TO THE ENGLISH GENTRY, and all others studious of the MATHEMATICS, which shall be Readers hereof.  
The just Apology of WIL: OUGHTRED, against the slanderous insimulations of RICHARD DELAMAIN, in a Pamphlet called Grammelogia, or the Mathematical Ring, or Mirifica logarithmorum projectio circularis.  
HOnourable, and much honoured Gentlemen, I was of late at my coming up to London, for the performance of mine ordinary service in the house of my most Honourable Lord the Earl of Arundel and Surrey, and Earl Martial of England, by many of my loving friends presented with a most idle and scandalous Pamphlet written against me by Richard Delamaine, who professeth himself a Teacher of the Mathematics 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 engaged 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 Slander and Detraction. I did much wonder at it, to see myself so basely and impudently abused by one whom I never had wronged, but had done very many courtesies for, giving him access to my chamber in Arundel House day by day, teaching and instructing him in that faculty he professeth: not only satisfying his scruples in those things he partly knew: but even laying the very foundation of divers parts, whereof he was utterly ignorant. And I did not so much marvel to see him so bold with me a poor man, but dust and ashes; as I was amazed to see him so fearfully (yet without fear) to play with Almighty God, hypocritically and against his own conscience in things apparently false, invoking and challenging his all-knowing testimony: and in the midst of his most unmannerly railings, in his book; and his slanderous backbiting and depraving me, by audacious intruding himself upon my most honourable favours with false complaints, utterly to overthrow and discredit me; in a personated admonition against such uncharitable calumniations, to pronounce judgement against himself. 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 remaining to my declined years) I met with such a patchery and confusion of disjointed stuff, that I was stricken with a new wonder, that any man should be so simple, as to shame himself to the world with such a hotchpotch.  
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 King's Majesty. 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 plainly 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 divulger, and what not, in six whole leaves, a question about the asses shadow, I should have said, whether the ring, or the Index at the centre, be the better? that word BETTER cruelly wrings him. What, such a comparison of BETTER? such a comparative aspersion of BETTER? Too great, and too lose an aspersion: An unsavoury report indeed: which savours of too high a conceit of the one, and too great a detraction from the other: Endeavouring, what in him lieth, to annihilate and beat down the way, which I writ upon, and to glory in the raising up of his supposed own: thereby not only possessing men with an untruth, but making ME also ignorant in MY choice, 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 world's rumour: which may teach ME and others carefulness 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 mar what others make: such who have stings like Bees, and arrows to shoot: sharpwitted Critics, Diogenes like snarling, who while they will needs have many callings, neglect their own. Good Sir be pacified: who troubleth your patience? I, whom you make your adversary (a better friend than you deserve) never, I assure you, delivered that comparative attribution: I disclaim it utterly: I never made comparisons with you: you must seek 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 go 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 yourself much with a portentous invention of your great Cylinder, for a study (he that will be at the charge (subaudi) were a great fool) of a yard diameter: which brave conceit 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 equal parts. After this, twenty two whole leaves being already past, you begin in pag. 1, with your Pamphlet printed 1630; worthy indeed for the learnedness of it to be enroled 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 look about us: for here is a vast hiatus, a huge Gulf. And upon an instant from pag. 24 we are hurried to pag. 53: Where tenthly we have a third Epistle to the Reader, that promiseth him wonders in Astronomy, Horolography, in plain triangles, applied to dimensions, Navigation, Fortification, etc. marry this etc. 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 pick out of the labours of some other: and then challenge it as coming within your intentions: and thence supply your vacuum.  
After all this he rambleth back again, 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 fairly rolled Sisyphus stone: but to make amends, we have a few scrambling uses in Astronomy, in dialing in plain triangles, from pag. 56 to 67. And then the Flag of encomiastical verses, of p. 24, is again gloriously displayed in pag. 68 Fie upon foolery! Fie upon vainglory! Fie upon such miserable penury of matter! Now make room: Here comes a new projection of circles enlarged, either by a movable and fixed circle, or by a single projection with an Index at the peripheria, or centre: for here is plenty and variety. A wondrous secret it is, that a man may divide either one circle, or else four, or ten circles, or as many as one will, into 1000 equal 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 joiner: yet not one word of Browne: only I am a beam in his eye. And herein lieth a mystery of his skill: He holdeth it no mastery to join forces with a joiner: but by setting on a bold face, if with petulant insolences he shall dare me; he thinketh the attempt will be more glorious. Wherein I thank him for putting a little difference in his estimation for matter of art between me and a joiner. 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 several centres) may to the ignorant (for such they are that Delamaine must persuade) seem to intimate things different in nature: and so make good his claim against Browne. This part he cuts off short in two leaves only; reserving all the rest, that aught to be spoken thereof (which he will find harder than he conceiveth) to his large intentions.  
