A DISCOVERY of sundry errors and faults daily committed by Landemeaters, ignorant of Arithmetic and Geometry, to the damage, and prejudice of many her majesties subjects, with manifest proof that none ought to be admitted to that function, but the learned practisioners of those Sciences:  
Written Dialoguewise, according to a certain communication had of that matter.  
By Edward Worsop, Londoner.  
Every one that measureth Land by laying head to head, or can take a plat by some Geometrical instrument, is not to be accounted therefore a sufficient Landmeater, except he can also prove his instruments, and measurings, by true Geometrical Demonstrations.  
AT LONDON, Printed by Henry Middleton for Gregory Seton.  
ANNO 1582.   

TO THE RIGHT Honourable and his singular good Lord, Sir William Cecil, Baron of Burghley, Knight of the most noble order of the Garter, Lord high treasurer of England, and one of the Lords of her majesties most Honourable privy Counsel.  
AMong the number of our worthy acts of Parliament (right Honourable & my most singular good Lord) the statute of land measure is of great importance, and equity. Certain persons (wanting sufficient knowledge for the executing of that statute) notwithstanding intrude themselves into that weighty function as sufficient. Sundry of their false rules, and untrue ways of measuring, as also sundry true rules (by some of them) falsely applied, in this small treatise are discovered. Mine intention was not in the time of penning thereof, nor long since, to publish the same: but of late upon great urging, and persuasion of him (at whose request I did write this talk) and of certain other my friends and acquaintances: I yielded at their requests to the publication thereof. The necessity, and worthiness of the matter require learned and exquisite ordering, which I must resign to be performed hereafter by the learned. By this treatise I may be likened to a broiled founder, whose only charge is to make mixture of metals, and to roughcast them. The filing, graving, and polishing, are done by other artificial workmen, who goodly set out the same to the eye according to the richenes of the metal. I, a simple man among the common people, have set forth this discourse to their behoof, by the plainest ways I could devise, and for their easiest understanding: Sundry learned works of the Mathematicals (for such as understand or affect learning) are extant in our vulgar tongue: as Euclid, the works of Doctor Record, of Master Leonard Digges, of Master Thomas Digges, and of some others. But because these learned books can not be understood of the common sort, and that they be as jewels, and riches, shadowed or wrapped up from their sight: I have thought good by a plain and popular discourse, to lay open unto the understanding of every reasonable man, the necessities and commodities of those singular works and knowledges, and the great abuse, inconveniences, and injuries, the common weal sustaineth by crediting and retaining of ignorant doers, and neglecting of learned and skilful writers, and practisioners. As wise and learned men, when they speak unto a simple and unlearned man: frame their speech to his understanding, which in the like cause they would utter otherwise if they spoke to one learned: so must some man to the behoof of the common weal manifest those enormities popularly, that the hurt which ignorance bringeth in this weighty matter may universally be known. I (although far unmeet to take so weighty a cause in hand) have adventured for the discharge of my conscience, and my duty to the common weal: to manifest (as I best could) certain great inconveniences which the common weal daily sustaineth by unlearned practisioners, humbly submitting myself where reformation is needful, to the correction of the learned. And for because it is universally known, that the continual application of your noble heart and mind, is to the furtherance of learned knowledges, of equity in causes, suppressing of ignorance, and to the commodity of the weal public (whereof your Honour is a principal pillar) and for that your Honour hath been mine especial good Lord, I do presume (as enforced thereto by duty) to dedicate unto your Honour this small treatise: most humbly requiring pardon for such my great boldness, as also that your Honour would vouchsafe to receive the same into your noble patronage.  
Your Honour's most humble to command, EDWARD WORSOP.   

The copy of a Letter sent with this Book.  
TO perform my promise, and satisfy your request: I have set down in writing (as near as I can call to remembrance) the communication had in our journey, touching untrue measuring of land, insufficient landmeaters, and why they are still permitted. For the further proof of these matters, I have drawn sundry figures like unto some of those you saw in my book: which proofs the unlearned in Geometry may easily conceive. I pray you reserve this book for the satisfaction of yourself, and your friends. I would be loath it should come to the hands of learned Mathematicians, for they may justly reprove sundry of my demonstrations, and declarations: because they are not penned as learning, and art require. If they were penned in artificial order, and terms: you could not understand them, because you are ignorant of the Mathematicals. If you will be instructed in Arithmetic, Euclid, Tectonicon, and Pantometria, according to your earnest protestations: and study those books earnestly, because they are the best writers, extant in our vulgar tongue touching the Mathematical part of survey: you shall then perceive, what great pleasure, and commodity, is received from learned, and artificial writers, over that can be had from them, which in their writings descend to the capacity of the vulgar sort. Then also you will yield yourself more beholding unto me for writing this popular discourse at you request, to the diminishing, and adventuring of mine estimation among learned Mathematicians: then now while you think it artificially done. Although my knowledge in Geometry is very small, yet I would not abase myself by penning any demonstrations popularly: but to pleasure you, and your friends, and for that I would many should understand, the great hurts the common weal sustaineth by landmeaters ignorant of Geometry. When you have attained knowledge, I hope you will deal with me as good natured men deal with their nurses. Good natured men during their lives love their nurses, because they received their first sustenance from them: although their stomachs would loathe to suck their milk as they did in their infancy. When you shall find yourself learned in Geometry, and that you can understand the demonstrations of learned writers: you will repute my writing as cold and thin milk, in comparison of other meats, that are strong and of good nourishment. From London the two and twenty of September. 1581.  
Your loving Friend Edward Worsop.  
 printer's device probably of Henry Middleton: McKerrow 215, "Ornament of a lion's face over a shield, two owls, and the initials H. M."   

An advertisement to the Reader.  
SCales, compasses, and sundry sorts of geometrical instruments in metal, are to be had in the house of Humphrey Cole, near unto the North door of Paul's, and at the house of john Bull at the Exchange gate: in wood, at john Reads in Hosier Lane, at james Lockersons dwelling near the Conduit at Dowe-gate, and at john Reynolds at Tower Hill. Every figure in this Treatise is drawn according to some Scale, therefore the having of scales and compasses, and applying them to those figures, will make the demonstrations, and proofs herein very easy to the readers thereof, though they understand little or nothing in Geometry. I have thought good to give advertisement hereof, because many that would provide such things, know not where to have them.   

A DETECTION OF Sundry errors, committed in Landmeating.  Speakers. M. Peter. Ihonson a Clothier. Worsop a Surveyor. M. Watkins. Steven a Servingman. M. Peter. 
THis seemeth to be rich pastureground, a tenant (in my judgement) may safely give a mark by year, for every acre thereof.  johnson 
I would take a pasture ground with us, and give that price for every acre, measured with the perch of xvi. foot, and an half, called statute measure, and ten shillings for every acre, if it be measured with the perch of xii. foot.  Worsop 
An acre measured by the statute perch, containeth (almost) twice so much ground, as an acre measured by a perch of xii. foot. If the statute acre be rented at xiii. s. iiii. d, the acre measured by the perch of xii. foot, will not come to seven. s. i. d, rate like. You should deceive yourself two. s. xi. d. in every such acre by that account.  johnson 
You are greatly deceived, for by all reason, the acre measured with the perch of xii. foot, must be almost three quarters of the statute acre, because xii. foot, are almost three quarters of xvi. foot, and an half.  Peter 
How much ground of statute measure, are xi. acres of woodland measure, the woodland perch being xviii. foot?  Worsop 
Above xiii. acres, & xiiii. perches, to my remembrance.  Peter 
Your remembrance, or your casting have failed you. You are greatly deceived in both your reckonings.  Worsop 
I shallbe very sorry, if I be deceived in either of them: for I have made sundry surveys where occasion hath served to reduce such acres as have been measured by the xviii. foot perch, & the xii. foot perch unto statute acres. The xviii. foot perch for woodland is used in most places hereabouts: I have not seen the xii. foot perch used in these parts: but far from London in some Manors, that measure is allowed of, and is called in some places, tenant right, in other some, curt measure.  Peter 
I always thought, and have sundry times heard that xi. acres measured with the perch of xviii. foot, make xii. statute acres. And this reason hath always induced me to think it true, because the xviii. foot perch exceedeth the statute perch by half a yard, which is a twelfth part thereof: for the one perch is xii. half yards long, and the other but xi. therefore seeing the perches differ but a tewlfth part the one from the other, the acres (in mine opinion) measured with those perches, can not make any other difference.  Worsop 
You do not know, or not consider, that when you talk of the diversity which unequal perches make in land measure, that then you speak of the measure of planes and flats. You think you are in the comparison of lengths, when as in deed you are in an other matter. Ye must understand that Geometry treateth of three sundry measures. The first of lengths, which is called liniarie measure, or the measure of lengths, or lines. By this part, you may know how far any place is from the standing of your foot, also the distance between place and place, & how much higher, or lower any place is, than the level of your eye, or foot. The second of length, and breadth, called superficial measure, or the measure of planes, or flats. By this part of Geometry is measured, all manner of land, board,, glass, pavements, waynskotting, hangings, and such like. The third of length, breadth, and thickness, called , or bodily measure. This part showeth how to measure all manner of timber, stone, vessels, and such like. M. Peter said truth, that the perch of xviii. foot, and the perch of xvi. foot and an half differ in their lengths, as xii. differ from xi. for the one is xii. half yards long, and the other but xi. But ye must understand, this difference is only in respect of their lengths, called liniarie measure. In land measure (which respecteth length and breadth) the difference is otherwise: as I will make plain unto you by an easy example. Suppose you have two tables, or boards, the one iiii. foot every way, the other six. How much is the one longer than the other?  Peter 
By the one half.  Worsop 
You say truth, and therefore you account the one table to be greater, than the other, just by one half.  Peter 
It must needs be so.  Worsop 
I pray you how many foot of wainscot doth a table contain, that is iiii. foot every way?  Peter 
xvi.  Worsop 
It doth so, and then by your account the other table of vi. foot every way, must contain xxiiii. for the half of xvi. is viii. which if you put unto xvi. they both make xxiiii.  Peter 
You say true.  Worsop 
I pray you how much is vi. taken vi. times?  johnson 
Six and thirty.  Worsop 
By your reckoning it should be, but xxiiii.  johnson 
We all know, that six times six, is six and thirty, but how proveth this, such diversity in the acres?  Worsop 
It showeth unto you at the first, that measures cast up by their breadthes and lengths, must otherwise be considered of, then measures whose lengths only are compared together. A table that is iiii. foot broad, and vi. long, containeth xxiiii. foot of board, therefore a table that is vi. foot every way, must needs contain more.  Watkins 
This standeth so by reason, that it must needs be as you say.  Worsop 
I have in my cloak bag certain figures drawn in a book, (which I must give unto a friend of mine) that will explain this error, and sundry others, which landmeasurers (unlearned in Geometry) often commit.  Peter 
I pray you let us see those figures.  Worsop 
You shall when we come to our Inn.  Peter 
It will be late ere we come thither, therefore we shall have small time then to talk of these matters: because men scatter when they are lighted. Also we must part company in the morning. Therefore I pray you let us see them now, which if you vouchsafe, I, in some other matter, will requite your courtesy. It standeth me upon to understand the troth of this matter, by reason of a wood sale, that I, and an other should pass.  Worsop 
To pleasure you, I will presently show them. Here is the book: these three figures prove that which I have spoken.  three grids to prove that multiplying length and width yields area: 4 x 4, 4 x 6, and 6 x 6  Peter 
I see in deed that iiii. every way maketh xvi. and that vi. every way maketh six and thirty. and iiii. broad and vi. long make xxiiii. What mean you by this word (Scale) which I see in so many places of your book?  Worsop 
The Scale is a measure used in plaiting, taken at the will of the plat maker, either greater, or less, to set forth the plat measured in true proportion, and Symmetry, upon paper, or any other superfice.  Watkins 
I understand not this definition.  Worsop 
Here (as ye see) are sundry scales, and every of them is just five inches long.  
