quite alter the nature of it: and I will freely acknowledge you to be a man of art: and not at all impute unto you any plagium, or Mounte-banke tricks.

But ſeeing you have already • nvayled your want of wit, I will take a little paines for you to unvayle your want of honeſty; to helpe the fight of theſe Gentlemen our judges, to ſee what truſt they may repoſe in ſuch an Inſtrument-monger and player of leger-de-la-main, as you are. While hee was printing his tractate of the Horizontall quadrant, although he could not but know that it was injurious to me in reſpect of my free gift to Maſter Allen, and of William Forſter, whoſe tranſlation of my rules was then about to come forth: yet ſuch was my good nature, and his ſhameleſſeneſſe, that every day, as any ſheet was printed, hee ſ •• t, or brought the ſame to mee at my chamber in Arundell horſe to peruſe. which I lovingly and ingenuouſly did, and gave him my judgement of it. When we were come to the ſaid pag: 44, to 51, I gently ſhewed him the falſity of thoſe propoſitions. And he ſaid, o • no • they be wrought then? No, replyed I, not by the Inſtrument as now it is, without ſome addition. I can worke them; but you cannot he asked, why cannot I as well? I anſwered, becauſe you are ignorant of the ground of this Inſtrument and projection. What ſhall I doe then? ſaid hee. you muſt, ſaid I, be content to loſe that •• eet, and new print it: After a little pawſe, he was not aſhamed to reſolve with theſe very words, though your ſight be ſo ſharpe, that you can note theſe faults, yet many hundreds that ſhall ſee the booke will never be able to ſpye them. and withall told me that he had penned that booke in a fortnight with great haſt: I ſaid I did eaſily beleeve as much: for Canis feſtinans caecos parit catulos. This was at that time our communication, and his gallant reſolution. And if this be not jugling, never did any Hocus-pocus jugle. That unleſſe a man were given over to ſhame and ſhameleſneſſe: he would never ſo ſhamefully abuſe his learners, and ſo ſhameleſſely hazard his (I cannot ſay good) name, and reputation. Yet ſticketh he not moſt vainely (that I may ſay no worſe) to conclude his ſaid booke with this braving flouriſh, But if any man deſire to ſay more upon this Horizontall quadrant, then I have done, I have made way for him, and unvayled the ſubject to helpe his ſight.

But he ſaith the projection was none of mine: for Munſter hath it and Blagrave, and ſome others, this latter writ ſome yeares ſince I beganne to uſe this Inſtrument: and that in Munſter is no projection, but a reſemblance of a concave D •• ll: which likeneſſe can no more argue this Inſtrument, then Delamains blacke clothes can prove him to be a ſcholler. And it were a wonder, that ſeeing the writers of theſe Arts doe imagine their Diagrammes upon the plaines of ſeverall Circles, as occaſion requireth: if none ſhould be found that have made their delineations upon the plaine of the Horizon. But of ſuch as ever have uſed the ſame for an Inſtrument, before me, he neither can, nor hath ſhewed any.

Of the Circles of proportion.

FOr theſe I muſt freely confeſſe, I have not ſo good a claime againſt all men, as for my Horizontall Inſtrument: though againſt Richard Delamain I have. The honour of the invention, next to the Lord of Merchiſton, and our Maſter Briggs, belongeth (if I have not been wrongly informed) to Maſter Gunter, who expoſed their numbers upon a ſtreight line. which being once done, was there any ſuch maſterie to bring the ſame line about into a circle? And what doth this new Inſtrument (call it the Circles of proportion, or call it the Ring, or what other name you liſt) ought elſe, but onely bowe and inflect Maſter Gunters line or Ruler.