But now (woe is me therefore) my punishment is at hand. All the rest of this worthy Pamphlet, which is thirteen leaves (except the last page only, which 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 scandal, full of hypocrisy. In pag. 73 I am argued of spreading unsavoury rumours: who (God knows) 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 appear, 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 been abused, as well as himself, with a false rumour raised by some rude & ignorant tongue: by their malicious fantasy: and that he (good soul) did not intent to take this course, but sought peace, and his right by a private and friendly way: but failing 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 vain in his opprobries, I dallied with him: now this so deep taxing me of want of charity, in refusing peace sought, and prosecuting contention and discord, contrary to my Christian duty, pierceth to the quick: 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 slander, and with lies cuttest like a sharp razor! When didst thou ever seek peace of me, and I refused it? when did I not but most mildly and modestly behave myself unto thee? returning thee good words fo● ill: which my Christian humility thou hast, it seemeth in thy price interpreted abjectness, and grown 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 ways hast thou most intolerably provoked me; by railings to my face, and threatening thou wouldst overtop me, by letters into the country; and all to urge me to impatient speeches, that thou mightest get occasion of a suit at law, as thyself acknowledgedst, to have a personal action at the King's bench Bar against me? When I was from London, thou madest enquiry after me and my coming up, in a distempered and threatening manner. When I came to London, thou soughtest me out, and openly in the audience of diverse witnesses reviledst me about my book & instrument called The circles of proportion (which yet I set not out, nor ever sought to make one penny benefit by) while I only stood silent and amazed to see thy audaciousness and desperate conscience: till at last extremely provoked with thy braving reproaches I only said, what strange impudence is this? You know that I know what is in you, and that you have no skill in divers arts, which in your table you profess: or if you have any, you may thank 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 answered, then belike I have all I shall have. And I said, unless you can better deserve it. Afterward when I was in the country above a quarter of a year together, in derision of my calling you sent some Porter dressed up like a wand'ring 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 myself into your calling: and neglecting mine own: and such like peaceable stuff, which letter I would not keep, lest by it I might hereafter be provoked against you: but closing it up again, delivered it to the Porter, willing him to return it back into your hands, and bid you peruse it with a better mind. And when afterward I sent up to you a Canon of sins, tangents, and secants, which I had borrowed, you asked if I had not also sent some scornful answer to your letter. After this (despairing to get any advantage out of my words) you shamelessly exclaimed upon me to my Lord Marshal, and to my Lord of London, and to as many of the Nobility, Gentry, and Clergy, 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 seek 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 devilish intentions and designs, as many as have evil will against the innocent. Thus have you seen in him (honoured Gentlemen) the lively character of a querulous, clamorous, injurious, ill natured man: that like an angry cur can together bite and whine: crying out upon wrong, when he himself is the only wrongdoer.  
But reason is we should hear his plea: in which he still playeth his own part, that is of scurrility, calumniation, outfacing, and hypocrisy. A pitiful case it was indeed that the world should spy out his vanity in assuming to himself the first discovery of the horizontal projection and circles of proportion: It was a malevolous disposition of envious detractours: famousing some, and infaming others: which did not a little disturb the quiet and peace, which formerly he enjoyed: when in his greedy hopes he had swallowed down the golden bait of vainglory, and of a large fee out of every Instrument the workman should sell. But also slacked his intentions: or else there had been yet greater help for such as affect Mathematical (he would have said Manual or Instrumental) practices: Not out of mercenary respect, nor interlaced (O stay there: tell the very plain truth: and say, Not without mercenary respect: interlaced) with delusions & humbast stuff by way of illustration, if not confusion: Had he not been prevented by some others, whose callings might have invited them to spend their hours better: and which have work enough at home: whose ambition to be somebody hath incited him forward to deliver some supposed new stuff, or scrambling pieces, if not confused fragments of his own, or some others to a public view, in obscure and various phrases: a thing supposed to be forged of sundry heads, rather than one alone: seeing there is such roving from the text: only so fare to be trusted, as is agreeable to the text and doctrinal method: amongst whom to blow some smoke thereto, there was some gross 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 shown not to take the crop, but the glean, holding it easier to follow a beaten path, then to hazard a discovery. A blind guide, and a Parats speech are not much different: the one walks he knows not whither, and the other speaks he knoweth not what: and such are all precepts in arts, which lead, and make men speak without demonstration: which do not only protract the studious, and frustrate the affectionate, but maketh an ingenious spirit (who is ever more rational than practical) to contemn such circumlocutions, and laugh in private, if not in public, at the learned style of some Authors making themselves by their obscure kind of writing seemingly famous, stick not to calumniate othe●s to make them infamous: It is an ancient Proverb among us, Good wine needeth no bush: But the wine must not be fast locked 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 public Conduit heard a Tankard-woman in her furious and railing fit; till she hath run herself quite out of breath, and sense. But Richard Delamain, are you so mad upon the frustrated prey of your vainglory and lucre, that neither the sacredness of my function, nor the reverence of mine age, nor my many good deserts, nor my innocence of any ill demerit, 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. Only I will soberly tell you that William Forster, whom you call a Parrot speaking he cannot tell what, is a fare more grounded Artist in all parts of the Mathematics than is R. D: and better knoweth what belongeth to demonstration then R. D. doth: as may soon be tried And as for my Clavis Mathematica, at which you make yourself so merry, though I dote not, as you do, upon mine own (for I suppose you will not lay claim to that too) yet I confess I like it the better, because it pleaseth not your palate, to which nothing can savour, that is learned and analytical: but only the superficial scum and froth of Instrumental tricks 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 smallness? 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 rational Scientiallists, not of ground-creeping Methodicks. He 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 proffered myself gentle and courteous. He that liketh it not, may let it alone. But to him that can rightly use that key, it will unlock the hardest mysteries of those Sciences, and of the writers thereof; as is not unknown to many, who to their great contentment have been and are versed therein.  
My calling ministereth to R. D. a divers and contrary matter, both of mirth and scandal. His mirth I willingly leave unto him, as not unbefitting the rest of his good manners: for hypocrisy and profaneness may well symbolise together. His scandal, being taken at the good gifts of God, cannot also but be 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 Theology, have been also conversant in the study of the Mathematics; most profitably making them to serve and ancillate to their highest contemplations: and they that have wanted such help, have hearty 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 express p●ints of his heavenly & infallible truth, then in these Sciences: in which only the mind and understanding of a man can find secure rest and sure footing; all other knowledges being involved with a thick 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 lazy and drowsy indormition and servile assent to dialectical and conjectural probabilities and spurring it forward, and supplying it with means, 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 than 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 rational man: worthy only of some rude and reasonless dulman.  
But he upbraideth me for taking liberty enough to the less of time: and neglecting my calling. I must confess this scandal cutteth deep: and hath w●th the●, to whom I am not known, wrought me much prejudice and disadvantage in answering whereof I must crave your patience in all humble modesty, to make a brief recital of the course of my poor laborious and painful life.  