 compass with three scales each five inches long, each with one of the inches divided into 4, 5, or 10 parts The first, hath one inch divided into iiii. parts, the second into five, the third into ten, ye may apply these inches and divisions, to what denomination you list. The Geographer apply them to miles, or furlongs. The Surveyor, to perches, the Carpentor, to feet, and so may any other arts man, in naming any other measure greater, or less. Suppose I should describe a country, that lieth in square form, xviii. miles on every side, upon a piece of paper, that is less than v. inches square. In this case, the scale of iiii. will best serve my turn. For one inch being divided into iiii. parts, doth represent the length of iiii. miles, therefore iiii. inches represent the length of xvi. miles, and two. parts of the divided inch added to them, must needs represent xviii. miles. But if I should describe a Shire, or Country, upon the like paper, that lieth three and forty miles square, in this case I must be driven to use the scale ten: that is to say, I must take in inches, and three parts of the ten, in the inch divided into ten parts, which represent three and forty miles. For iiii. inches represent forty miles, and the three divisions taken in the said inch divided into ten parts, represent the three odds miles. The self same scales will serve, if you should plat closes, within the like scantling of v. inches, the one being xviii. perches on every side, the other xliii.  Peter 
I now perceive what is meant by this word scale. I remember I have seen the like lines, and compasses set inmappes, but I never understood what they meant till now.  Worsop 
The knowledge, how to apply the compasses to the scale, is commodious, for thereby when maps, or carts, are perused, it may be known how far any one Region, City, or place is distant from any other, either by land, or sea. Also, when a Surveyor hath delivered up his plat, the Lord sitting in his chair at home, may justly know, how many miles his Manor is in circuit, and the circuit of any particular grounds, and wastes: and how many perches, or furlongs it is, from any one hedge, or corner of hedge, to any other hedge, or corner.  johnson 
I perceive also what you meant, when you said, ye may apply these divisions, to what denomination you list. As if you would know by any cart, or map of England, how many miles it is from Northampton to Sarisburie, than miles are the denomination: but if you would know by any plat of land, how many perches any ground is over, than perch●s are the denomination. And you call the opening and extending the compasses upon the scale, the application of the compasses to the scale.  Worsop 
You conceisse the meaning rightly.  johnson 
What mean you by these several words, in true proportion, Symmetry, and superfice.  Worsop 
To set forth a plat, in true proportion and Symmetry, are to say, to take, and set forth any plat in such sort, that you may readily tell thereby, every angle, bought, crook, and strait line in the thing measured, and how far any place is distant from other. Also you may know by your plat the whole circuit, & outboundes of your land, which Geometers call the perimetrie. Superfice is to say, the upper face of any thing, as in measuring of land, pavements, hangings, & such like, we desire only to know the content of the outward plain, or upper face of the thing, not regarding thickness, weight, grossness or depth: but only the measure of the upper parts as in grounds: which consist only of length, and breadth, whether they be flats, or levels, hills, or valleys. It would be too tedious to describe them at large: therefore I refer you to learned authors for your further instructions of their proprieties, and accidents.  johnson 
What is meant by this word, Parallel?  Worsop 
Parallel lines, are such lines, as (being drawn upon any plain, or superfice) are equally distant the one from the other. If you draw them of never so great a length, yet will they never concur, or meet together. If they incline never so little the one to the other, they are not parallels, but inclining lines, as you may see by the  parallel lines ab and cd; inclining lines ef and gh examples of these lines a. b. etc. d. which are parallels, and the lines e. f. & g. h, which are inclining.  Ihon. 
Why writ you such strange & far fetched words & terms, seeing you can write their meanings in plain english, if you would?  Worsop 
He for whom I have written this book, will not think them strange, or far fetched, because he giveth himself to the studies of Arithmetic & Geometry, and therefore acquainted with words and terms of those arts. There is not any doctrine, or science, but hath of necessity his peculiar terms: neither doth any learned man in any science, condemn an other learned man, in an other science, for a strange and far fetching speaker, because he understandeth not many of his words and terms. Many of the profoundest learned men in the Universities, understand not a number of terms, pertaining to the common Laws, which a young student of less than a years continuance, understandeth very well. And contrariwise, a great number of profound learned men in the laws of the Realm, understand not a great number of terms, used in Philosophy and Logic, which a young Logician understandeth very well. The Civilian, understandeth not many terms of Physic, nor the Physician many terms appertaining to the Civil Laws. The Greek terms appertaining to Arithmetic, Geometry, and other Mathematical sciences, seem stranger unto all sorts of men, than the terms of other sciences, and therefore, of the ignorant very much derided, who account them more curious than necessary. Yea some men that are learned in other sciences, but ignorant in the Mathematics, think them terms of hard and dark knowledges, and not greatly necessary, because they think much vanity in them. Both these sorts of men, which condemn before they know, are in great error. The ancients, and best learned writers of Mathematical sciences, were Grecians: the Latins, receiving their knowledge from learned Greek authors, never altered the Greek terms, but used them aswell in works of their own making, as in translations. The Italians, French men, and Germans, finding them in the Latin, used also the Greek terms, as followers of the Latins. Therefore the learned might judge a great presumption, and lack of discretion in us, if we should translate these Greek terms, into our English words: seeing the learned of other nations, retain them still, though they can write more compendiously, than we. We are not able to utter Greek terms compendiously, but by circumlocution. I think one special cause, why learned writers in the best languages, use the Greek terms in all their works, is, because readers of their books should compare them, with Greek, and Latin authors, in whom they shall find the self same terms, whereby the knowledge of these sciences, is much easier attained unto. For if a man find one thing in sundry languages, and divers ways defined demonstrated, and applied, he is very hard of capacity, if he shall not be able to understand some of them.  Ihonson 
I thought verily before you told these causes, that you, and your friend for whom you have written this book, had devised terms much like the devise of peddlers French, because you would not have your cunnings in land measuring known to any but to yourselves.  Steven 
And I would have thought them, words of conjuration, because being once in a place, and half a dozen others beside myself, where lay a book that had many crosses in it, & a great number of like figures, and circles, and as one of our company did read such strange words, one other said: my friend, you were not best to read too far in that book, lest you fetch one up, that will ask what he shall do, and if you can appoint him nothing, neither know how to lay him down again, he will do much hurt. And because it was in a Priests his house, I may say to you, it so feared some fools of us, that we were glad when we were out of doors. I never heard that the Priest was suspected for conjuring, he could do many pretty feats, for he made dials upon walls, and in gardens, he could measure land, and tell how wheels, and other gins for milnes should be made. He hath told how things should be made and mended, concerning water works, and milnes, that if the country had lacked his help, a great deal of money would have been spent in vain by most men's sayings. I heard him say unto landemeasurers, that they must needs make wrong measure, if they proceeded by such way as they had cast their work, and determined to proceed. One time (as I waited on my master when he went to the measuring of a meadow that lay two. miles from his house) there was great talk, and arguing by the way, whether it were possible to tell how far one place in view is distant from an other: & how much one place is higher than an other, except it were first measured. Master Morgan answered that it was possible, & very easy to be done. Then Master Allen asked him if he could do it by any of those instruments we carried with us. He answered that he could. Whereupon M. Allen suddenly staying, said: I pray you tell me how far it is from the place where I stand to yonder oak. I will, said he, and immediately he piched one of his instruments, and looked thorough a fine knack, or jig, and measured a good pretty way from him, not towards the mark, but sidewise: and at the corner where his measuring ended, he looked again through his jig, and casting a little with his pen, he told justly almost how many perches it was from his foot to the oak: for he miss not a perch in a length that was above five furlongs. When we came to the oak, whose height from a certain knot in a bowgh, down to the ground was almost three and fifty foot, he told within two inches the just height by looking through an other jig. One did climb the tree, and laid one end of a wire line to the knot, and there held it, and let the other end fall down, by which means we made trial. We that saw how near he had told the length, and height, before they were measured, said it was prettily done. M. Allen asked if any good service, or commodity to the common weal might ensue by these fine sleights. Yea said M. Morgan, very much. For except a man can take lengths and distances, he is insufficient to measure land: because in land measuring, the measurer many times through the impediments of thickets, waters, myers & such like, must be driven to take lengths, & distances. Neither hills, nor dales, for the most part can truly be measured, except their heights and depths be taken. Also he that can exactly take them, can give a very near guess, when he cometh on any ground whether it will contain his general's army or not. He also can tell what quantity of ground the enemy's camp overspreadeth: and give a near guess (if he see the enemies in battle ray) what number is of them. Also to know how to take lengths, & heights, be chief points in undermining: namely if the undermining begin far from the place that should be blown up. The height of towers, stéeples, and wales, are known hereby, so that scaling ladders may be made fit: and it may be known how much is between story and story in any house, without measuring them. Also how many foot high any tree dothbeare timber, and most requisite to batteries, & bowgeing, and to know how far any piece beareth point blank. The degrees of longitude, and latitude, the elevation of the poles, and the height of the sun, things in navigation of great necessity: namely in long and far viages, when they would know unto what coasts, and countries they are nearest, are known, and found out by geometrical instruments prepared for the taking of heights, lengths, and distances. The chieffest piece of art in the description of countries, is the taking of heights, lengths, and distances. The knowledge of them are incident to many other necessary matters.  Peter 
Call you these pretty feats, and fine sleights, and such instruments, knacks, and jigs? Me thinketh he that can do these things, performeth matters of great weight in the common weal, and aught as much to be accounted of, and advanced for these knowledges, as learned men in other faculties for their knowledges.  Steven 
When the land was parted between my Mistress, and her three sisters, M. Morgane was a whole month with my master, and measured for him. There were then certain lawyeres, surveyors, and country measurers, and for three or four days great controversy was among them, and such a stur as I never saw amongst wise men. Some would have the land measured one way, some another: some brought long poles, some lines that had a knot at the end of every perch, some lines that were sodden in rosin and wax, M. Morgane had a line of wires. They measured the poles, and lines with two foot rulers, & yards, whereof some differed from other, half an inch, which made great variance, for every man justified his own ruler. If I durst to have adventured at the first, I could I have gained twenty nobles by laying on master Morgane his doings. There was such lusty bargaining on all sides, that crowns, and angels were but trifling lays. Master Morgane laid little or nothing, but always as he said, so it was agreed upon: he could always give such reasons, and so well prove his doings.  Peter 
Then he measured for them all.  Steven 
Nay, that he did not. The land was to be divided into four parts. The sisters and their husbands agreed that every of them should bring their surveyors at the time appointed: so that when any ground was to be measured, rented, and valued, it might be agreed upon by their general consents. Order was taken that a certain mead should first be measured, & that every measurer, should measure by himself, and that none of the other measurers should be with them: and that every man when he had done, should deliver up his content of acres unto Master Allen, who went with them to receive the same, and to see that one should not tell another how much he made it, because it was thought good to see how they would agree. But when their reckonings were compared together, they disagreed very much. For one made it xxiii. acres, an other xxi. and an half, an other xvi. and iii. roods, and Master Morgane made it xvii. and almost a rood. Hereupon rose great contention and wagering, but at last all gave place to Master Morgane his measure. He that made it xvi. acres and three roods, found that he misreckoned himself almost iiii. acres too little, and afterwards he swore by God's soul that he was glad thereof, because by that occasion his content came nearest to Master Morganes.  Ihonson 
I marvel what may be the causes of their so great disagreings, and differences in one, and the same so small a piece of ground.  Worsop 
No marvel, for the common ignorant measurers by their general rule are for the most part subject to make grounds greater in quantity then in troth they are.  Peter 
I would very feign see how it can be proved, that xi. acres by the xviii. foot perch, make of statute measure xiii. acres and xiiii. perches. When I am satisfied in that matter, we will hear further of that partition.  Worsop 
Number the square feet, contained in these three figures. The figure A. showeth the square feet contained in the statute perch, which are CC. lxxii. and a quarter. The figure B. the square feet in the xviii. foot perch, which are C C C. xxiiii. And the figure C. the square feet, in the xii. foot perch, which are. C. xl. iiii. Your opinions are, that a measure made with the xviii. foot perch, is greater than a measure made by the xii. by the one half, because xviii. is xii. and the half of xii. But ye see it is far otherwise, for C C C. xxiiii. the greatest square, containeth C. xliiii. the lest square, twice, and xxxvi. over, which is the fourth part of C. xliiii. So that one acre measured by the xviii. foot perch, is equal unto two. acres, and a rood, measured by the perch of xii. foot. Such proportion as the  surveyor's diagrams: grids showing the number of square feet in (A) the statute perch (16-1/2 feet); (B) the 18-foot perch; (C) the 12-foot perch squares of perches have each to others: the grounds by them measured have also. But because you are ignorant of Geometrical proportions, that is to say, of Geometrical relations, comparisons, or respects, & that the proportion of the square of the statute perch, to the squares of the other perches, fall so upon the fraction, as I cannot express them by number to your understandings: therefore I will set aside art, and artificial terms, in this our talk, and frame my speech as I best can to your understandings. Ye all know that eight score perches make an acre, as eight score pennies make a Mark of money. Whether our coin be fine, or base, eight score pennies ever make a Mark: so whether the perch be little, or great, eight score perches ever make the acre. When ye talk of two. unequal perches of land, ye must not think that ye talk of two. such unequal poles, or lines, as Surveyors measure with, for they are instruments to lay out the sides of a perch of land, and not perches of land. If a man buy a piece of Dornixe of a yard broad, to hang a room withal, and when his hanging is made up, he lacketh a yard of stuff to perform the same: which he buyeth. In this case the square yard of bought s●uffe, performeth the hanging, and not the yard where with the stuff was measured. As a yard of Dornixe cut off from the piece, is contained within the bounds, and limits of four edges, or seluages, every one being a just yard in length: for that quantity of Dornixe is called a square yard of Dornixe: so is that quantity of ground, called a perch of land, which is contained within the limits of four perches being laid square. And as eight score pennies, make a Mark of money, so eight score such parcels, or pieces of ground, make an acre. Ye have told that C C C xxiiii. square feet are contained in the perch of eighteen foot, which sum eight score times, maketh fifty one thousand eight hundred and forty. For one hundred foot eight score times make sixteen thousand, than two 3 hundred eight score times, must make eight and forty thousand. And eight score, four and twenty times, make three thousand eight hundred and forty.  johnson 