The manner how I fell upon it, was thus. I have in my ſtudie and practice of the Mathematics been not a little converſant in calculation. And that I might both facilitate the labour, and try the worke: I invented many ſolerties and compendiations in logiſtica, for the one: and framed diverſe kinds of Inſtruments and mechanicall practices, for the other: that when I ſhould find the performance in both wayes not to diſagree, I might be aſſured of my juſt dilligence in numerary computation. Among other Inſtruments I much liked the ſame line or Ruler: onely this defect I found that it required many times too great a paire of Compaſſes, which would bee hard to open, apt to ſlip, and troubleſome for uſe. I therefore firſt deviſed • o have another Ruler with the former: and ſo by ſetting and applying one to the other, I did not onely take away the uſe of Compaſſes, but alſo made the worke much more eaſy and expedite: when I ſhould not at all need the motion of my hand, but onely the glancing of my ſight: and with one poſition of the Rulers, and view of mine eye, ſee not one onely, but the manifold proportions incident unto the queſtion intended. But yet this facility alſo wanted not ſome difficulty, eſpecially in the line of tangents, when one arch was in the former mediety of the quadrant, and the other in the latter: for in this caſe it was needfull that either one Ruler muſt bee as long againe as the other; or elſe that I muſt uſe an inverſion of the Ruler, and regreſſion. By this conſideration I firſt of all ſaw that if thoſe lines upon both Rulers were inflected into two circles, that of the tangents being in both doubled, and that thoſe two Circles ſhould move one upon another; they with a ſmall thread in the center to direct the ſight, would bee ſufficient with incredible and wonderfull facility to worke all queſtions of Trigonometry both rightlined and Sphaericall. And according to this my ſpeculation, above twelve yeares agoe, I with mine owne hand made me two ſuch Circles, which I have uſed ever ſince, as my occaſions required.

In the long vacation 1630 I ſhewed both the Rulers, and the Circle to William Forſter (ſomewhat more praematurely then for the deſire I had to leade him on in the right way of Art, I intended) at my Parſonage houſe, as in his Epiſtle before his Tranſlation hee doth himſelfe teſtify. To whom, exhorting me to publiſh them, I ſaid I would not appeare to the world in ſuch toyes: but if hee would take the paines to tranſlate ſome rules I had written into Engliſh, we would beſtow upon Elias Allen (if he ſhall thinke they may bee beneficiall to him) both thoſe Circles of proportion, and alſo another Inſtrument, conſiſting of two halfe circles moſt plainely and eaſily giving the Proſthaphaereſes of the Plannets according to the Theory of Copernicus (which I have had fairely drawne with mine owne hand above theſe twenty yeares) which might be ſet upon the other ſide of the plate: and would together make up the moſt compleat Inſtrument for all Aſtronomie, that ever yet to my knowledge came forth. And of this intire Inſtrument at my comming up to London in Michaelmas Terme following, to attend my ſervice, I did accordingly make a moſt free donation to Elias Allen by the ingagement of my promiſe. And had alſo performed it long agoe (I doubt not but to your good contentment) had not this Trifler ſo unſeaſonably blurted out his ſcrimble-ſcramble of Grammelogia, like an unlicked Bear-whelp. Wherein under ambiguous words, and large unlimited intentions, and the generall names of Circles, Rings, and Grammelogia or declaration of lines, hee endeavoureth very honeſtly to hooke in within his privilege, and to faſten upon as his owne, whatſoever invention any other Artiſt ſhall in a round or circular forme hereafter produce.

Will you be pleaſed to have an inſtance of this? Shortly after my gift to Elias Allen, I chanced to meet with Richard Delamain in the ſtreet (it was at Allhontide) and as we walked together I told him what an Inſtrument I had given to Maſter Allen, both of the Logarithmes projected into circles, which being leſſe then one foot diameter would performe as much as one of Maſter Gunters Rulers of ſixe feet long: and alſo of the Proſtaphaereſes of the Plannets and ſecond motions. Such an inuention have I ſaid he: for now his intentions (that is his ambition) beganne to worke: but how wiſely you ſhall ſee. He not conſidering the proportion of the circumference to the Diameter, which is more then triple, dreamed that I underſtood a Circle of ſixe feet Diameter, by it to worke the Proſthaphaereſes: as you may ſee in the very end of his tractate of Grammelogia. which ſo monſtrous conceipt never entred into my mind. but this may ſerve as a faire intention to lay claime to my Proſthaphaereticall Inſtrument, if ever it ſhall come forth: whereof hee knoweth no more then the cap upon his head.