Next after E●ton school, I was bred up in Cambridge in King's College: of which society I was a member about eleven or twelve ye●res: wherein how I behaved myself, going hand in hand with the rest of my r●nke in the ordinary Academical studies and exercises, and with what approbation, is well known and remembered by many: the time which over and above those usual studies I employed upon the Mathematical sciences, I redeemed night by night from my natural sleep, defrauding my body, and inuring it to watching, cold, and labour, while most others took 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 Colleges also: which some at this time (men far better than myself in learning, degree, and preferment) will most lovingly acknowledge. Ever since my departure from the University, which is about thirty years, I have lived near to the Town 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 Country thereabout, both Gentry and others, to whom I am full well known, will quickly inform him; my house being not past three and twenty miles from London: and yet I so hid myself at home, that I seldomly traveled so fare as London once in a year. Indeed the life and mind of man cannot endure without some interchangeablenesse of recreation, and pawses from the intensive actions of our several callings: and every man is drawn with his own delight. My recreations have been diversity of studies: and as oft as I was toiled with the labour of my own profession, I have allayed that tediousness by walking in the pleasant and more than Elysian fields of the divers and various parts of humane learning, and not of the Mathematics only. In all which knowledges if I have attained to no more ripeness and perfection, then to be reputed, and dared out by Richard Delamain with such contemptuous challenges, as a match scarce equal for him, it is surely a great meanness and defect of natural gifts in me (wherein I have just cause to be, and indeed am, humbled) and not altogether so much my loss of time.  
About five years since, the Earl of Arundel my most honourable Lord in a time of his private retiring to his house in the country, then at West Horsley, four small miles from me (though since he hath a house in Aldebury the paris● where I live) hearing of me (by what means I know not) was pleased to send for me: and afterward at London to appoint me a Chamber in his own house: where, at such times, and in such manner as it seemed him good to employ me, and when I might not inconveniently be spared from my charge, I have been most ready to present myself in all humble and affectionate service: I hope also without the offence of God, the transgression of the good Laws of this Land, neglect of my calling, or the deserved scandal of any good man. And R. D. too, (if he had so much grace or wit) may tax himself of malapert sauciness to call in question the privileges and wills of Noblemen, the dispensations of the Laws, and the consciences of others, by such uncharitable and scandalous censures. But he and his like must be suffered to prescribe laws for others, and not so much as keep good manners themselves.  
And although I am no mercenary man, nor make profession to teach any one in these arts for gain and recompense, but as I serve at the Altar, so I live only of the Altar: yet in those interims that I am at London in my Lord's service, I have been still much frequented both by Natives and Strangers, for my resolution and instruction in many difficult points of Art; and have most freely and lovingly imparted myself and my skill, such as I had, to their contentments, and much honourable acknowledgement of their obligation to my Lord for bringing me to London, hath been testified by many. Of which my liberality and unwearyed readiness to do good to all, scarce any one can give more ample testimony than R D. himself can: would he be but pleased to allay the flame of this his hot and eager contention, blown up only with the full bellowes of intended glory and gain; and to speak the truth. Yea neither is he so unkind: but some furtherance from me in trivial matters he 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 horizontal Instrument the least touch of furtherance from him or any man breathing, either by transcript or verbal direction: for if I had, it may be presumed, I should as ingenuously have confessed it, as I do 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 lie. And mark how caut●lous and subterfugious (though he jest at the words) his acknowledgement is: other trivial matters. What do you here acknowledge, when you reserve power to deny every particular thing? Well, we will take what you please to bestow. they were trivial matters. Such a learned Author as you are, to be furthered in trivial matters? If you need such furtherance in trivial, we shall suspect you in greater. Because you scorn to mention such trivial things, I will help you out with them: they were the first elements of Astronomy concerning the second motions of the fixed stars, and of the Sun and Moon: 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 divers things also which you profess, whereof you knew very little. I recite not these things for exprobration: but that you may a little remember yourself.  
I have, I hope, even now cleared my calling, and claim that I may make to these arts of Mathematics, so far forth as I use them I may therefore with better manners ask you, how you obtained that calling and profession: for you challenge both names to yourself. What University, what degree, what court of faculties, what other lawful way, conferred it upon you? I believe you can answer me never a word: but will be horribly to seek in your plea. Well, I will stand your friend once more, and help you out, and derive you a fair title to the inheritance of a vulgar Teacher. When you had learned to read, you went to the Writing school: and can in deed if you list write a fair hand. Then you learned over your accidence: Afterwards, I heard you say, you went into France (it may be to the Isle jernsey) where your name got the French garb: but little or nothing of the tongue brought you home with you. Next you took the degree of a justice's Clerk, or a Doctors of Physic, or both: to make Warrants or Mittimus, or it may be Recipes, provided they were not in Latin, or in French. From thence you were advanced to keep a Writing school in Drury lane: and so had opportunity to hear the Lectures at Gresham College: and to have the benefit of conference with learned men. When you now thought you could cant in the Instrumentary idiom, you requested john Thomson the maker of Mathematic Instruments in Hosier lane, to help you to some Scholars. And is not this a fair 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 Latin, contrary to the fashion of his name, and the many shreds and thrums of Latin he doth so artificially wove into the web of his Pamphlet, I will without any slander tell you a true story. Between four and five years ago, a young Dutch Gentleman whose name was Dunheft coming into this Land, so journed in a friend's house of mine in London: and because the Gentleman addicted himself to the wars, he was desirous to have the help of some learned Teacher of the Mathematics. My friend thinking Richard Delamain to be such an one, sent for him; to whom the Gentleman spoke (I cannot say signified) his desire in Latin: but our learned Professor stared him in the face as if he wondered, but answered him not: which the Gentleman perceiving spoke 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 Latin? No. Can you not speak French? No. How shall I then that understand not English learn of you? And so our grand Master went away as wise as he came without his Scholar. which great misfortune of that poor young man to lose such learned fundamental Mathematical Doctrine may be a fair 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 helped by this our great oculist and unvayler of the subject Richard Delamain. But here by the way some malevolous Detractor may spitefully collect, that if our Professors Latin, and French, and Greek be but mere contrefaict, which yet he doth so ventilate for his glory: his Mathematics may well be suspected to be of the same stuff.  