I understand very well that this is true.  Peter 
I have tried it in multiplying 324 by 160, and find it to agree that ways.  Worsop 
Ye have told also that two hundred three score and twelve foot and a quarter, are contained within the statute perch, which sum eight score times, maketh xliii. thousand, D. ● lx. squ are feet.  Peter 
We have cast this among ourselves, and find it to be as you have said.  Worsop 
Take the lesser sum out of the greater, and note how many remain.  Ihonson 
There remain viii. thousand, two hundred and fourscore.  Worsop 
Ye say truth, and ye perceive that the one acre exceedeth the other, so many square feet of ground. Can ye tell how many times C C. lxxii. and a quarter are contained in eight thousand C C. lxxx?  Peter 
As we have cast, thirty. times, and C xii. foot and an half over.  Worsop 
Then ye perceive that the acre measured with the perch of xviii. foot long, is greater than the acre measured with the statute perch, by thirty. perches of land and Cxii. foot and an half over. How much is thirty eleven times?  Peter 
C C C. and thirty.  Worsop 
How much is C. xii. and an half, eleven times?  johnson 
xii C. xxxvii. and an half.  Worsop 
How many statute perches is that?  Peter 
Four statute perches, & an half, xii. foot, and a quarter and an half of a foot.  Worsop 
Thus ye have found C C C xxxiiii. perches & an half, & a few odd feet, which is two. acres, xiiii. perches & an half. If you put them to xi. acres, than you have xiii. acres, and above xiiii. perches, according to my former saying.  johnson 
I pray you let us try the diversity, between the statute acre, and the acre of xii. foot perch.  Worsop 
Ye see the xii. foot perch containeth C xliiii. square feet: how much is that sum eight score times?  Peter 
C xliiii. eight score times is, xxiii. thousand and xl.  Worsop 
How many times is C C lxxii. and a quarter contained in xxiii. thousand and xl.  Peter 
Four score, and four times, and an half, xxxiiii foot, and seven parts of a foot, the foot being divided into eight parts.  Worsop 
Ye know that those lxxx. and iiii. times are so many statute perches?  Peter 
We do so.  Worsop 
How much money is lxxx. and iiii. penies?  johnson 
Vii. s.  Worsop 
Ye see by your own reckoning, that if the acre measured by the xii. foot perch, did make lxxx. and v. statute perches, as ye see it doth not fully, that your rent could be but seven. s. and a penny, after the rate of xiii. s. iiii. d. for the statute acre.  Ihonson 
It is most true.  Watkins 
These reckonings, and profess, are very finely, readily, and plainly contrived. Till now I never heard ground cast up to half a quarter of a foot, and so plainly proved to every man his understanding. And yet I have heard that some will not miss an inch of ground when they measure.  Worsop 
It is a small matter for one to cast up any measure that he hath made within less than an inch, but to measure exactly within less than an inch is a greater matter than I ever knew any would take upon him to do. For albeit the art doth exactly teach the way, yet are we not able (such is our imperfection) truly to execute the same. And where you think that this account hath been finely, and readily cast up: you much mistake it: for it hath been very grossly done. The five ways are done by Arithmetic. I will by Arithmetic do more in a line, then thus in a leaf: and in the space of two. minutes, which this ways can scantly be done in half an hour. He that is a good auditor will quickly cast such a reckoning with his counters. But because neither time nor place would permit me to use any of those means, I was forced to prove this in such sort, as every of ye might best understand me.  Watkins 
I think I understand what you mean by these words, square feet, square perches, but yet make further explanation of them I pray you.  Worsop 
That figure is called a square, which hath all his iiii. angles right angles. Every plain, or superfice bounded with iiii. sides, hath iiii. angles, or corners, as ye may perceive by these figures, A. B. C. D. You may try by the scale of ten that every side of  diagrams comparing squares (A) and (C) with parallelograms (B) and (D), where the sides of (A) are the same length as the sides of (B) but the areas are different, and likewise for (C) and (D) the figures A. and B. are xx. in length, and every line is a straight line: and yet the one figure is greater than the other. The figure A. is the greater, because it is a square figure: and the figure B. is much less than the figure A. because it lieth not in square form. Like wise the figure C. is a long square, and therefore much greater than the figure D. which lieth not square, and yet the sides of the one are equal to the sides of the other. Three kinds of angles are to be considered of, by landmeaters: namely the right angle, the obtuse angle, and the sharp angle. It can not be said that any figure, or close lieth square, except his corners be found right angles. Who so is ignorant of certain peculiar properties, and conditions appertaining to these three kinds of angles, can not truly measure land. It is not enough for a measurer to know the sides of grounds, by laying his pole, or line, but he must know moreover the contents of the corners: for the square lying, narrowness, or broad opening of the corners in closes, make the contents divers, although the sides be found equal by measure.  Watkins 
Is he that knoweth the particular properties of those three kinds of angles, to be accounted a sufficient measurer?  Worsop 
No more than he is to be accounted a sufficient Grammarian, that knoweth but three rules appertaining to the first part of speech.  johnson 
Notwithstanding your sayings, I like best the old manner of measuring, by laying head to head, and side to side, taking their halves, and that ways to cast up the contents.  Worsop 
That way is not true, but where the corners of the close be right angles, and the hedges straight. You shall not find one close amongst an hundredth to lie in that sort. The measurers' eye, is not able to judge exactly whether grounds lie square (though he have great experience and good art) if he have not some Geometrical instrument to direct him. If a ground of four sides, have not at least two right angles, it may not be cast up by laying head to head, for that kind of casting will produce a false content. Tell me I pray you, how many acres a close of four sides containeth, if every side be just xl. perches in length?  johnson 
Forty times, forty pence, is xx. nobles, and xx. nobles, is ten acres.  diagrams comparing square A and rectangle C with parallelograms B and D, where the sides of A are the same length as the sides of B but the areas are different, and likewise for C and D  square A, each side measuring 40 units  Worsop 
This is a true content if the close lie in such fashion, as the figure A representeth: having all his sides straight, and angles right. But if it lie in fashion like to the figure B, than it is but eight acres. The cause of this diversity is, the difference of the angles. By judgement of your eye, you may perceive, that the close A, is greater than the close B. All the sides of both the closes, or figures, are equal in length, and every of them lieth straight. By the figure a. b. c. d. e. f. g. h. you may see the proof of this diversity. Every side of the figure a. b. e. f. is xl. perches, as you may try by the scale x: and because his angles be right angles, therefore his content  parallelogram B, each side measuring 40 units  diagram of parallelogram B superimposed on square A (from the figures on the previous two pages) to demonstrate the difference in area is just ten acres. The figure h. d. e. f. hath also every of his iiii. sides xl. perches, and yet a close lying in form like to that figure, is but 8. acres. The figure a. b. c. g. is parcel of the figure a. b. e. f. which figure a. b. c. g. is xl. perches one way, & viii. the other. Forty pence. 8. times, is two. acres: which two. acres, being taken from x. acres, there remain viii. acres: which are included in the figure g. c. e. f. And ye may easily perceive, that the figure h. d. e. f. is equal to the figure g. c. e. f. for the triangle c. d. e. is equal to the triangle g. h. f.  Peter 
If the triangles. g. h. f. etc. d. e. be equal, than your meaning is, to put unto the figure h. c. e. f. the figure g. h. f. in steed of the figure c. d. e.  Worsop 
You conceive it right. For suppose I would cut of a piece of ground, from a close, or ortyeard, as here the piece of ground c. d. e. is cut of from the close h. d. e. f. and on the other side, namely on the side. f. h. I would take in another piece for it, in like fashion, and bigness, as the piece cut of, was, because I would have the ground lie in square form, for the pleasure of mine eye: your reason gives you, that there is no difference in respect of quantity of ground, between the first close, and the last, because so much is taken in on one side, as was taken away from the other.  Peter 
If the ground taken from the one side, and the ground added to the other side, be truly measured, it must needs be as you say: but how can you prove that these two triangles c. d. e. and g. h. f. be equal?  Worsop 
The equality of these two triangles is proved by the fourth proposition of the first book of Enclide his elements. But because you understand not geometrical demonstrations, I will not prove it unto you, as the art requireth, but by a gross, and unlearned way, for you shall so best conceive the proof. Ye may try by the scale, and compasses, that the side c. d. is equal to the side g. h. and the side d. e. to the side h. f. and the side e. c. to the side f. g. Then lay a white paper under the triangle c. d. e. and with a pin, or needle, let that paper be pricked in the corners c. d. e. & laying your ruler to those pricks, draw finely three straight lines, and they will include a triangular superfice equal to the figure c. d. e. then with a knife, or sisers, cut out the triangle drawn upon the white paper, and lay it upon the triangle g. h. f. and ye shall find, the one paper, just as big as the other, without more or less. If the papers be equal in bigness, than your reasons must needs give you, that the figures h. d. e. f. & g. c. e. f. are equal. The self same troth that is in the measure of paper, is also in the measure of ground: one reason serveth forboth. Thus ye see, that the figure h. d. e. f. is equal to the figure g. c. e. f. & therefore much less than the figure a. b. e. f. And yet the sides of the figures h. d. e. f. are equal in length, to the sides of the figure a. b. e. f. and the hedges of the one, are as straight, as the hedges of the other.  johnson 
If land may not be measured by laying head to head, how should it then be measured?  Worsop 
I am no more able to instruct you by one days talk, how to measure land: then a learned Physician, is able to make you a good physician in the space of a week. There is not any that can measure land as it ought to be, except he first be well instructed, studied, and exercised in the sciences of Geometry and Arithmetic. He that taketh upon him to be a land meater, and is ignorant in these sciences, is no other wise to be accepted for a good land meater, (although by hap he measure some fashioned grounds truly) than he for a good physician that cureth some certain disease by chance. I show not these figures, and proofs of errors, that I think thereby, ye may be made good land meaters upon a sudden: but that ye may perceive, that your unlearned measurers, which you allow of, and suppose to do well, do utterly abuse you, in delivering up false contents. There be three erroneous ways in great use, among unlearned land meaters. One is, to lay head, to head, another, to measure a ground round about, and to cast the measure of the whole circuit, into four parts, or sides: and then to cast it up, as though it lay square. Many use this way in measuring of copies, woods, and bushy grounds, when they can not see how the hedges lie: but how untrue that kind of measuring is, you may perceive by the square figure. a. b. c. d. which is much bigger, than the figure included within it, and yet the hedges of the included figure, are longer than the hedges of the said square figure a. b. c. d. If you measure the crooked lines with fine threads, you shall find them longer than the straight lines, as the crooked line a. b. is longer than the straight line a. b. by the length of the line b. e. In like sort, you may try the rest. Thus ye see, whether they lay head, to head, or cast the whole circuit into four parts: yet either way they make the lesser ground, contain more, than the greater. For those crooked hedges being cast up as though they lay straight, will yield a far greater  diagram of an irregular piece of land shown within square ABCD to demonstrate that crooked lines cannot be used to calculate area in the same way as straight lines quantity of ground, than the square close a. b. c. d. doth: and yet the square is greater, for the close with crooked hedges, is included within it. The third way is, they will lay out a square (here represented by the pricked lines, which in deeed is not a square) and afterwards they will make allowance, for all the nooks, and corners. This were a good way, if they could lay out a square truly, and also truly cast up the corners. But seeing the learned in Geometry, can not lay a square truly, but by the help of some geometrical instrument: the unlearned (being ignorant how to use such an instrument) can much less do it. I dare lay with any of those good fellows, xx. to one: that they cannot lay out a piece of ground perfectly square, only by the judgement of the eye: & other help, I never saw any of them use. They also cannot measure the nooks and corners truly: because they know not how to cast up triangular superfices, by such rule as their form requireth. There be sundry kinds of triangles, as well of right lines, as of spherall, spiral, and mixed, to every of which appertain peculiar rules, to the attaining of their contents. In woods, rough grounds, and marshes covered with waters, they, which have art, cannot for the most part lay out squares, but be driven to measure, and to take their angles on the outsides, or upon the banks, or walls. If arts men can not lay out squares in such grounds, the ignorant can much less do it.  Watkins 
It seemeth unto me, by that you have showed, and proved, that if all the hedges of a piece of ground be cast into one sum, and divided into four equal parts, if then those iiii. hedges be laid square, that such a close, would contain more ground, then if it were laid in any other fashion.  Worsop 
You must understand that this is only meant of closes of four straight sides. I can lay closes in divers forms, whose hedges shall be straight, and but viii. score perches about, and every of them shall contain above x. acres, and differ, one from another, in their contents.  Peter 
I never heard in all my life, that more ground than ten acres, could be contained within the compass of viii. score perches. How much ground can you lay within that compass?  Worsop 
Twelve acres and almost three quarters of an acre: it shall not lack iiii. perches thereof.  Peter 
In what fashion, must such a piece of ground lie?  Worsop 
In a perfect round, like unto this round figure.  johnson 
In our Country we measure such a piece of ground round about, and then cast it into iiii. sides, and we think it truly cast.  Wor. 