But he ſaith, Then after my comming home I ſent him a ſight of my projection drawne in paſt-board. See how notoriouſly he jugleth without an Inſtrument. Then after: how long after? a ſight of my projection: of how much? More then ſeven weekes after on December 23, he ſent to mee the line of numbers onely ſet upon a circle: which I marvell he ſhould be ſo ſimple to boaſt of, ſeeing Ioyners, and Carpenters, and other Mechanics about this towne, and elſewhere, yea and ſchoole-boyes, in imitating Maſter Gunters Ruler incurvated only into a circle, might have, and ſome have drawne, to more good purpoſe then ever yet Delamain did. and ſo much onely he preſented to his Majeſty: but as for Sine or tangent of his, there was not the leaſt ſhew of any. Neither could he give to Maſter Allen any direction for the compoſure of the circles of his Ring, or for the dividing of them: as upon his oath Maſter Allen will teſtify how hee miſled him, and made him labour in vain above three weeks together, untill Maſter Allen himſelfe found out his ignorance and miſtaking, which is more cleare then is poſſible with any impudence to be outfaced. Yea and the concluſion of his tractate of Grammelogia pag: 22 doth plainly enough intimate as much: ſaying, If there be compoſed three rings, &c. So if you move the ſine of 90 degrees unto the Tropicall point, &c. Againe in the Circle of the tangents if you bring, &c. Where you ſhall find his deepe intentions ſet downe in words then which Sphynx it ſelfe never had more implexed: and teacheth nothing, but mocketh his Reader, as I have ſomtimes ſeen a child crying for a wild bird deluded, with bidding him get the bird, and lay ſalt upon the tayle, and ſo he ſhould catch it.

It will not be impertinent, but peradventure much to the purpoſe, that you may rightly know our Challenger, to let you underſtand how he hath dealt with the Ioyner Thomas Browne of whom I ſpake before. Richard Delamain hearing that Brown with his Serpentine had another line by which he could worke to minutes in the 90 degree of fines: uſed a device to get Browne to come and bring his inſtrument to ſome place where he himſelfe ſhould alſo be: there he inſinuateth with Browne pittifully complaining of the wrong Maſter Oughtred had done him, and to make the matter good readeth to him in his Pamphlet, glorying much how he had laſhed me therin: and then gave the booke to Browne: who in thankfulneſſe could not but gratify Delamain with his Lines alſo: and teach him the uſe of them, but eſpecially of the great Line: with this caution on both ſides, that one ſhould not meddle with the others invention. Two dayes after Delamain ſent a Porter to Browne for the booke he had given him, becauſe he had found ſome things to be altered therin, and that he would for it give him a better and more perfect book. Brown refuſing to ſend it by the Porter, the next morning Delamain vouchſafed himſelfe to come to his houſe neare Algate: and asked for the booke, (Browne ſuppoſing he would then have corrected it) but as ſoone as he had got it in his hands he rent out all the middle part with the two great Schemes & put them up in his pocket & went his way, leaving only what he blaterated againſt me: and did not only thus to Browne, but laboureth to recall all the bookes he had given forth, (which were many) before the ſight of Brownes Lines. And ſhortly after this he got a new Printer (who was ignorant of his former Schemes) to print him new: giving him an eſpeciall charge of the outermoſt line newly graven in the Plate, which indeed is Brownes Verg line: and then altering his book and craking of wonders in Proſthaphaereſes, he diſperſeth them by foures and ſixes. But ſee how it pleaſed God (who confoundeth the proud in their owne imaginations) to bring to light Brownes right and Delamains falſity. Browne himſelfe was preſent when the Plate was brought to the Printer, and heard the charge given concerning the new line: and ſince by Brownes friends have beene gotten diverſe of Delamaines former bookes and ſome Schemes of his Inſtruments, in none of all which that great line of Browne is to be found: And yet ſuch is Delamaines and a city (not knowing what can be ſhewn) that he ſtands to it to Browns face, that the ſaid great line was in the ſchemes in his former books. Wherfore we will (without ſtealing) borrow our Authors own words, The window hath bin as yet cloſe, and darkneſſe poſſeſſeth the place, I now withdraw the curtaine that the ſunſhining light may appeare to expell thoſe miſts that have beene ſcattered, and by a true and ſincere medium remove that which by Rich: Delamain hath been falſely ſuggeſted.