God knows how unwillingly and with how grieved a mind I writ 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 scandals, calumniations, brave, and outfacing, and all mixed with more than Thrasonical arrogancy, throughout his whole Pamphlet: which that he may be sure to scatter every where, he sendeth up and down to his acquaintance by half 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 been showed to me: and it may be I shall prevail to have them produced. Besides in his daily talk to every man he basely traduceth me, and glorieth in reading unto them his Pamphlet, and his letter which he sent me into the Country, marveilously pleasing himself at the sport he maketh with his scoffs 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 threatening, sometimes scornful messages: challenging, and even daring me to make him an answer. What should I, what can I do in this case? If I let him alone in all these his despiteful and in humane injuries; all men may scorn me, and the very boys in the street point at me; and he (as hitherto he hath done) by my patience and meekness grow into a higher degree of pride and insolency, and be more obfirmed. I speak unfeignedly, that in my heart I pity 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 himself, and his friends. I could have written much more, and more sharply: but less than I have done, and with greater mildness (considering the heinousness of his injuries, not only in print reviling and disgracing me publicly, but also by secret slanders and malicious clamouring labouring utterly to discredit and undo me) I could not write.  
The Instruments I do 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 obscurity, to mount up into glory, and the knowledge of men: I could have done it many years before this pretender knew any thing at all in these faculties. And when at William forster's request I was contented to give way that he might publish them, I had not the least thought to be seen or acknowledged by them: but only to gratify and do some good to Elias Allen, whom he very spitefully, yet more foolishly (contrary to the general repute had of him in this and other lands) termeth an unexpert Workman. Now judge, I beseech you, had it not been extreme simpleness in me, to stand by, and hold the candle; while a vainglorious braggart, who had by mine, and Elias Allens means gotten the overture of those Instruments, should so perk up himself in stolen feathers, and audaciously out face me in mine own: and make Elias Allen his farmer for my free gift, not to work, but at his devotion, and for his profit? Might not I then justly have been laughed at, and styled the Bawd and Pander of the vainglory, and shameful 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 show of argument; but only presumptions, braggings, brave, outfacing, beggings of credit, scoffings at me, and reproachings. Will any Reader but an affectionate one (and affectionate he had need to be and partial) be persuaded with such pitiful stuff? Honoured, and most worthy Gentlemen, I will lay down those two Instruments, the horizontal, and the circles of proportion at your feet: and only in the plain word of an honest Christian man, without any one braving lie, 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 horizontal Instrument.  
LOng ago, when I was a young student of the Mathematical Sciences, I tried many ways and devices to fit myself with some good Dial or Instrument portable for my pocket, to find the hour, 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 else were patched up with a diversity of lines by an unnatural and forced contexture. At last I considering that all manner of questions concerning the first motions were performed most properly by the Globe itself rectified to the present elevation, by the help of a movable Azumith: I projected the Globe upon the plain of the Horizon, and applied to it at the centre, which was therein the Zenith, an Index with projected degrees, for the movable Azumith. in which projection I first found what I had before with much study and pains in vain sought for. And because I seldomely came to London, where I might have the help of large Compasses, and other Instruments, for drawing the arches of very big circles: I was forced to betake myself to such shift, as Art would afford me: and invented many Theorems, problems, 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 drawn. Which rules I have yet in my paper book, carrying their antiquity in their very show: and are acknowledged by this challenger to have been seen by him. And though I invented them being young, yet they will pass the skill of his gloriosity, but even fitly to apply them to use, much more to demonstrate them.  
About thirty years since I presented one of them drawn with min● own hand to the truly reverend Prelate Doctor Bylson Bishop of Winchester, by whom I was made presbyter.  
About five and twenty years ago I bestowed one upon a noble Lady, the wife of a worthy and learned Knight, then abiding near the place where I live, but since dwelling in Worcestershire; which Lady with ingeniousness and solertie more than feminine took 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 years after I sent in a letter to Elias Allen; and are they which Delamain acknowledgeth to have seen, but slighteth. I remember I did upon that Instrument trick out in colours and mettle, the coat arms of both those families joined in pale, the draught of which arms I yet have together with those rules. And I doubt not but that noble Lady doth as yet keep that little Instrument; and will be pleased for the vindication of my credit to produce the same.  
In the Spring 1618. I being at London went to see my honoured friend Master Henry Briggs at Gresham College: who then brought me acquainted with Master Gunter lately chosen Astronomy reader there, and was at that time in Doctor Brooks his chamber. With whom falling into speech about his quadrant, I shown him my horizontal 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 own Instrument printed off from one cut in brass: which afterwards I understood he presented to the right Honourable the Earl of Bridgewater, and in his book of the Sector printed six years after, among other projections setteth down this: herein ingenuous that he did not challenge it to himself (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 College 2 jun. 1618.: and the postscript 4 june: and which came to my hands june 10. In which letter are these words Master Gunter doth here send you the print of a horizontal Dial of his drawing after your Instrument. This very letter hath been left by me in the hands of Elias Allen above these two years to be seen of any one that will require it. Yea and our challenger himself in his Epistle to the Reader before his book of the horizontal quadrant doth acknowledge the sight of this letter, and setteth down the very words. Which maketh me wonder at the stupidity of his audaciousness, so without all shame and sense contradicting himself. Unless he think to have this evasion, that I devised the projection, but knew not the use of it when I had done. I prithee R. D. why did I show it to Master Gunter then? was it only for the pictures sake? And what did he like it for? because it was so fairly lineated? Or was it not for the excellent and copious use it hath above any other Instrument of that nature? But hear his plea, or rather his play and juggling with God and man, and his own conscience: The extendure of God's hand in his donations is manifold, and where his spirit pleaseth to breathe there is a door opened: they possess the world with a contrary opinion, thereby wronging God in his dispensation, and man in his reputation. Gentlemen, doth not your hair stand an end with horror at such profane hypocrisy? for shame repent. but why do I call for shame where is none?  
About two years after I had showed that my Instrument to Master Gunter, I bestowed the very same individual one upon a young Gentleman, now a Baron, my very honourable and most entire friend, a man full of virtue, full of learning, full of all goodness, 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 confirm that he himself so many years ago knew the uses of that Instrument: and yet our challenger never unvayled it to him: nor dareth prescribe for so long time.  