You may perceive that to be erroneous by the circle and pricked square a. b. c. d. which giveth you 8. score perches in square, & also viii. score perches in round. You shall find by the scale ten, that every side of the square is iiii. inches, that is to say xl. perches, therefore all the iiii. sides are xvi. inches, which make viii. score perches. Also if you measure the circle, with a fine thread of xvi. inches long, from the streike in the top, round about, you shall find the same also to be just xvi inches about, even as the circuit of the square a. b. c. d. is. Your eye giveth you, that there is much more paper included within the circle, then within the square, and yet no more perches are in the circuit of the one, then in the circuit of the other.  diagram of a circle  Peter 
I will not ride any further, till I have tried this, for I have a silk thread in my bag. First I will measure the iiii. sides of the square, & cut of the thread at that length. Now I will measure round about the circle, from the strike in the top. I do assure ye they agree to an heirs breadth. It is very evident to the eye, that much more paper is contained within the circle, then within the square: therefore common sense giveth, that if grounds be enclosed with hedges of like lengths, and fashions, that more ground must be contained within the round  diagram of square ABCD superimposed on a circle hedge, then within the square.  johnson 
I never (in all the days of my life) could have devised such a proof as this, my head is so gross. I marvel much how you can lay viii. score perches in a round, without more or less. I take it to be a great piece of cunning. Can you do the like upon land, as you have done upon paper?  Worsop 
I can lay out grounds in any fashion, as well upon land, as upon paper: but more time must be had, to the doing of the one, then to the doing of the other. How to transform figures, according to their sides, or contents, to any other fashion, or kind of figure, ought (of necessity) to be known unto landmeaters. I find two. sorts of people of great contrariety in their opinions, concerning the attaining unto the knowledge of land measure. The one thinketh it but a sleight, and learned by and by: the other dispaireth of his understanding, thinking his senses over dull, and gross, to attain the knowledge thereof. Both these sorts of people, are in wrong conceits. He that thinketh it but a sleight, is of such courage, that he will (according to the common saying) leap over the style, before he come near it. For saith he, If I might be but one week in the company of a cunning measurer, and have but a little instruction from him: I could learn all his cunning in that space. So slender a knowledge is land measure in his silly conceit. If this jolly fellow know how to take a plat by any one instrument, and cast up the same, by Multiplication, and Division, in whole numbers, taught in the vulgar Arithmetic, he thinketh himself to have cunning sufficient. He will never trouble his head, with the vulgar fractions appertaining to those numbers, for they serve but unto the parts of perches. Such a measurer may be likened to one that will take upon him to be a keeper of accounts, though his knowledge serve not further, then to cast such sums only as be in pounds: if there be shillings and pence, he will never trouble himself with them, nor beat his brains to learn how to cast them. Such measurers know how to make their plat join, although neither last angle, nor last length be correspondent to their scale, and instrument. If the two. last lengths join, either by in ward, or outward angle, they think their work very good. I have known some (when a plat hath been well taken) so erroneously cast up the same, through false rules in casting the triangles, and ignorance of the fall of the perpendicular, that the measurer which worketh only by the perch, laying head to head, would have given up a truer content than they. The ignorance of the time is such, that to talk by rote of measure, with making show of some instrumêts procureth great credit to such measurers. Whoso cannot prove his instrument, his plat, and the casting up there of, by Geometrical demonstration, is not otherwise to be accounted of for a good land meater, than he for a good Latinist, who can only recite certain sentences, being unable to pierce one word: or he for a good Orator, that is ignorant of the parts of an Oration, and the Rhetorical figures. As one that never read in the Bible, and yet will take upon him to be a Preacher, or one that never read Litleton, will notwithstanding take upon him to be a Counsellor in the laws, aught to be accounted insufficient for those functions: even so ought he to be accounted insufficient for a land measurer, the hath not red Euclides Elements, but is ignorant of his definitions and propositions: especially such, as concern liniarie & superficial measures. As Euclid is a greek author, so is the name of his Elements greek, to a great number of such land meaters, as hold their credit, by the sign of the instrument. Other tenure they can not plead, than the sign of the instrument, and a gross, and unlearned order of plaiting, which they attained unto by an imitation and exercise, and not by learning and understanding, why it is so done. As in Divinity, Law, and Physic, none are admitted to be practisioners, before they be so studied in the best authors, entreaters of those knowledges, that they are able to prove their doings, by good doctrine, so should not any be admitted to land measure, except he be so studied in Euclid his Elements, and other good writers of Arithmetic and Geometry (whereof great plenty are extant in divers languages) that he is able to prove, and demonstrate his doings by their definitions & propositions.  Watkins 
What is the cause why insufficient landemeaters be suffered, and that order is untaken, that none shall be permitted to measure land, but such as can sufficiently do the same: being thereunto admitted, by the learned in Arithmetic, and Geometry, appointed by authority for that purpose. It seemeth unto me (as I gather by your speeches) that the ignorant win unto themselves great good opinions, and by shows and brags, carry away the doings from the learned.  Worsop 
The abusing and contemning of the mathematicals, is the chiefest cause▪ In the time of Popery most singular knowledges were shut up. A Ciceronian, was accounted an heretic. They could not abide the opening of learned knowledges. They made darkness, and ignorance, two of their pillars. They fed the people with scum and dross, as well in human sciences, as in divine. For as in stead of divinity, they brought in superstition and idolatry: so in stead of the pure Mathematical knowledges, they used conjurations, sorceries, invocations of spirits, enchantments, and other unlawful practices, under the names of divinatory and judicial Astrology.  Watkins 
Conjurations, sorceries, invocations of spirits, enchantments, witchcraft, and such like are cut off by our statutes, so that none use them, but felons, and reprobates. I understand not what you mean, by divinatory, and judicial Astrology.  Worsop 
divinatory, and judicial Astrology (as a learned author saith) entreat of the revolutions of the years of the world, of nativities, of questions, of elections, of intents and thoughts: it teacheth moreover to foretell, to call back, to avoid, or fly the ends of all things that may happen, and the secret disposition of God's providence. An other saith, that the practisers thereof say, that they can tell of all things that are not come to pass, before they come to pass, by the course and moving of the stars. By this they make their Prognostications, that tell of rain, and fair weather: sickness, and health: war, and peace: plenty, and dearth: with such like. By which also, they cast nativities, tell fortunes, pretend to give knowledge of things that be lost: and last of all, appoint you days, and times, good or ill, when to journey by land, when by water, when to marry, when to buy, and when to sell. Some of these doctrines, and practices, are unlawful. The Prophet Esay in his xlvii. Chapter saith, Let the heavengasers, and the beholders of stars, and mooneprophets, come on now, and deliver thee, yea, & let them show, when these new things will come upon thee. Behold they shall be like straw, which if it be kindled with fire, no man may rid it, for the vehemency of the flame: and yet it giveth no synders to warm a man by, nor clear fire to sit by. Thus are they with whom thou hast wearied thyself. By this it appeareth, that heaven gazers, beholders of stars, and mooneprophets, can not by their prognostications foretell the secret disposition of God's providence. Therefore they are ill suffered to foretell of wars, of plagues, of famines, of unseasonable weathers, to their own destruction, as straw consumed with fire, and to the deceiving of the people, who can receive no more good by their divinations, than warmth and light, from the synders of  straw. jeremy saith in his tenth Chapter, Ye shall not be afraid for the tokens of heaven, for the Heathen are afraid of such. Yea all the customs, and laws of the Gentiles are nothing but vanity. By these words they of the household of faith are taught, not to fear, howsoever planets threaten by aspects. In the eighteenth Chapter of Deuteronomie, among other prohibitions, it is forbidden that there be not any chooser of days, among the Israelites: for the choosing of days is an abomination before the Lord. It is one of the sins, for which God cast out certain nations before the Israelites. So abominable are such elections in the sight of God. One of the ills which Manasses did in the sight of the Lord, even after the abominations of the Heathen, was, that he maintained tellers of fortunes: and built altars for all the host of of Heaven, and worshipped all the host of Heaven, as it appeareth in the one and twenty Chapter of the fourth Book of the Kings. Therefore, the casting of nativities, the telling of fortunes by Palmistry, and by such like ways, are also abominations before the Lord. The Priests of the Gentiles, (being ignorant of the true God) devised these abominations. They brought the people in belief that certain ingenious men, and women (after their natural deaths) were stellified. They named certain stars after the names of such men, and women, and made the people believe, that they were Gods, and Goddesses, and that they had placed themselves in the heavens, to behold the earth, and doings of men, and to order men, and human things, according to their pleasures, and dispositions, when their turns of regiment came about. The Chaldeans, and Egyptians, having observed certain courses of stars, planets, and constellations, which God appointed them in their first creation, say, that that planet shallbe lord of the ascendent for that year, which is in the sign ascendent above our horizon, at the hour when the Sun entereth into the first minute of Aries. And that all things that year are governed here on earth, chiefly according to the disposition of that planet. Therefore they caused Temples to be erected in the honour of them, which they devised for their gain, and estimation, and for the better pleasing, and ordering of the people. They feigned a certain man called Mars, (who in that age, was the most politic, valiant, and fortunate in martial affairs) to be the God of battle after his death, and that he was placed in the heavens to our sights, in the shape of a red, and fiery star, according to the nature of fierce warriors: appointed unto him, for his habitation a large heavenly region. An other called Mercury (because he had a deep and ready wit, and was singular eloquent while he lived here on earth) after his death they brought the people in belief that he is the God of eloquence, & the messenger of the gods. Therefore Poets feign, that he tied wings to himself, when he went on any message, & painters paint him with wings, as they fond paint Angels. To him also, they appointed an heavenly region. They feigned a certain woman called Ceres, to be the Goddess of corn, because she first devised the yoking of oxen, the plough, and that order of tillage. The invention of the art of whoring, is attributed unto Venus, who therefore was reckoned in the number of the Goddesses, and called the Goddess of love. For she being unchaste, and occupied in all excess of carnal pleasures, taught the women of Cyprus, to please men with their body for money. This so pleased the priests & the people, that they have appointed the brightest planet (the sun & moon excepted) in remembrance of her, to the greater celebrating of her honour. Many other men and women, they feigned to be turned into Gods, and Goddesses, as jupiter, Apollo, Saturn, juno, Pallas, and such others, some for their human virtues, and some for their vices: assigning stars, and planets, and erecting Temples and Oratories in the honour of them. We read in the Acts of the Apostles of jupiter his Priest, and of the Temple of Diana the great Goddess of the Ephesians. These Chaldean, and Egyptian Priests, and fabling Poets, feigned stars, planets, and constellations, to be the chief governors of men, and human causes by turns, much like the choosing of some kind of officers, one year in, the next year out, and within a few years after, in again. For one while Mars is Lord of the ascendent, an other while jupiter, an other while Saturn, and so of others. When jupiter is Lord, they prognosticate a prosperous, and happy year: But when Mars is Lord thereof, they prognosticate chief of wars, and destructions, namely if Venus be retrograde, that is declining from him. But if she be in conjunction with him, the fury is not only then qualified, but turned unto pleasantness: and in stead of great wars, they prognosticate great adulteries, insolences, and unchastities. Thus these divinors behight generally unto the whol● world, an universal spending of the year, according to the dispositions, and usages of licentious persons. The universal people at their appointmentes, must spend the whole year, either providently, and virtuously: or dissolutely, and viciously. If any be desirous to understand at large the vanities, contrarieties, lyings, falsehoods, heresies, and other abominations, proceeding from abused judicial, and divinatory Astrology, let them read the treatise of johannes Picus Mirandula, Cornelius Scepperus, and Cornelius Agrippa against such Astrology: And also two English treatises, the one entitled, An invective against Astrology, the other, An admonition against Astrology judicial, and