Well then, to come at laſt to a concluſion concerning the Inſtrument called the Circles of Proportion, as it is ſet forth, not having, as I have ſaid, the one halfe of my intentions upon it; nor with a ſecond moveable circle and a thread; but with an opening Index at the center (if ſo be that bee cauſe enough to make it to bee not the ſame, but another Inſtrument) for my part I diſclaime it: it may goe ſeeke another Maſter: which for ought I know, will prove to be Elias Allen himſelfe: for at his requeſt only I altered a little my rules from the uſe of the moveable circle and the thread, to the two armes of an Index.

And now moſt noble Gentlemen my Readers and Iudges, I humbly thanke you for the great patience you have ſhewed in hearing me alſo ſpeake for my ſelfe. I doe not requeſt of you any partiall reſpect or favour towards me at all: but onely what your wiſdomes ſhall ſee the ſimple honeſty of my cauſe doth deſerve. And what ſentence ſoever you ſhall be pleaſed to give herein; I will moſt ſubmiſſively, without any farther appeale, reſt in it. Onely I ſhall beſeech you to looke backe and conſider whether R. D. hath any the leaſt colour of ſhew for his ſo vile and baſe behaviour toward me, in ſcoffing, ſlandering, calumniating, back-biting, and exclaiming againſt me: contrary to all rules of charity and Chriſtianity, yea even of humanity and good manners. What wrong can he charge me, or indeed doth he charge me with, for which he may have a ſeeming ground of his ſo great malice? Was it becauſe ſo many yeares before I ever heard of his name, I prevented him in the invention of thoſe Inſtruments? That was the gift of God, and his proſpering my painfull ſtudy. Was it becauſe I have not made them more public all this while? That was my modeſty. Was it becauſe I at laſt produced them to light? Neither was this my doing, but permiſſion only. Was it for not giving way to him, when hee was pleaſed to lay hold upon both, to mount up with the wings of vain-glory by? I withſtood him not, nor once opened my mouth againſt him: but rather furthered him. And if underſtanding men, knowing his in abilities, and ſeeing the folly and ignorance he ſheweth in his Pamphlets, did even cry him downe, and almoſt with one conſent and voice acknowledge the true Authour: I ſought it not. Was it for not hindering William Forſter to publiſh the tranſlation, which with a great deale of labour hee had brought to an end: or not diſavowing it when it was printed? I neither had ſuch power over him: nor any reaſon at all to fruſtrate his long taken paines, for the ambition of another. Was it for making compariſons with him? I made none. Was it for my paines taken with him in teaching and inſtructing ſo ill natur'd a man? My gentleneſſe and good will deſerved better reſpect. Or was it for my ſo long and patient bearing his injurious reproaches, and unmannerly bravings of me? It was my meekneſſe, humility, and good nature. What other cauſe he could have againſt me, in the very ſtricteſt examination of my conſcience, I can find none. But hee had a mind to climbe, and thought my necke might make a fit ſtep for him to get up by. Indeed ſuch is the furious appetite of ſome wicked men, after their ambition and profit, that not the ſacredeſt tyes of Chriſtianity, friendſhip, or benefits received can with-hold them: but they will not ſticke even to cut the throats of their beſt deſerving friends, ſo that they may attaine to their intended purpoſes thereby I pray God ſuch be not his mind. for I heare he affecterh and is ambitious of public action and imployment: and ſomething he thinkes he muſt doe, that he may ſeeme ſomebody, and make himſelfe famous.