In Michaelmas Term 1627. I came to London, and Elias Allen having been sworn his Majesty's servant, had a purpose to present his Majesty with some New-year's 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 Dial at Whitehall: and what fit Instrument could he have then my horizontal, which was the very same represented in flat? and that I would upon the backside set the theorics of the Sun and Moon. And so by help of both sides Eclipses might be calculated with great facility. He liked it well. The horizontal side was begun by my direction. I was not long at home, but Master Allen being at a stand in his work, sent to me for help. I writ him a large letter two sheets of paper long: wherein I taught him the uses of the Instrument especially the horizontal: and afteward the fabric or delineation of it: and how to find the semidiameters and centres of the several circles both great and lesser, and the way to divide them. Which letter Master Allen yet keepeth: and is the same I spoke of before: and which Delamain confesseth he saw.  
Observe here I pray you, the subject even by his own confession was unveiled before he meddled 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 deal of sin and shame. But hereby we may discover his worthy intentions, whereof he braggeth so much: He seeing Master Allen to neglect it, and myself not to make any great account of it, took it up as a wayft or stray: and had a purpose long ago to have famoused himself thereby: first calling it the Grammelogia: And then had he been pitifully 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 Schoolmaster of Saint Clements was defected by death. Yet the name Grammelogia would serve as well for the other Instrument, as soon as he had heard of it, although by a spiteful accident he (being not yet ascended to the height of a profligated shamelessness) was hindered in the production of that his first plagiarious birth.  
For some good tract of time after this, when I was now in my Lord's service, and Delamain frequented my chamber: One day after he was gone down: another man came up and told me, that Delamain was in Master Allens shop showing unto divers a little Instrument in brass of a triangular or rather harpe-like form, with which he could perform all the questions of the Globe for any part of the world, and make dials, and describe Countries, and carry Mines under the earth as fare as between Temple bar and Westminster, and such like wonders, which I knew impossible for and such Instrument to perform. I said surely he mistook: 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 myself to be a witness 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 go to his house, and see it. I came to his house pretending some other occasion. He shown me a great quadrant of Gemma Frisius he had begun: and after that a quarter of the Analemma: which I viewing told him that the Meridian's were falsely drawn. Indeed said he I cannot make them answer to any Centre. Whereat I smiling said, it is no marvel, for they are not arches of Circles: and shown 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 news that ever he had heard of any such thing. Well, at last I asked him for the strange Instrument he had showed: and would not be answered but he must needs show it me: which with much tergiversation he did. Tush said I, this is nothing but half my horizontal which he also acknowledging: I asked who drew it? myself said he. Is it possible said I that you that cannot make the Analemma, should draw this projection? Do you know the use of it? Yes said he: I have written some notes of the uses of it: and shown 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 own apprehension. I went homeward: and seeing Master Allen in his shop, said to him, I pray answer me a question, but answer me truly▪ he perceiving what I meant to ask, prevented me with these words, indeed I did: he had the letter of me a whole fortnight, almost as soon as you sent it: and I believe he writ it out: for the summer following, unknown to me, he got my servant to make it for him: for which I was angry. The rest of this business let Master Allen himself tell you.  
Well: this might have been all spared, you will say: the sight of that letter and of those uses is confessed: but they were ordinary, mean, and trivial: and he slighted them. That my very letter is yet extant at Master Allens making appearance to answer to the disgraceful taxations of Richard Delamain. In which letter dated December 3. 1627. you shall find these uses following.  

1 To find the declination of the Sun 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 Sun, and his setting; and the diurnal arch or length of the day, or of the night.  
4 To find the distance of the Sun's 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 Sun on the Instrument at any time of the day.  
6 To find the hour of the day.  
7 To find the Azumith or vertical circle in which the Sun is: or the horizontal distance of the Sun from the Meridian.  
8 Again the Azumith of the Sun being given, to find the altitude of the Sun, and the hour.  
9 To find at what hour the Sun cometh to be full East or West every day in summer  
10 To find the height of the Sun at high noon every day, and likewise at every hour. Whereby is made Master Gunter's 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 Topical Instruments, for the finding out of the hour, and other like conclusions. And likewise the reason of finding out the hour of the day by a man's 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 Compass without a needle: yea more exactly then with a needle.  
12 To find the declination of any wall.  
13 To find at what hour the Sun cometh unto any wall, or window every ●●y in the year: as also when it leaveth it.  
14 To find h●w many, and what hour lines are to be drawn in every plain Diali.  
15 To find how low the Sun is under the Horizon at any hour of the night: and in what point of the Instrument the true place of the Sun than is.  
16 To find in which of the twelve houses the Sun is at any time of the d●y or night.  
17 To find the length of the crepusculum or twilight every day.  
18 To find out the hour of the night.  
19 To find the sign and degree in which the Sun is every day.  
20 To find the declination of the Sun every day.   
But I could beside these add divers 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 Equinoctial in the Meridian at any time: and the degree of the Equinoctial 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, mean, and trivial uses, which I delivered, and are to be seen in my letter. And hath Delamain unveiled any I do not say more (for he runneth division) but other uses than I have done? Yes marry hath he. for in his book of his horizontal quadrant, from pag. 44 to 51, you shall find these uses.  

Eighth-ly, to find the inequality of time in equal months, or equal number of days.  
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. 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 hour.  
Thirteenthly, 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 hour.   
O Sir (may Richard Delamain say) now I have overtopped you: in these things you cannot deny, but that I have unveiled the subject to help your fight. Not so neither: for every work is ascribed to him that first found it out. Nor is the Author therefore to be accounted ignorant, or to want fight, though some other after him shall make some addition or access thereto: seeing it is an easy matter to add to an invention once discovered. But yet let us see what learned and rare uses those are, which you have unveiled.  
The eighth is utterly alien from this Instrument: and requireth necessarily the knowledge of the true, and proper motion of the Sun, 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 vain flourish.  