other curiosities. Abused Astrology, is a greater hinderer and depressor of lawful Astrology, and Astronomy, and the other singular and lawful mathematical knowledges: then rank weeds of good corn. We may read in the first Chapter of Genesis, wherefore God made the Celestial bodies, where it is thus written. And GOD said, Let there be lights in the firmament of heaven, that they may divide the day and the night, and let them be for signs, and seasons, and for days, and years. And let them be for lights in the firmament of heaven, that they may give light upon earth: and it was so. And GOD made two great lights: a greater light to rule the day, and a less light to rule the night, and he made stars also. And God set them in the firmament of heaven, to shine upon the earth. And to rule the day and the night, and to make difference between the light and the darkness. Here the word of GOD showeth for what causes the Sun, Moon, and stars were made: namely to divide the day and the night, and to be for signs, for seasons, for days, for years, to give light upon earth, to rule the day and the night, and to make a difference between light and darkness. Lawful Astrology, and Astronomy entreat not of the Sun, Moon, and Stars, nor of their courses, and aspects to further end than these. Who so goeth further, committeth as great evil, as he that addeth to the word of GOD, or maketh the word of GOD a cloak to cover his wicked divine. All sensible people perceive, that these lights, govern, and divide the day and the night, for when the Sun is above our horizon, then is it day with us: when under, than night. They be signs unto us of God's great power, majesty, and goodness. By the courses which GOD hath given unto these signs, we know the approaching, present, and declining times of spring, Summer, Harvest, and Winter. Navigation into far Countries can not conveniently be without taking the height of the Sun and certain stars, whereby men know in what part of the world they are, and by the age of the Moon, they know when it is full sea, or low water in any haven, or port, whereby the safest times of bringing in their vessels is known unto them. These and sundry other great commodities, receive we by these signs. We see also that our seasons for ploughing, sowing, setting, planting, shredding, cutting, felling, reaping, and gathering, are known by the courses and influences of these lights, and celestial bodies.  
When the Sun is in the tropic of Capricorn, then is it with us winter season: when in the Equinoctial, spring time: when in the tropic of Cancer, summer. These & all other seasons are known to skilful Astronomers by the courses of the celestial bodies. The knowledge of the day natural (which is the space of four and twenty hours) and of the day artificial, which is the time between Sun rising, and Sun setting, is of great necessity in our human affairs. In like manner to know in what space of time the year is accomplished, is a thing of great commodity unto us. C C C lxv. days, vi. hours, and a small portion more of time, make the year: which Astronomers have found out by observing the course of the Sun through the whole zodiac. If the revolutions and courses of the celestial bodies, should not yearly be exactly observed by Astronomers, they could not set forth almanaches, and if we had not almanaks, great losses, inconveniences, and confusions in human affairs would immediately ensue. Philip Melanchton saith in an Epistle of his, that it is a great, and manifest profit to keep a true, and certain account of the year. How great would the confusion be of present business, of contracts, of bargains, of judgements, & how great disorders would there be, if there were not a distinction of years and months? If the numbering of years were taken away, what great obscurity would there be in Histories? The beginning of the World could not be thought on, neither the beginnings of religions discerned, nor the alterations of kingdoms distinguished. It is evident, that the knowledge of these things are greatly necessary to divinity, and to many parts of our life. Wherefore the ingratitude, or rather the perverseness of many can not sufficiently be marveled at, which reprove this doctrine of the heavenly motions, and description of the year. The greatness of the profit, & the judgements of the wisest Princes, and of the best learned, who with great labour, search, and diligence, have set the year in order: ought to move the ignorant to detest the hearing, and using, of such doltish and scoffing reproofs, as are used against good arts, so excellently set out, as it were by divine inspiration. The worthiest princes, magistrates, and philosophers, have had a great care rightly to describe the year: that times may be discerned, & the memory of things set forth, and conserved. We must needs grant that our first fathers the patriarchs and Prophets, who excelled in wisdom, and godliness (as it were by divine inspiration enforced) have observed, and set forth, the distinction of years. We read the Patriarch Abraham taught the Egyptians Astronomy, and Geometry. And godly job nameth certain stars by proper names. Great reasons, profess, & authorities, as well from Divinity, as from Philosophy, and natural reason, might be brought, how worthy and needful the Mathematical knowledges are. Therefore they are greatly too blame, and much overshoot themselves, in bewraying their ignorance, and ill disposition, which scoff at Mathematicians, calling them fantastical, and vain fellows. They which have no understanding in Mathematical arts, when they see a fellow with a running head, or light brain, especially if he be studious, and given to solitariness, say in way of scorning, he hath a mathematical head. They think they speak finely and aptly, but they make themselves more ridiculous unto the learned by using this new term, than the simple man, that calleth an arbitrement, a bikerment, and him very unrude, whom they would condemn for carterlines. In their imagination, a running or fantastical head, and a mathematical head, are of one signification, which is far otherwise. Tully saith, If art, and nature meet in an Orator, the excellency thereof is such as he cannot express the same. In like manner, if a man have a Mathematical head, & mathematical art, that man is to be reputed a most excellent and most necessary member of the common weal. For most certainly such a man can perform great, and weighty actions, to the benefit of his Prince, and Country. How ungrateful, I may rather say how dishonest, and despiteful are they which mock at the makers of Almanaches: terming them fantastical, and mathematical heads, & keakers on the new Moon: when as themselves continually carry an Almanac about them, and set one up in their houses, as a most necessary instrument to their private affairs. Evidences are daily brought unto lawyers, that the expirations of leases, and of prescriptions, and the continuance of descents, and pedigrees may be known. Men think a fee well bestowed upon their Counsellor, to be truly informed in any of these cases. Astronomers have so reduced the years of our Lord, and the reigns of Kings, that the expirations of terms, may readily be known. These reductions are extant in our vulgar tongue, in three, or four varieties, and every of them of small price. Yet Astronomers, are not only unrecompensed for their pains taken to pleasure the common weal, but are called vain fools for their labours.  johnson 
What is the meaning of this word Mathematician, & what sciences be they which you call mathematical sciences, or mathematicals?  Worsop 
He that hath cunning in mathematical sciences, is called a Mathematician. And those learnings, or sciences, which may plainly be proved by true demonstration, apparent to sense, are called sciences mathematical. Philosophy, Logic, and certain other worthy doctrines, are not learned by most certain demonstration, but perceived by reason, and studious search. Most men wrongfully conceive, that certain unlawful practices attributed to Astrology are parts of the Mathematical sciences, which chiefly bringeth such great discredit, and contempt of Mathematicians, and of the pure, and single mathematicals. Some professing Astrology, impudently usurp the name of Mathematicians, as popish, and superstitious Priests, the names of Divines. As Papists abuse the word of God by joining Psalms, Epistles, Gospels, and other parts of the Scriptures to their superstitious, and idolatrous abominations: so have certain abusers of Astrology, intermingled their false, and vain doctrines with mathematical operations. They make the mathematicals cloaks to cover their wicked doctrines, as Papists do the Scriptures to cover theirs. Divines, and other learned men (ignorant of Mathematical sciences) and in manner all sensible men, perceiving how directly against the word of God, and how utter false, their prognostications of drowthes, floods, war, peace, sickness, health, plenty, scarcity, and such like are: and also the untruths, vanities, and superstitious curiosities in elections, and settings of figures: neglect, and condemn the mathematicals in general, because they think these vanities proceed from them, which is nothing so. It is daily seen, that evil disposed persons convert and abuse good things to wicked actions. As good wine to drunkenness, good meats to surfeiting, a weapon to murder, and robberies, marriage to debate, money to usury, the law to bribery, the word of God to heresy. Yet wine, meats, weapons, marriage, money, law, and the word of God, may not be rejected and contemned, because lewd disposed persons abuse them. In all age's Arithmetic, Geometry, and Astronomy, have been accounted liberal sciences: and must they now be disdained, and rejected, because some usurping the name of Astrologers have abused them? It behoveth our University graduates (who are, or aught to be seen in the Mathematicals) to uphold as much, as in them is, the seven liberal sciences. They know Plato forbade any to come within his school that was ignorant of Geometry. He called Arithmetic, and Geometry the two wings with which he raised himself into the heavens. He knew, that hearers ignorant of those sciences, could receive small profit by his lectures of Astronomy, or of sundry parts of Philosophy, and Logic. I have heard some Masters of Art say (which have been but meanly studied in Euclides Elements) that they should never have understood Aristotle his meaning in sundry places, if they had continued ignorant of certain his propositions, and demonstrations. A Doctor in Divinity, who was universally known amongst our learned men, to be a singular Grecian, and schoolman: confessed to the like effect, after he understooden by instruction the two and thirty, and seven and forty propositions of the first book. He would oftentimes say, that Logic, and Philosophy, could not rightly, and perfectly be understood, except some reasonable understanding of Arithmetic, and Geometry, were first had. And that those things which are of most difficulty to schoolmen, would be unto them as easy as the easiest, if they had any reasonable understanding in those sciences. Plato willeth that children should be exercised in numbers, and numbering. If that course were taken with them, they should (when they came to years of discretion) pass their affairs more understandingly, and with a greater facility than now they do. Some judicial Astrologers please well the fancies of many, because they will prognosticate good fortune unto them. Many Genethliakes (to please the vain, and incredulous parents) behight good fortune to their children. When any at years of understanding, is so fond that he will have his nativity cast: such Genethliakes will learn by one means, or other, the course, and some special chances, of his passed life. The declaring of them winneth such credit, that the foretelling of the other part to come is believed, and expected. Certain cozening mates are dispersed in many parts of this Realm, called of the people cunning men, or wise men. Some others as foolishly (though they think they speak wisely & aptly) call them Astronomers or Mathematicians. Silly maidens, & foolish wives, daily run unto these cozeners, to know how many husbands, & children they shall have, & how long their husbands shall live, & whether they shall leave them rich, or not. These companions will take upon them, to tell, and direct folks how they shall get again into their possession such goods as they make account to be lost, or stolen from them. Yea, they will appoint unto hazarders, and thieves, fortunate times, and hours to make their attempts. They say if thieves make their attempts when certain planets are in such and such aspects: that they shall not only obtain their purposes, but also it shall never be known that they were the robbers. Many of these wise or cunning men are so unlearned, that they know not any one definition, or principle of Astronomy, Astrology, or of any other part of the mathematicals. They know Astronomical characters of planets, aspects, and certain constellations: and perhaps so much of the vulgar Arithmetic as a quick witted youth will learn in xiiii. days. They have commonly an Ephemeris calculated by some learned ginger which is a necessary book for many good purposes. The Ephemeris is an almanac, or register, in which is showed among other things what aspects the Sun, Moon, Planets, and constellations every day in the year have each to others, as the vulgar Almanaches show where the sign is, and the age of the Moon. He that can tell when the Moon changeth, or where the sign is, by looking in the common Almanaches, may as well be called an Astronomer for that small cunning, as they for telling the aspects of Planets, and constellations only by looking in the tables of Ephemeridis. They have also certain Chaldean, Arabian, Assyrian, and Egyptian authors, as Haly Abenragell, Mizaldus, Hermes Trismegistus, Albumazar, Erra Pater, Abraham Avenezra, Abables filius Zaed, and such others. These authors presuming only upon their observations (for they can not prove their judgements by natural reason, nor by Mathematical demonstration) take upon them to foretell by the constitution of the heavens, otherwise said by the aspects of Planets, & constellatious: aswell what shall every year generally befall in human causes, as to every man particularly. The strange names of these Heathen authors, cause the more credit to be given to their blasphemous doctrines, and fables, according to these verses:  

If one affirm he learned it of a jew:  
The silly people think it must be true.   