Concerning that he hath in the behalfe of vulgar Teachers, and others.

THere is yet a more fearefull Adverſary remayning, at the very thought of whom I am ſtriken with dread & trembling: which is your indignation and diſpleaſure moſt honoured and noble Gentlemen, and you moſt learned and expert Profeſſours of the Mathematicall Sciences: all whom this Challenger, as if his former injuries (moſt undeſerved on my part) were too little, in the higheſt ſtraine of his malice laboureth to exaſperate and incenſe againſt me: that I with words downe-right and pernitious ſhould both glaunce upon many noble Perſonages with too groſſe, if not too baſe an attribute, by • earming them doers of trickes, and as it were to juggle; checking you groſſely, and abbridging you of your liberties: and alſo by vilification ſhould ſtile the Teachers of Mathematics vulgar (common Teachers he would have them called) ranking them with Iuglers, and teachers of trickes. Farre be ſuch unreverent and unmannerly aſperſions againſt you from me, ever to approach neere my thoughts: much more to proceed forth of my mouth.

And I beſeech you obſerve with mee by what degrees his malicious ungratefulneſſe doth aſcend to the height of calumniation: firſt he ſaith, my words, if they be truely ſcanned, rebound to the Nobility and Gentry: then ſhortly after, that they are downe-right in their plaineneſſe. which two accuſations ſeeme to imply a contradiction; if they needed ſcanning, and yet did but rebound even now: how are they ſuddenly become downe-right in their plaineneſſe? And laſtly both openly in his Pamphlet, and in his rayling invectives againſt me in all company where he commeth, yea and (ſuch is his impudence) to my face, that mouth which hath very often implored my helpe, and ſubmiſſively acknowledged my courteſy, that very mouth, I ſay, hath not been aſhamed moſt ſlanderouſly to accuſe and charge me, That in expreſſe words I ſhould call many of the Nobility and Gentry doers of trickes and juglers: which his bold and vile report, no doubt with many that know me not, nor the truth, but have given credite to his audacious aſſerſions, hath bred me much envy and diſcredite. Will it therefore pleaſe ſuch as have been ſo ill perſwaded, to vouchſafe to accept of a true and briefe information: As I did to Delamain and to ſome others, ſo I did to William Forſter: I freely gave him my helpe and inſtruction in theſe faculties: only this was the difference, I had the very firſt moulding (as I may ſay) of this latter: But Delamain was already corrupted with doring upon Inſtruments, and quite loſt from ever being made an Artiſt: I ſuffered not William Forſter for ſome time ſo much as ſpeake of any Inſtrument, except only the Globe it ſelfe; and to explicate, and worke the queſtions of the Sphaere, by the way of the Analemma: which alſo himſelfe did deſcribe for the preſent occaſion. And this my reſtraint from ſuch pleaſing avocations, and holding him to the ſtrictneſſe of precept, brought forth this fruit, that in ſhort time, even by his owne skill, he could not onely uſe any Inſtrument he ſhould ſee, but alſo was able to delineate the like, and deviſe others: yet for all this my ſevere hand I ſaw him obliquely to glaunce his eye upon ſuch Inſtrumentary practices: whereat I being jealous, leſt I ſhould loſe my labour, and he his end, which was Art: I brake out into that admonition which in his Epiſtle Dedicatory to Sir Kenelme Digby he (I thinke in my very formall words) ſetteth downe. That the true way of Art is not by Inſtruments, but by demonſtration: and that it is a prepoſterous courſe of vulgar Teachers, to beginne with Inſtruments, and not with the Sciences, and ſo in ſtead of Artiſts, to make their Schollers onely doers of tricks, and as it were juglers: to the deſpight of Art, loſſe of precious time, and betraying of willing and induſtrious wits, unto ignorance and idleneſſe. That the uſe of Inſtruments is indeed excellent, if a man bee an Artiſt: but contemptible, being ſet and oppoſed to Art. And laſtly, that hee meant to commend to mee the skill of Inſtruments, but firſt he would have me well inſtructed in the Sciences.