The ninth is nothing else but to find out the Sun's obliqne ascension.  
The tenth, eleventh, twelfth, and thirteenth (which indeed were excellent uses, if he could show them) are utterly false. In all which you have unveiled nothing but your own want of skill, and most gross ignorance of the very ground of this projection. And now have you not very fairly h●●●en my sight, and the sight of others, to see your rashness and lack of art? which all your facing (though your face, if it be possible, were harder than it is) will never be able to make good.  
Yet for all this (and now I challenge you) let us see the performance of these questions upon the horizontal 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 Mountebank tricks.  
But seeing you have already ●nvayled your want of wit, I will take a little pains for you to unvayle your want of honesty; to help 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 he was printing his tractate of the horizontal 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 shamelesseness, that every day, as any sheet was printed, he s●●t, or brought the same to me at my chamber in Arundel 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 shown him the falsity of those propositions. And he said, o● no● they be wrought then? No, replied I, not by the Instrument as now it is, without some addition. I can work 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 do then? said he. you must, said I, be content to lose that ●●eet, and new print it: After a little pause, he was not ashamed to resolve with these very words, though your sight be so sharp, that you can note these faults, yet many hundreds that shall see the book will never be able to spy them. and withal told me that he had penned that book in a fortnight with great haste: I said I did easily believe as much: for Canis festinans caecos parit catulos. This was at that time our communication, and his gallant resolution. And if this be not juggling, never did any Hocuspocus jugle. That unless a man were given over to shame and shamelessness: he would never so shamefully abuse his learners, and so shamelessly hazard his (I cannot say good) name, and reputation. Yet sticketh he not most vainly (that I may say no worse) to conclude his said book with this braving flourish, But if any man desire to say more upon this horizontal quadrant, than I have done, I have made way for him, and unvayled the subject to help his sight.  
But he saith the projection was none of mine: for Munster hath it and Blagrave, and some others, this latter writ some years since I began to use this Instrument: and that in Munster is no projection, but a resemblance of a concave D●●ll: which likeness can no more argue this Instrument, then Delamains black clothes can prove him to be a scholar. And it were a wonder, that seeing the writers of these Arts do imagine their Diagrams upon the plains of several Circles, as occasion requireth: if none should be found that have made their delineations upon the plain of the Horizon. But of such as ever have used the same for an Instrument, before me, he neither can, nor hath showed any.   

Of the Circles of proportion.  
FOr these I must freely confess, I have not so good a claim against all men, as for my horizontal 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 straight line. which being once done, was there any such mastery 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 only bow and inflect Master Gunter's line or Ruler.  
The manner how I fell upon it, was thus. I have in my study and practice of the Mathematics been not a little conversant in calculation. And that I might both facilitate the labour, and try the work: I invented many solerties and compendiations in logistica, for the one: and framed divers kinds of Instruments and mechanical practices, for the other: that when I should find the performance in both ways not to disagree, I might be assured of my just diligence in numerary computation. Among other Instruments I much liked the same line or Ruler: only this defect I found that it required many times too great a pair of Compasses, which would be 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 only take away the use of Compasses, but also made the work much more easy and expedite: when I should not at all need the motion of my hand, but only the glancing of my sight: and with one position of the Rulers, and view of mine eye, see not one only, 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 needful that either one Ruler must be as long again 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 centre to direct the sight, would be sufficient with incredible and wonderful facility to work all questions of Trigonometry both rightlined and Spherical. And according to this my speculation, above twelve years ago, I with mine own hand made me two such Circles, which I have used ever since, as my occasions required.  
In the long vacation 1630 I shown both the Rulers, and the Circle to William Forster (somewhat more praematurely then for the desire I had to lead him on in the right way of Art, I intended) at my Parsonage house, as in his Epistle before his Translation he doth himself testify. To whom, exhorting me to publish them, I said I would not appear to the world in such toys: but if he would take the pains to translate some rules I had written into English, we would bestow upon Elias Allen (if he shall think they may be beneficial to him) both those Circles of proportion, and also another Instrument, consisting of two half circles most plainly and easily giving the Prosthaphaereses of the Planets according to the Theory of Copernicus (which I have had fairly drawn with mine own hand above these twenty years) which might be set upon the other side of the plate: and would together make up the most complete Instrument for all Astronomy, that ever yet to my knowledge came forth. And of this entire Instrument at my coming up to London in Michaelmas Term following, to attend my service, I did accordingly make a most free donation to Elias Allen by the engagement of my promise. And had also performed it long ago (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 general names of Circles, Rings, and Grammelogia or declaration of lines, he endeavoureth very honestly to hook in within his privilege, and to fasten upon as his own, whatsoever invention any other Artist shall in a round or circular form 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 less than one foot diameter would perform as much as one of Master Gunter's Rulers of six feet long: and also of the Prostaphaereses of the Planets and second motions. Such an invention have I said he: for now his intentions (that is his ambition) began to work: but how wisely you shall see. He not considering the proportion of the circumference to the Diameter, which is more than triple, dreamt that I understood a Circle of six feet Diameter, by it to work the Prosthaphaereses: as you may see in the very end of his tractate of Grammelogia. which so monstrous conceit never entered into my mind. but this may serve as a fair intention to lay claim to my Prosthaphaereticall Instrument, if ever it shall come forth: whereof he knoweth no more than the cap upon his head.  