It is not long since certain rogues (pretending to be jews, or Egyptians) took upon them to tell all sorts of people their fortunes by looking in their hands. The people were too simple to let some rogues hold them by the hands, whiles others of their company cut their purses, and picked their pockets. Those rogues told fortunes as truly, as such Genethliakes can. The forenamed authors, and others their ancient sectuaries, give such differing, and contrarious Astrological judgements upon every particular constitution of the heavens, that our Astrologians know not which of them to believe, or follow. The chiefest cause why our prognostications are so contrarious, is, for that some of our prognosticators writ after the opinions of some one of those ancient writers, and some of an other. And they writing different, or contrary the one to the other, of necessity some must hit right. Their judgements are as the blind man casteth his staff, peradventure hit, but most commonly miss. Seeing unlawful divinatory and judicial Astrology, are so direct against the word of God: such seducers of the people from steadfast trust, and full depending in, and upon the deity: such slander, & discredit, to the pure, and single mathematical sciences, to the great hurt of our common weal: because such excellent, and most needful actions as Mathematicians (if they were duly esteemed) would perform to the behouse of the same, are neglected, and left undone: it is to be wished, and we ought daily to pray, that it would please God, to stir the Queen's majesties heart, and the hearts of her honourable Counsel, to appoint the learned Divines, and Mathematicians of her Realm, to cull, and separate, these ill doctrines, from the good, and lawful mathematical sciences. The last Parliament a worthy statute was enacted, which forbiddeth all divinations, erecting of figures, and such like practices, tending to her majesties most royal person. It were greatly to the honour of God, and benefit of the Realm, if they were cut off altogether. The Mathematicals being greatly applied to sundry vain, and ungodly practices, and little thought on, or regarded, to be applied to such weighty causes in the common weal as most requisitely they ought: may be compared to a sweet, healthsom, & plentiful fountain, standing near a City greatly distressed through the want of such a spring, and yet the Citizens rather let it run into soul ditches, and marshes, in which it doth no good, than they will convey it into their City, to their great pleasure, and health. We greatly esteem artificial strangers, for their devices; and workemanshippes: but we respect not the causes why their doings be more excellent than ours. The instructions, that such artificers, or Mechanitians, receive from Mathematicians; is the chiefest cause why they exceed us. He is called a Mechanitian, that can make certain Geometrical figures, and do certain Mathematical conclusions, by practice and imitation, according to instruction from his master, or some learned man: but regardeth not the demonstration thereof, which is, the speculation of the art. Some frenchmen writ themselves the King's Mathematicians, because they have office, and stipend, from the King to maintain their charge, and studies. Others writ themselves public professor of the Mathematicals of such an University. Also every City in France, Germany, and Italy, hath one Geometer at the least, who hath office in the same, and stipend from the chamber thereof. Some great Cities have three or four such Geometers at the least. Masons, Carpenters, joiners, Painters, clockmakers, In ginors, and such others: unto whose faculties most needfully appertain the knowledges of making squares, rounds, triangles, and many other figures, with their transformations according to any proportion assigned: resort unto these professors and Geometers, to learn certain grounds, & chief mechanical rules. Such of them as enter so far into speculation, as that they understand Euclids elements, prove most excellent men. Few, or none such come into this country. Mechanitians will serve our turn, yea we think them most singular men, we are so gross, & unskilful in arts. As a man having but one dim eye, is of blind men thought to be well sighted: so most of us think Mechanitians great cunning men. Ignorance as I said, and the abuses and contempts, of the Mathematicals, are the chief causes, why insufficient landmeasers he suffered to carry away the doings by shows, and brags.  Watkins 
divinatory, and judicial Astrology, and every part of them, (as I gather by your talk) should be abrogated as unlawful.  Worsop 
You gather over largely of my talk. I spoke not against lawful Astrology: but against such as attribute unto Astrology, & Astronomy, sundry actions contrary to the word of God. Astrology (not contrary to the word of God) is a commendable knowledge. Philosophy proveth sundry influences, proceeding from the celestial bodies, to the terrestrial, (first observed by Astrologers) against which, I will not rashly speak: But refer you rather to learned Melanchton that famous Divine, who calleth them Epicureos Theologos that impugn the lawful science of Astrology. These matters are so far above common understanding, that we will cease to talk any further of them: referring reformation where occasion serveth, to magistrates, and though godly learned. Master john Dee in his mathematical preface, learnedly showeth what Astrology is. In that preface you shall find, how some over reach: that is, unlawfully attribute more unto that science, then duly appertaineth thereunto.  johnson 
You found fault with me of late, for saying mine head was so gross, that I should never have devised such a proof as you made, when you proved that a close entrenched within a round ditch of viii. score perches, was greater than a close entrenched within ditches of the like number of perches, laid square. You seem to dislike that men should either show their cunning, or confess their ignorance.  Worsop 
I found not fault with you for confessing your ignorance, but because you showed yourself despaired of conceiving that, which every reasonable creature may conceive, if he will study Arithmetic, and Geometry. Neither do I find fault with the other sort for showing such cunning as they have: but for taking upon them more than they are able to perform: namely in so weighty a matter as land measure. Ye must not think that these comparisons of figures, & these proofs are my devices. My learning extends not to add a devise unto Geometry. I have gotten my small knowledge by instruction, & study of learned authors. Who so maketh any mathematical devise ought to prove the same in all parts, by Euclids elements: if he can not so do, his devise is but a guess, & therefore not to be allowed. But if he can prove it by mathematical proofs, than you may easily perceive that the like hath been heretofore devised, because he findeth rules for all the parts of his devise. As a Grammarian that is able to prove by the rules of Grammar that his Latin is true, must needs grant that the like Latin hath been spoken in times passed, because he findeth rules therefore: so if a man have devised any thing in Geometry that he can prove by the elements of that science, he must needs grant that the like devise hath been heretofore, or else those rules could not be extant. Most men when they see heights, depths, lengths, or distances truly taken, engines devised that with small strength draw up, & hold things of huge weight: manifest proofs why a close lying in such a fashion, containeth more ground than if it lay in such a fashion, although their circuits be equal: with many such like: have in great admiration the wit of him that performeth such actions. They think men attain unto these knowledges only by their own devise, and ingeniousness: and not by mathematical studies, and practices. They refer all to natural wit, they have no respect to art, nor think thereon. Every sensible man that will study Euclydes elements, and give himself to practise, may with as great ease understand the Mathematicals, as any of the other sciences liberal. The grounds, & reasons of Mathematical operations be so plain, so simple & so easy to be perceived after some reasonable instruction, & practise: that not any sensible man hath just cause to despair that he shall not attain those knowledges, for children about the age of xii. years, by those means may easily learn them, they be so plain. After a man is some what entered, he doth greatly marvel to see such weighty effects, proceed from such plain and simple rules. Every first entrance into the study of any of the sciences liberal is hard. How dry, hard, and unsavoury seem the rules of Grammar until ye come to construction, and proving by the Grammar rules▪ every word of the sentence to be in congruence. But when you can prove the congruence, then great pleasure is received from that, which before seemed so hard, and unsavoury? Even as a man must know, and understand those dry rules before he can attain the knowledge of the Latin tongue, so must he know, and understand, the definitions, and propositions in Euclides elements, and how to apply them to his workings, before he should be allowed a sufficient practitioner of the mathematical part, or charge of Astronomy, Perspective, cosmography, geography, Navigation, Martial exploits, survey of lands, mensuration of solides, architecture, engines, drenings or mountings of water, and many other faculties. If in the practice of these forenamed sciences, the mathematical part be defective: such practice may be compared to a natural living body, that hath some principal member or members, as arms, or legs, so benumbed, taken, or shrunk up, that they stand not in any stead, but hang on like dead things. The mathematical part is the head, or chief part of some of these sciences. If the powers of the head be stopped, or taken away, the body serveth to small purpose.  Peter 
I perceive that Euclides elements is a book of mathematical rules, and that by the knowledge of those rules mathematical operations are performed, even as the Latin tongue is attained by the knowledge of the Grammar rules, or reading by the knowledge of the alphabet, and the other accidents appropriate to that science.  Worsop 
You say truth. The elements of a science are the first, chief, and principal rules of that science: whereof all the operations of that science take their beginnings.  johnson 
Are there not other authors that have written those rules, as learnedly as Euclid, because still you nominate him?  Worsop 
There is not any comparable to him. For all his propositions are so fully, plainly, truly, orderly, and learnedly proved: that all singular, and learned writers of the Mathematicals since his time, have been content to be tried by his elements, so excellent an author he is, and so plain, pure, and simple is the subject of his matter, that he leaveth not any thing doubtful, or referreth you to a quere. These be the causes why learned Mathematicians, make the proofs of their doings by his propositions: and rely upon him as upon a most sure foundation. There is not any writer of human causes of whom so boldly a man may say, (Ipse dixit) as of Euclid, so free is he from errors and controlments.  Watkins 
In what age lived Euclid? You said he is a Greek author. Chief officers in martial affairs, measurers of land, masters of ships, ingenors, dreyners, mounters of water, and divers other arts men, of whose faculties (by your saying) the part mathematical is a principal member, understand not for the most part the Greek tongue. Few understand the Greek tongue but University men: would you not have any chief professors of these faculties but graduates?  Worsop 
Euclid was living about xl. years before the Reign of Alexander the great as Suydas chronicleth. Plutarch in his treatise of the life of Plato saith that Plato went from Athens to Megara, when he was xxviii. years of age to learn Geometry of Euclid. Some of Socrates his scholars gave themselves chiefly to the studies of moral, and natural Philosophy: as Plato, Xenophon, and Antisthenes. Other some to the Mathematicals, as Aeschines, Phedon, Euclid, and Aristippus. I have seen Euclides elements in the Latin tongue, in ten sundry translations at the least. They are also extant in French, Italian, Spanish, high Almane, & Dutch. But in the English tongue far exceeding all other impressions, most learnedly are they extant. Therefore our professors of faculties may learn and understand him sufficiently to discharge their functions, although they understand not the Greek. Graduates that perfectly understand the Greek tongue, and the other sciences (by which they receive their degrees) are without doubt fittest to be public readers, and instructors of the Mathematicals (although they should teach in the English tongue) and although the Greek terms are expounded in the English translation. They can best show the etymology, and derivations of words, and terms, the method, and other parts of learning.  