Theſe words are to Delamain like a candle unto weake and rheumatic eyes, his purblindneſſe cannot endure the brightneſſe of them, but maketh him ſmart, and pricke, and vexe, and cry out, away with this light it hurteth mine eyes, put it out: and meerely out of the deteſtation of this light, and the diſproportion it hath to his weakeneſſe, thoſe tragicall exclamations, wherewith his unlettered and unmannerly Pamphlet is ſtuffed, have proceeded. Other Teachers of theſe Arts, men of learning and skill, have (many of them) and do daily acknowledge the truth, & ſeaſonableneſſe of this admonition, and are ſorry for the wrong done unto Art it ſelfe under colour of me: Onely one Richard Delamain is found who forgetting truth, gratitude, good manners, and very ſhame, doth bewray his gald back by ſuch impatient winching. Little did I ever ſuſpect when I ſpake theſe words privately at home, they ſhould be ſcanned with ſo uncharitable and malicious a cenſure. Honoured Readers conſider I pray you who it is that doth you wrong, and offereth you this contumely: if it bee I who not ſo much as having the leaſt thought of any of you, privately tutored my learner with a modeſt, gentle, and ſeaſonable advertiſement: or if it be not Richard Delamain himſelfe, that moſt inſolently, to cloke his owne unskilfulneſſe, and miſleading you in Art, and juggling, doth put upon your ingenuities that baſe imputation, as if he had made ſome of you only Doers of tricks upon Inſtruments, and as it were taught you to juggle. What his courſe in teaching is I know not: but what his skill is I doe perfectly know. And concerning my honorable eſtimation of you moſt worthy Gentlemen, I doe unfeignedly glory in the behalfe of this our native Countrey, that no Land under the cope of heaven, is more happy with a gallant, and glorious flower of Gentry, and which is more liberally enriched by nature with ingenuity, and all excellent endowments both of wit, courage, and abilities of mind and body, and hath more propenſe inclinations to all good, then this our ſweeteſt and moſt indulgent mother of Great Britaine bringeth forth: only if we can take care to plant in our minds the good ſeedes of vertue, and knowledge: and not to neglect them to be overgrown (as the beſt ground will) with the weedes of evill and contraryous habits. whereunto on both ſides no one thing conduceth more then the wiſe, or inconſiderate choice of Teachers, and Inſtructers. And then conſider I beſeech you what ſlight account this our glorious Challenger maketh of your worthyeſt endowments; that having ſo long ordered your ſtudies, diſpoſed of your times, and received your money, hath even in his owne conſcience done you ſo little good, that there being but the very name of loſſe of time, jugling, and ignorance, occaſionally mentioned, is himſelf firſt of all ready moſt unmanerly for your ingenuity, yet more unadviſedly for his owne credite, to taxe you therewith, and pinne it upon you. And will you moſt clearely ſee how he ſeeketh not your good, but your intollerable expence, for his ambition and vain-glory, and no good at all of yours? His Ring forſooth muſt be made of Silver and Gold: Braſſe belike is too baſe, or he feareth the waſting of it, leſt there may not be enough left to furniſh his face. And they muſt be of ſixe feete diameter, of which whether the monſtrouſneſſe, unprofitableneſſe, or exceeding charge will be the greater, I cannot readily tell. yet as if this were too little to exhauſt your eſtate, he hath a far more hideous device then all this, that is a Cylinder of metall (Silver ſure it muſt be) three feet diameter, and of height ſufficient to receive 100 or more moveable rings, and as many fixed, having within it ingens, and movements, and I know not what Automata (nor he neither) for the turning of thoſe rings, which by computation of skilfull workemen can hardly be performed for three hundred pounds: And when it is done, and you with a great deale of labour, can tell the uſe of it, you are not any way in Art the wiſer, or better by three ſingle pence: but in farre ſhorter time, and with much leſſe labour, you may be taught with a booke of twelve pence to worke and performe farre more, and more exactly, then by that monſtrous barrell Delamain himſelfe can ever be able to effect. And doe you not now (moſt noble Gentlemen) cry ſhame upon ſuch teachers; ſhame upon ſuch loſſe of time; ſhame upon ſuch profuſion of money; ſhame upon ſuch vile betraying of willing and induſtrious wits unto ignorance and idleneſſe; And many ſhames upon ſuch diſhoneſty, to ſet out in print againſt his owne knowledge, ſo many falſe propoſitions, and precepts purpoſely to abuſe the ignorance of his Readers, and that they may eſteeme him for ſome extraordinary and more then a vulgar Teacher.