But he saith, Then after my coming home I sent him a sight of my projection drawn in pasteboard. See how notoriously he jugleth without an Instrument. Then after: how long after? a sight of my projection: of how much? More than seven weeks after on December 23, he sent to me the line of numbers only set upon a circle: which I marvel he should be so simple to boast of, seeing joiners, and Carpenters, and other Mechanics about this town, and elsewhere, yea and schoolboys, in imitating Master Gunter's Ruler incurvated only into a circle, might have, and some have drawn, to more good purpose then ever yet Delamain did. and so much only he presented to his Majesty: but as for Sine or tangent of his, there was not the least show 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 he misled him, and made him labour in vain above three weeks together, until Master Allen himself found out his ignorance and mistaking, which is more clear than 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, etc. So if you move the sine of 90 degrees unto the Tropical point, etc. Again in the Circle of the tangents if you bring, etc. Where you shall find his deep intentions set down in words than which Sphynx itself never had more implexed: and teacheth nothing, but mocketh his Reader, as I have sometimes seen a child crying for a wild bird deluded, with bidding him get the bird, and lay salt upon the tail, 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 joiner Thomas Browne of whom I spoke before. Richard Delamain hearing that Brown with his Serpentine had another line by which he could work to minutes in the 90 degree of fines: used a device to get Brown to come and bring his instrument to some place where he himself should also be: there he insinuateth with Browne pitifully 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 therein: and then gave the book to Browne: who in thankfulness 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 days after Delamain sent a Porter to Browne for the book he had given him, because he had found some things to be altered therein, 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 himself to come to his house near Algate: and asked for the book, (Browne supposing he would then have corrected it) but as soon as he had got it in his hands he rend 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 books 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 especial 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 six. But see how it pleased God (who confoundeth the proud in their own imaginations) to bring to light Brownes right and Delamains falsity. Browne himself 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 been gotten divers of Delamaines former books 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 shown) that he stands to it to Brown's face, that the said great line was in the schemes in his former books. Wherefore we will (without stealing) borrow our Authors own words, The window hath been as yet close, and darkness possesseth the place, I now withdraw the curtain that the sunshining light may appear to expel those mists that have been 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 half of my intentions upon it; nor with a second movable circle and a thread; but with an opening Index at the centre (if so be that be cause enough to make it to be not the same, but another Instrument) for my part I disclaim it: it may go seek another Master: which for aught I know, will prove to be Elias Allen himself: for at his request only I altered a little my rules from the use of the movable circle and the thread, to the two arms of an Index.  
And now most noble Gentlemen my Readers and judges, I humbly thank you for the great patience you have showed in hearing me also speak for myself. I do not request of you any partial respect or favour towards me at all: but only what your wisdoms 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 appeal, rest in it. Only I shall beseech you to look back and consider whether R. D. hath any the least colour of show for his so vile and base behaviour toward me, in scoffing, slandering, calumniating, backbiting, 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 years 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 painful 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 he was pleased to lay hold upon both, to mount up with the wings of vainglory 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 showeth in his Pamphlets, did even cry him down, and almost with one consent and voice acknowledge the true Author: I sought it not. Was it for not hindering William Forster to publish the translation, which with a great deal of labour he 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 pains, for the ambition of another. Was it for making comparisons with him? I made none. Was it for my pains taken with him in teaching and instructing so ill natured a man? My gentleness and good will deserved better respect. Or was it for my so long and patiented bearing his injurious reproaches, and unmannerly brave of me? It was my meekness, 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 he had a mind to climb, and thought my neck 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 ties of Christianity, friendship, or benefits received can withhold them: but they will not stick even to cut the throats of their best deserving friends, so that they may attain to their intended purposes thereby I pray God such be not his mind. for I hear he affecterh and is ambitious of public action and employment: and something he thinks he must do, that he may seem somebody, and make himself famous.   

Concerning that he hath in the behalf of vulgar Teachers, and others.  
THere is yet a more fearful Adversary remaining, at the very thought of whom I am stricken with dread & trembling: which is your indignation and displeasure most honoured and noble Gentlemen, and you most learned and expert Professors of the Mathematical Sciences: all whom this Challenger, as if his former injuries (most undeserved on my part) were too little, in the highest strain of his malice laboureth to exasperate and incense against me: that I with words downright and pernicious should both glance upon many noble Personages with too gross, if not too base an attribute, by terming them doers of tricks, and as it were to juggle; checking you grossly, and abbridging you of your liberties: and also by vilification should style the Teachers of Mathematics vulgar (common Teachers he would have them called) ranking them with jugglers, and teachers of tricks. Fare be such unreverent and unmannerly aspersions against you from me, ever to approach near my thoughts: much more to proceed forth of my mouth.  
And I beseech you observe with me by what degrees his malicious ungratefulness doth ascend to the height of calumniation: first he saith, my words, if they be truly scanned, rebound to the Nobility and Gentry: then shortly after, that they are downright in their plainness. which two accusations seem to imply a contradiction; if they needed scanning, and yet did but rebound even now: how are they suddenly become downright in their plainness? And lastly both openly in his Pamphlet, and in his railing invectives against me in all company where he cometh, yea and (such is his impudence) to my face, that mouth which hath very often implored my help, and submissively acknowledged my courtesy, that very mouth, I say, hath not been ashamed most slanderously to accuse and charge me, That in express words I should call many of the Nobility and Gentry doers of tricks and jugglers: which his bold and vile report, no doubt with many that know me not, nor the truth, but have given credit to his audacious assersions, hath bred me much envy and discredit. Will it therefore please such as have been so ill persuaded, to vouchsafe to accept of a true and brief information: As I did to Delamain and to some others, so I did to William Forster: I freely gave him my help 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 speak of any Instrument, except only the Globe itself; and to explicate, and work the questions of the Sphere, by the way of the Analemma: which also himself did describe for the present occasion. And this my restraint from such pleasing avocations, and holding him to the strictness of precept, brought forth this fruit, that in short time, even by his own skill, he could not only 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 glance his eye upon such Instrumentary practices: whereat I being jealous, lest I should lose my labour, and he his end, which was Art: I broke out into that admonition which in his Epistle Dedicatory to Sir Kenelm Digby he (I think in my very formal words) setteth down. That the true way of Art is not by Instruments, but by demonstration: and that it is a preposterous course of vulgar Teachers, to begin with Instruments, and not with the Sciences, and so in stead of Artists, to make their Scholars only doers of tricks, and as it were jugglers: to the despite of Art, loss of precious time, and betraying of willing and industrious wits, unto ignorance and idleness. That the use of Instruments is indeed excellent, if a man be an Artist: but contemptible, being set and opposed to Art. And lastly, that he meant to commend to me the skill of Instruments, but first he would have me well instructed in the Sciences.  