Peter Who translated him into our tongue?  Worsop 
Master Henry Billingsly one of her majesties chalmers for the port of London.  Peter 
The translation is made by a very honest Gentleman.  Worsop 
Even from his childhood I have heard from others, and noted to myself, such his great pains taken in study, his discretion, and such his virtuous inclination, and impressions, that my mind always gave me, some notable benefit to his country would proceed from him.  Peter 
How long hath this English impression been extant?  Worsop 
Ever since the year of our Lord God 1570. Great pains was taken at the time of the impression by M. Doctor Whitehead a profound learned man, and M. john Dee, who is accounted of the learned Mathematicians throughout Europe the prince of Mathematicians of this age: as Cicero named Cratippus the prince of Philosophers in his age. This M. Dee hath put unto these englished elements, many scholies, annotations, corollaries, and expositions which give great light, and facility to the understanding of them. Also his mathematical preface unto these elements, is a work of such singularity and necessity to all students of the Mathematicals, that I wish them to make it a manuel.  john. 
I pray you let us see some figures representing straight hedged closes just viii. score perches about, that shall contain more than x. acres. You said you could lay closes in divers fashions that should contain more than x. acres, and yet but viii. score perches about We have seen it proved in the round, now we would see the like proofs in some with straight hedges.  Wor. 
I will show you some examples, by certain regular figures. I call those figures regular, whose sides are equal the one to the other, and whose angles also are equal the one to the other. Every side of the five sided figure a. b. c. d. e. is xxxii. perches in length, as ye may try by the scale x. five times xxxii. make 8. score. It is manifest to your eye that the said figure is greater than the pricked square f. g. h. i. Every side of the square is xl. perches, and therefore as ye have seen by former proofs, it containeth x. acres: but this equilater, and equiangle pentagon, or figure of five sides, containeth eleven acres, and five perches.  
 diagram of a pentagon superimposed on a square  diagram of a hexagon superimposed on a square The figure k. l. m. n. o. p. is an equilater, & equiangle hexacon (that is to say a figure of vi. equal sides, & of vi. equal angles. Every side thereof is 26. perches, & two third parts of one perch. A close lying in such fashion, containeth xi. acres, an half, & 8. perches. And yet his 6. sides cast together, make but 8. score perches, and so many are the sides of the pricked square. q. r. s. t. whose content is but x. acres.  
 diagram of an octagon superimposed on a square The figure v. y. x. z. a. b. c. d. is a regular octogon, every of his sides are xx. A close lying in such fashion containeth xii. acres, & x. perches. And that close also is but viii. score perches about, & so much is the pricked square e. f. g. h. The more sides a regular close hath, the greater is his content. For the more sides the nearer he draweth to a circle: and every circle containeth more area within him, than any other figure of many straight sides can contain, if their circuits be equal in measure.  
 diagram of an irregular six-sided close superimposed on a square As all regular figures of more sides than iiii. must always contain above x. acres, if their perimetrie or circuit be just viii. score perches: so if they be irregular, that is to say, if their sides and angles or any of them be unequal, they may contain less than x. acres, as this close i. k. l. m. n. o. which is but ix. acres & an half, & therefore less than the square p. q. r. s. which containeth x. acres, but much less than the former equilater, and equiangle six sided figure, whose content is xi. acres, an half, and viii. perches. The nearer any figure cometh to regularity, the greater is his content. Ye now evidently see that land cannot be truly measured if the measurer be ignorant of Geometry: for if his knowledge extend not further then to lay head to head, and side to side, or to measure the whole circuit, and to cast the same into four equal parts: or to make cross measures making the one the head, and the other the side, most of his contents will be false.  Watkins 
We see evidently that the proofs which you have made are true, and that common measurers make much false work: but seeing the statute for landmeasure doth not mention any thing of angles, circles, or other Geometrical figures, but only of length, and breadth, most men think that we are to respect our statutes, & to follow them: and not to follow the new begun professors of Geometry: as though they were wiser, and knew better what belongeth to landmeasure, than the wise, learned, and experienced men of the Parliament in those days. It seemeth by the ancient, huge, and sumptuous buildings, and by the acts for all manner of measures, and assizes, that as skilful Mathematicians were in those days, as in these. The statute saith when an acre of land containeth x. perches in length, it shall contain xvi. in breadth. When xx. in length, than viii. in breadth. When xl. in length, than four in breadth. Therefore if I measure the side, and the head, which are the length, and the breadth, I measure according to the statute, and other kind of measure then the statute appointeth the people desire not.  Worsop 
That statute is well, and rightly penned, but of many (ignorant of the Mathematicals) it is misunderstoode. Though ye find not terms of art therein, but usual words, yet those exact appointments, and reductions of breadths to every length in that statute nominated, could not be done but by a Mathematician. And although some of those breadths be untruly set down, yet they of understanding perceive the faults to be either in the Printer, or in the corruption of their copies. The hardest, and most cunningest reductions are truly printed: but certain easy reductions are printed falsely. The varieties of lengths, and breadths in that statute expressed, tend to drive men to learn, and consider, what the measure of an acre of land is. I told ye not long since that viii. scorrsquare perches make an acre. If ye have a piece of ground, that is xx. perches long, and 8. broad, lying square like to the figure a. b. c. d. such an enclosure is an acre of ground, for viii. times xx. is viii. score. But closes in fashion like to the figures e. f. g. h. or r. s. t. v. are but three roods, though every of the heads e. h: f. g: r. v. and s. t. be equal in length to the head a. d. or b. c. and every of the sides e. f: g. h: r. s. and v. t. equal to the side a. b. or c. d. For every of those vi. heads are 8. perches broad, & every of the vi. sides xx. perches long, as ye may try by the scale of four. The inward inclination or bending of the sharp angle e. h. g. abateth two perches in the breadth of the figure i. k. g. h. which figure i. k. g. h. is equal to the figure a. b. c. d. and therefore that figure e. f. g. h. is equal to such a figure as is vi. perches broad, and xx. long: namely to the figure m. l. g. h. which is but three roods. For vi times xx. make vi. score, and vi▪ score representeth three roods. The line q. o. is the breadth of the figure e. f. g. h. and not ●. h. as the ignorant of Geometry erroneously suppose. And the line v: x. is the breadth of the figure r. s. t. v. one demonstration serveth to them both. Breadths must be measured straight, and upright, called of Geometers, perpendicular, or rectangular measure▪ as all the lines in the figure a. b. c. d. are perpendicular lines, for they stand upright upon the line c. d. neither bending inward making a sharp angle as the line ●. h. doth with the line h. g. nor falling outward making an obtuse angle as the line r. v. doth with the line v. t. The line n. o. in the figure e. f. g. h. lieth not uprightly as lines of breadth should: but slopingly, for if it were laid or measured uprightly, it would reach to the line i k. as ye may try by the upright line o. p. which is equal in length to the said slope lines. n. o. or. e. h. The eye of the cunningest Geometer that is, cannot exactly judge when he measureth land, upon what parts of hedges perpendicular measure, that is to say measures of breadthes must fall, but by the help of some geometrical instrument. Ye may by the example of the three figures whose heads are viii. and sides xx. try and find that the like, and as great errors may befall in every of  diagrams comparing the areas of rectangles and parallelograms  square ABCD the other limitations of breadth, and length in the said statute specified, as in these. An acre of ground included in a quadrate) that is to say) within iiii. equal right anguled sides, or bounders: as the square a. b. c. d. must have every of those sides to be in length xii. perches and an half, two. foot, iii inches and an half, and the fiftieth part of an inch. These▪ iiii sides added together make▪ fifty perches and an half, xi. inches, & the twelfth part of an inch and somewhat more, as ye may try by the scale of four. That length cast into a round close, like unto this circle▪ e. f. g. h. and measured from east, to west, here represented by . e g. and from south to north represented by . f.h. (as many erroneously use to do) taking the one measure for the length the other for the breadth: they shall produce by that way of measuring one acre, and an half, and half a rood, which circuit in square form maketh but one acre. Such a round close by true measure is one acre, one rood, and three perches. Therefore such a round close by that manner of cross measure is made one rood and xvii. perches more than it ought to be: and by casting such a round circuit into a square, they  circle EFGH superimposed on square make the land less than they ought, by one rood, and three perches. The words, and meaning therefore of the statute certainly is: that in what fashion soever grounds do lie, that just viii. score square perches must always make the acre. We must not think so worthy a stat●●… for so weighty▪ a matter to be made upon so weak a foundation or consideration: that the meaning was to allow of measures so greatly disagreeing each from other, and so greatly swerving from the troth sometime by excess, and sometime by want. There can be but one true content of a piece of ground, which cannot allowably be found by any measurer, but by such a one as can prove the same by the elements of Geometry.  
 diagram comparing rectangle and trapezoid The greater number of measurers make their measures, by laying head to head, and side to side, as though all closes lay in right angles. By which doing I may compare them to a shoemaker that hath two or three hundred pair of shoes in his shop made all upon one pair of lasts, For some feet his shoes must needs be too large, for others too little, for some by chance they may be fit. Suppose there be a square close, having either of his sides xii. perches long, and either of his heads vi. perches broad like to the figure a. b. c. d. How much ground doth such a close contain?  Peter 
Six, twelve times, is lxxii. that is vi▪ s. If it were viii. perches more, it were half an acre.  Worsop 
Suppose there be an other close, the one side whereof is xxi. perches long, the other but xii. and either of the heade●●● perches broad, lying in fashion like to the figure e. f. g. h. How much doth such a close contain?  johnson 
Xxi. and xii. added together make xxxiii. The half thereof is xvi. perches, and an half. These xvi. and an half I take for the length, & taking vi. for the breadth, I find that xvi. d. ob. six times, is viii. s. iii. d. which representeth half an acre and nineteen. perches. If it were but one perch more, it were half an acre, and half a rood. I see that three sides of the one figure are equal to three sides of the other: and that their difference is only in one side: for the heads a. c. and b. d. of the one figure are equal to the heads e. h: and f. g: of the other figure: and the side c. d. is equal to the side h. g. but the side e. f. is longer than the side a. b. by ix. perches, for the one is xxi. and the other but xii. therefore the longer sided close containeth more ground than the shorter by half a rood and seven. perches. For if ye take lxxii. perches, the content of the figure a. b. c. d. from four score and nineteen, the content of the figure e. f. g. h. there will remain xxvii. perches, which is half a rood, and seven. perches. Ye see before your eyes that the figure e. f. g. h. is on the one side almost as long again as the figure a. b. c. d. if it were three perches longer, it were full twice so long as the other.  Worsop 
Measurers' ignorant of Geometry deliver up such contents. Sundry buyers, partners, exchangers, lessees, and takers of land as ignorant as they, content themselves with such measures. When the blind leadeth the blind, they fall both into the ditch. Ye have great respect how much the close e. f. g. h. is longer than the close a. b. c. d. but ye respect not how much the said close a. b. c. d. is broader than the other. The shorter close a. b. c. d▪ by reason of his square lying containeth seven. perches more than the longer. But for the easter proof I will admit it to be but vi. perches, as may be  diagram with trapezoid superimposed on rectangle to demonstrate the calculation of area for each proved by this figure a. b. c. d. e. f. g. h. i. The pricked square a. b. c. d. in this figure, is equal to the other figure a. b. c. d. And e. f. c. d. in this figure is equal to the other figure e. f. g. h. And the two triangles e. g. c. and h. f. d. which are parcel of the figure e. f. c. d. are equal the one to the other. The pricked triangle f. i. d. is equal to the triangle h. f. d. therefore the square h. f. i. d. is equal to the two triangles e. g. c. and h. f d. Therefore also the figure g. f. i. c. is equal to the figure e. f. d. c. The figure g. f. i. c. is xvi. perches and an half in length, and four in breadth, which make v. s. vi. d. but the figure a. b. c. d. being twelve in length, and six in breadth, cometh to vi. s. therefore the figure e. f. c d. is less than the figure a. b. c. d. by vi. perches. So that by your way of measuring ye make that viii. s. iii. d. which should be but v. s. vi. d. which is all one reckoning as if ye made that three acres, which in troth is but two. For viii. s. iii. d. is equal to v. s. vi. d. and to the half thereof which is two. s. ix. d. Those two sums cast into one, make viii. s. iii. d. You said if the side of xxi. perches in length, had been xxiiii. that then it had been double to that of xii: and you suppose that a ground so sided, would be greater than that, whose side is xxi. wherein you are greatly deceived. It is impossible to include any superfice or quantity of ground within a close having either of the heads vi. perches, the one side xii. and the other xxiiii. For the two heads vi and vi. and the side xii. cast into one sum, make but xxiiii. Therefore the side xxiiii. laid unto them driveth the other iiii. sides to a straight line: not suffering them to make any angles, so that they be as it were two straight hedges the one standing upon the other, not including any quantity of ground. Two right lines cannot include a superfice by  diagram of a trapezoid the sixth petition of the first of Euclides Elements. The close a. b. c. d. having all his angles right, is greater than any other close can be, if any one side of his length be made more than xii. For the obtusenes or declination of angles diminisheth quantity of ground, as ye have seen by the other figures, and more plainly may see by this figure m. n. o. p. which hath three of his sides equal to three sides of the figure a. b. c. d. but the fourth side is xxiii. perches and an half.  