Thus have I anſwered to the three parts of his plea: And I ſuppoſe that by this time you wonder as well as my ſelfe, what juſt cauſe there ſhould be of all his clamorous and malevolous inveighings againſt me. But you muſt give him leave to uſe his owne nature and manners. I am not the firſt, that have beene in this petulant manner provoked by him. Who indeed hath eſcaped him? The ſtirring humour of ſome is, that if they thinke they know any thing, they love to make a great noiſe, and raiſe a great duſt, till all become weary of them. Of this condition is our Challenger: whatſoever he hath, he muſt have it with ſuch a breath, that all the world ſhall heare of it, and all that come in his way ſhall ſuffer for it. England is too little, and his mothers tongue too barren (and yet if his mothers tongue were like his, it were copious enough) to yield him names, titles, inſcriptions, and expreſſions. But France, and Greece, and Lat • um muſt be raked and harrowed for him. to ſuch a height of courage and ſpirit ſelfe-admiration hath wrought him. The Aſſe in Aeſop having got on a piece of the Lyons skinne beginneth to ſtrut and ruffle among the Beaſts. I am not only contemned by him (for that mattereth not much) But that incomparable Maſter Henry Briggs the mirrour of our age for excellent skill in Geometry, and therewith for exceeding meekneſſe, was ſo vilifyed and ſlighted by this nifle in a bagge, a little before his death, that the good old man forgetting his owne mild nature, at his laſt departure from London, being on horſe-backe for Oxford, and taking his leave of a friend, ſpake the laſt words, farewell, and tell Delamain from me that he is an abſurd fellow. and that we may not wrong the dead, but give every man his due, we muſt ſuffer him to poſſeſſe the legacie of ſo worthy a friend. Yea and Maſter Gunter too (whom he would ſeeme to admire) eſcapeth him not without a ſhrewd laſh. for in the beginning of his booke of the Horizontall quadrant pag: 3, he braveth him ſaying, this Maſter Gunter delivers ſo OBSTRVSELY in his 66 page of the Sector, that if a man had not more fundamentall Mathematicall doctrine then his booke teacheth, he ſhould never attaine to it. It is well for him Maſter Gunter is not now to give him a ſecond legacie: and to tell him a lyar had need of a good memory. for in that part of his plea which is an anſwer upon his Quadrant towards the end, hee writeth that Ioyners, and Carpenters, and ſchoole-boyes, and ſundry Gentlemen and others, having not had the leaſt aſsiſtance from any, but the direction of Maſter Gunters Booke alone, as upon oath they have been examined, have drawne the projection fully and compleatly. which two places being ſo quite contrary are worth your comparing, that you may know Richard Delamain aright.