These words are to Delamain like a candle unto weak and rheumatic eyes, his purblindnesse cannot endure the brightness of them, but maketh him smart, and prick, and vex, and cry out, away with this light it hurteth mine eyes, put it out: and merely out of the detestation of this light, and the disproportion it hath to his weakness, those tragical 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, & seasonableness of this admonition, and are sorry for the wrong done unto Art itself under colour of me: Only one Richard Delamain is found who forgetting truth, gratitude, good manners, and very shame, doth bewray his galled back by such impatient wenching. Little did I ever suspect when I spoke 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 be 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 himself, that most insolently, to cloak his own unskilfulness, 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 do perfectly know. And concerning my honourable estimation of you most worthy Gentlemen, I do unfeignedly glory in the behalf of this our native Country, 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, than this our sweetest and most indulgent mother of Great Britain bringeth forth: only if we can take care to plant in our minds the good seeds of virtue, and knowledge: and not to neglect them to be overgrown (as the best ground will) with the weeds of evil and contrarious habits. whereunto on both sides no one thing conduceth more than 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 worthiest endowments; that having so long ordered your studies, disposed of your times, and received your money, hath even in his own conscience done you so little good, that there being but the very name of loss of time, juggling, and ignorance, occasionally mentioned, is himself first of all ready most unmannerly for your ingenuity, yet more unadvisedly for his own credit, to tax you therewith, and pin it upon you. And will you most clearly see how he seeketh not your good, but your intolerable expense, for his ambition and vainglory, and no good at all of yours? His Ring forsooth must be made of Silver and Gold: Brass 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 six feet diameter, of which whether the monstrousness, unprofitableness, 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 than all this, that is a Cylinder of metal (Silver sure it must be) three feet diameter, and of height sufficient to receive 100 or more movable 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 skilful workmen can hardly be performed for three hundred pounds: And when it is done, and you with a great deal 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 fare shorter time, and with much less labour, you may be taught with a book of twelve pence to work and perform fare more, and more exactly, then by that monstrous barrel Delamain himself can ever be able to effect. And do you not now (most noble Gentlemen) cry shame upon such teachers; shame upon such loss of time; shame upon such profusion of money; shame upon such vile betraying of willing and industrious wits unto ignorance and idleness; And many shames upon such dishonesty, to set out in print against his own knowledge, so many false propositions, and precepts purposely to abuse the ignorance of his Readers, and that they may esteem him for some extraordinary and more than 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 myself, what just cause there should be of all his clamorous and malevolous inveighing against me. But you must give him leave to use his own nature and manners. I am not the first, that have been in this petulant manner provoked by him. Who indeed hath escaped him? The stirring humour of some is, that if they think 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 hear of it, and all that come in his way shall suffer for it. England is too little, and his mother's tongue too barren (and yet if his mother's 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 Ass in Aesop having got on a piece of the Lion's skin 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 mirror of our age for excellent skill in Geometry, and therewith for exceeding meekness, was so vilifyed and slighted by this nifle in a bag, a little before his death, that the good old man forgetting his own mild nature, at his last departure from London, being on horseback for Oxford, and taking his leave of a friend, spoke 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 possess the legacy of so worthy a friend. Yea and Master Gunter too (whom he would seem to admire) escapeth him not without a shrewd lash. for in the beginning of his book of the horizontal quadrant pag. 3, he braveth him saying, this Master Gunter delivers so OBSTRUSELY in his 66 page of the Sector, that if a man had not more fundamental Mathematical doctrine than his book teacheth, he should never attain to it. It is well for him Master Gunter is not now to give him a second legacy: and to tell him a liar had need of a good memory. for in that part of his plea which is an answer upon his Quadrant towards the end, he writeth that joiners, and Carpenters, and schoolboys, and sundry Gentlemen and others, having not had the least assistance from any, but the direction of Master Gunter's Book alone, as upon oath they have been examined, have drawn the projection fully and completely. 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 fare more skilful than himself: divers of whom I have heard complain 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 fear, lest his ignorance might chance to bewray itself, as doth an Ass by his long ears.  
I Must now borrow a word or twain with the Gentleman which writ the first Verses in the beginning of this Pamphlet, and styleth himself a friend to the Inventor of the Logarithmes projected in circles. Sir I see you are not disfavoured of the Muses and Apollo: your verse is good, and the conceit well continued throughout: worthy of a better subject: or if you were pleased to play and show your skill in so poor 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 hear me — deny it was found out by you? Did I ever tell you — it was mine own? would I have professed and owned these and such slight toys, I could have done it long before your Inventor had any ability of invention in this way. No I did nothing in publishing hereof: I only gave way and permission. and it was not I that did addict it to myself: but his known worthlessness that did abdicate it from him. Neither is your argument of any force:  
But if it were not thine, how dared 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 vainglory? And is it consequent, because he said if the line were decupled therefore 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 four. 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 challenged too, 
I think you will prove yourself to be a truer vates then you were ware of: though not by me (who have not esteemed such minutiae worthy of me) but by Thomas Browne the joiner, whose indeed it is, and not your supposed Inventors. Sir you will be pleased to accept some reason in plain prose for your verse: and understand I do you a favour to acknowledge you so fare.  
And thus most honourable and noble Gentlemen having (as I hope even in your judgements also) vindicated my truth and honesty from such base petti-larcionary, as to steal his labours, and pilfer the wares of so poor a pack; and cleared my credit 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 seem to take his injuries nearer to heart then in wisdom I should do from so contemptible an adversary; not to impute it to passion: but courteously to consider the unsufferablenesse of his most unworthy calumniations, and evil usage of me. It may peradventure be expected that I should also read him a lecture of good manners: But I will not take any more pains in tutor so ungracious a scholar. Only I wish him to study over his own instruction. Yet this good advertisement I will receive from him, that I have work enough at home: and that my calling inviteth me to spend my hours better, than any more to trouble myself with answering him according to his folly.   
Dixi. WILLIAM OUGHTRED.