Which his uſage of Mr. Briggs and Mr. Gunter excuſeth him the more that he is ſo ſupercilious & ſtrange to others, who are alſo teachers of thoſe Arts, and farre more skilfull then himſelfe: diverſe of whom I have heard complaine and ſtomach at Delamains ſtanding ſo aloof, and keeping them off at ſuch diſtance from him, as not worthy of his noble profeſsion: & vehemently ſuſpect, that beſides his arrogancy, there was alſo a diffidence, and feare, leſt his ignorance might chance to bewray it ſelfe, as doth an Aſſe by his long eares.

I Muſt now borrow a word or twaine with the Gentleman which writ the firſt Verſes in the beginning of this Pamphlet, and ſtileth himſelfe a friend to the Inventer of the Logarithmes projected in circles. Sir I ſee you are not disfavoured of the Muſes and Apollo: your verſe is good, and the conceipt well continued throughout: worthy of a better ſubject: or if you were pleaſed to play and ſhew your skill in ſo poore an argument, you might have ſpared me, who never offended you, and whom peradventure you know not ſo much as by ſight. Did you ever heare me—deny it was found out by you? Did I ever tell you—it was mine owne? would I have profeſſed and owned theſe and ſuch ſlight toyes, I could have done it long before your Inventer had any ab • lity of invention in this way. No I did nothing in publiſhing hereof: I onely gave way and permiſſion. and it was not I that did addict it to my ſelfe: but his knowne worthleſſeneſſe that did abdicate it from him. Neither is your argument of any force:

But if it were not thine, how durſt thou ſay, Thou wouldſt augment the ſame another day?

Why, what can he not ſay? What dareth he not ſay, that may conduce to his vain-glory? And is it conſequent, becauſe he ſaid if the line were de • upled therfore he firſt invented it? If you are as good at the Mathematics, as you are dexterous in making Meter; you cannot be ignorant that the breaking of the Circles one into many is no new invention; but is performed in the Circles of Proportion, as they were ſet out: wherein the Canon of Sines is broken into two circles, and the Canon of Tangents into foure. and I hope by the ſame reaſon I could have broken them, or (if you will ſo call it) augmented or muſriplyed them, into as many circles as I had deſired. But whereas you Poetically jeſt at me,

Tis ten to one this will be challeng'd too,

I thinke you will prove your ſelfe to be a truer vates then you were aware of: though not by me (who have not eſteemed ſuch minutiae worthy of me) but by Thomas Browne the Ioyner, whoſe indeed it is, and not your ſuppoſed Inventers. Sir you will be pleaſed to accept ſome reaſon in plain proſe for your verſe: and underſtand I doe you a favour to acknowledge you ſo farre.

And thus moſt honourable and noble Gentlemen having (as I hope even in your judgements alſo) vindicated my truth and • oneſty from ſuch baſe petti-larcionary, as to ſteale his labours, and pilfer the wares of ſo poore a pack; and cleared my credite from the ſcurrilous and unmannerly calumniations & ſtanders, which he hath ſo unjuſtly endeavoured to faſten upon me: it will be high time to eaſe and free your patience from the trouble of ſuch idle altercations. And I humbly beſeech you, that if any where I ſeeme to take his injuries neerer to heart then in wiſedome I ſhould doe from ſo contemptible an adverſary; not to impute it to paſſion: but curteouſly to conſider the unſufferableneſſe of his moſt unworthy calumniations, and evill uſage of me. It may peradventure be expected that I ſhould alſo reade him a lecture of good manners: But I will not take any more paines in tutoring ſo ungratious a ſcholler. Onely I wiſh him to ſtudy over his own inſtruction. Yet this good advertiſement I will receive from him, that I have worke enough at home: and that my calling inviteth me to ſpend my houres better, then any more to trouble my ſelfe with anſwering him according to his folly.

Dixi. WILLIAM OVGHTRED.