Measurers' ignorant of Geometry, commit the like errors in measuring of triangular, or three cornered closes. Most men think that a three cornered close whose sides are thirty. xl. and lxv. perches, doth contain more ground than an other three cornered close whose sides are but thirty. xl. and l. because the side lxv. of the one figure, is longer than the side l. of the other figure, by xv. perches. But the longer sided close, namely the triangle p. q. r. is less than the triangle s. t. v. by one acre, half a rood, and three perches. For s. t. v. the shorter sided close, containeth three acres, and three roods, where the longer sided namely p. q. r. containeth but two acres, and an half, & xvii. perches.  Watkins 
I am now fully resolved that they which measure with the pole, or line, (if they be ignorant of angles) do they know not what, and that they greatly abuse them for whom they deal.  johnson 
The world was merrier, before measurings were used than it hath been since. A tenant in these days must pay for every foot, which is an extreme matter. I know surveyors that use not measuring when they make their surueies, which fashion I like best.  Worsop 
There is greater cause of good mirth, and joy, in these days, than was in those you speak of. We have the light, and freedom of the Gospel, so that our souls may joy in the true salvation. We have a wise, and merciful Prince, who as God his good instrument hath all the time of her Reign preserved us from wars, spoils, and heavy taxes. If your meaning be that smallness of rents, and cheapness of victuals make the merry world: then was that world merrier when the statute for land measure was first made, and duly executed: than it hath been at any time since the neglecting of the same. We may find in our Chronicles, that in those days a fat ox was commonly sold for a noble, a sheep for vi. d. a quarter of wheat for two. s. Most tenants that take land after the common measuring pay for more than they should. Therefore if the tenant had true measure, he might live merrier than he doth. Seeing most Landlords covet to let their grounds to the uttermost, and most tenants seek to sell their wares at the highest prices: it is very requisite for both sides, that the land be truly measured. True measure is not extremity, but good justice. By the Laws of our Realm, and by common reason, such like equality, and troth of  diagrams of triangles PQR and STV, separately and overlaid measure in landletting ought to be between Lord and tenant: as is between buyers and sellers of cloth, silks, grain, liquors, stone, timber, or of any other commodities for which our statutes have appointed standards, and assizes. I know sundry honest gentlemen professors of survey, that many times omit measuring. survey consisteth upon three principal parts: that is to say the Mathematical, the Legal, and the judicial. Unto the Mathematical part belongeth true measuring, which is Geometry: true calculation of the thing measured, which is Arithmetic: and true plaiting, and setting forth of the same to the eye, in proportion, and symmetry, which is Perspective. To the Legal part belongeth the knowledge of keeping courts of survey, of the diversities of tenors, rents, and services, likewise how to make terrors, rentals, particulars, suit rolls, customary rolls, & also how to engross books, with many other things appertaining to that part, as may appear in the statute, called Extenta Manerij, but more at large in the treatises of M. Fitzharbert, and Valentine Leigh touching survey. The judicial part consisteth upon the consideration, and knowledge of the fertility, vesture, situation for vent, health someness, commodiousness, discommodiousnes, and such like of every kind of ground, building, and increase, in his own nature, & kind. Some make apportionation, & valuing a member of this part, other think them more worthy the name of a principal. I suppose them to be in common to all the three parts. It is impossible for a surveyor to make a true value of lands, except he first know the tenure, rents, custons, & services to them appertaining in their proper natures, & kinds. He must have great respects to the part legal when he valueth. And also as great respects to quality, and quantity, which are the parts judicial, and Mathematical. Quality, and quantity be inseparable companions, they must of necessity be joined together in apportionation, & valuing. Who can tell, what a cloth, or a piece of velvet is worth if he be ignorant how much they contain by measure? A skilful man knoweth by colour, fineness, making, strength, & other points judicial what every yard of them is worth: but he can not value them, except he also know how many yards either of them containeth. So is it of grain in heap, & of liquors, of which the value of a bushel, or of a gallon may judicially be rated, but the value of the whole cannot be known, till true quantity, that is, the number of bushels & gallons be also known. Some surveyors use not to measure, because they are ignorant of the parts mathematical: but refer the measuring to such, as take upon them the knowledge thereof. They show themselves honest, in not taking upon them beyond their skill. Many are skilful in the part Legal, and in many points of the part judicial, which understand little in the parts Mathematical: and therefore they deal not further than their knowledge extendeth. Sometimes also the Lord desireth not further information then in the parts Legal, and judicial: because by his evidences, records, and accustomed nomination what number of acres every ground containeth he is satisfied touching the quantity. In cases of partition, exchanges, buyings, sellings of land, woodsales & such like: exact, & true measure are most requisite.  Pet. 
Two gentlemen (both my very friends) are very desirous to make an exchange. The one hath CCC. acres lying very near unto the mansion house of the other. Lands of like value (which lie not passing 4 miles from those CCC. acre's) should be given for them. They have desired me to find means how this exchange may indifferently be made. In less than two. days it would be dispatched. If I may have your help, you shall have good cheer, be very welcome to them both, and pleased for your pains. We will all bear you company, and help you the best we can.  Wor. 
When opportunity on all sides serveth, I will gladly make an equal exchange for them. If the grounds be so great as you say they are, it is not possible to measure, and rate them in so short a time. As I have divers times measured about CCCCC. acres in a day, so in some other days, having had the like time, & help, and as fair weather, & taking as great or greater labour I could not over come xl. The forms & fashions of grounds are the chief causes why measures are either long or speedy in doing. Many grounds that lie long, & narrow, by an indenting, crooking, and winding brook side, cannot truly be measured, without great labour, & much expense of time. Many such grounds have I measured (the ritchnes whereof hath been such) that many men would have given above xx. pounds for the inheritance of every acre thereof. When the weighty buisinesses of partitions, exchanges, & sales fall between men: it behoveth that the measurer have good skill, and that he use great diligence, exactness, & circumspection in his measurings. If he should misdo one acre in xx. in such kind of grounds: it were above xx. li. loss to the one side, & an unlawful gain to the other: which is a weighty matter to the soul, & conscience of him that either ignorantly; or negligently shou●●eth up such weighty buisin●sses. It is impossible for measurers' ignorant of Geometry, truly to measure such crooked grounds. They can not miss so little as one in twenty. Many men (rather than they would wrongfully lose half an acre of their inheritance) would spend an hundredth pounds in the law for the maintenance of their right. Many times through the ignorance of unskilful measurers, they lose scores of acres: yea sometimes in great grounds hundreds. But that which the eye seethe not, the heart ruth not. The blind eat many flies they know not of. Many think that a Geometer can measure land in shorter time, than a common measurer that measureth only with the pole. Unskilful, and unlearned measurers (for the most part) make more haste then good speed. The ignorant think if a Geometer but once look through the sights in his instrument, that thereby he knoweth presently how many acres the ground containeth. True Geometrical measure asketh longer time then only running over a ground with a perch, or a line. Great cheer, and company keeping, binder much in the time of surveying. A good surveyor will avoid them. Diligent and exact surveying so fully occupieth both the body, and mind of the whole man, as he can have small leisure for talk, or recreations.  johnson 
I know some that will justly tell, how many acres every parcel of ground containeth only by the view of them: not using either pole, or instrument.  Worsop 
divers surveyors by their great experience, and by the help of deeds, terrors, particulars. jurors, and report of the inhabitants, can give a great guess at the true contents of lands: and thereupon will set down their judgements, which manner of surveying differeth from exactness. He that is much exercised in the tals of money can give nearest guess how much bags, and heaps contain upon the view of them. Likewise they which are greatly exercised in buying of pieces of velvets, silks, and : can by their bulks give sometimes near guesses at their contents: but yet their guesses are uncertain, and most commonly untrue. The records of such conjectural surveys, ought not to be produced as good, and sufficient evidence for proof of the quantity.  johnson 
Is then a Mathematician the best surveyor, ought not any to be admitted unto survey but he?  Worsop 
He that understandeth all the parts of survey, best deserveth to be admitted to that function. There be divers Mathematicians that understand. Geometry, Arithmetic, and Perspective sufficiently for the Mathematical part of survey: that understand little in the parts Legal, and judicial. Also there be divers that understand the parts Legal, and judicial, that understand little of the Mathematicals. Therefore when partitions, exchanges, buyings, and sellings by the acre, are to be made, they to whom these matters appertain, if they will have their businesses exactly done: should get such a one as understandeth all the parts of survey, or else two who by their knowledges joined together are able to make a perfect survey. If defection be in any of the three parts, the residue of the survey is little better than labour lost, such great errors will ensue thereof.  Peter 
I would feign be acquainted with some that understand all the parts of survey perfectly. You know many such.  Worsop 
I know very few such. Ye have heard of M. Thomas Digges, he is very skilful in all the three parts. All surveyors are greatly beholding unto him, for setting forth three books of Geometry, in which he learnedly teacheth Geometrical measurings. For the part mathematical all good surveyors own unto him great reverence, because he is a lantern unto them, aswell in the speculation, as the practice. He and M. Leonard Digges his father have been the first, and chiefest that have given light, and taste of this necessary part of survey in our vulgar tongue. M. Thomas Owen one of the counsellors of the City of London (of any learned man towards the Law) best understandeth all the parts of survey as I have heard from them that be skilful, and for aught that ever I could perceive otherwise. He well understandeth divers tongues, and is so well furnished of the best authors in divers languages, that he hath gotten much and rare knowledge from them. M. john hills an Auditor (of any man whose learning and practice I know) in my judgement is the perfectest, and readiest man in all the parts thereof. He understandeth Arithmetic, Geometry, and perspective, both speculatively, and practically singularly well. His knowledge and daily exercise of Auditory, mixed with the study of the common Laws, & his great search and practise of the part judicial, have brought him to a profound judgement and knowledge. M. Fardenando Malyn, and M. john Malyn his brother can survey singularly well. They understand the Mathematical parts perfectly, and are of good study, and great practice in the other. M. Fardenando is the readiest man in the field that ever I saw. M. Deuhurst, M. Grent, & M. Godfrey can survey very well. M. Godfrey hath very good knowledge in Perspective. I assure myself that many others are very skilful, and can do very well in all the parts thereof: but I can not report the skill of any upon mine own knowledge, saving of these.  Peter 
Me thinks many should give themselves to be skilful professors of survey: and to understand the knowledge, and practise of all the parts thereof. What be the causes why there are so few surveyors, that can sufficiently survey?  Worsop 
Such sufficient skill as a surveyor should have, before he ought to execute that office, can not be attained but by a longer study, and a greater practice, then is commonly thought to be had thereto. It is also one of the chargeablest studies, that one can enter into. There are few that will take the pains to give perfect instructions to young beginners, & to set them in the right course of study and practise, which is a great cause of much vain expenses. The Mathematical part seemeth so dry, and hard, at the first entrance, that some (as wearied) give over before they have passed half way. Also measurers ignorant of Geometry make quicker dispatch, than the learned and skilful can: which so pleaseth the ignorant because it diminisheth present charge, that they therefore little regard him, that maketh true measure, which in troth is penny wisdom, and pound foolishness. Also through lack of good order in this weighty matter, bragger's that by show of their instrument win credit, are sooner retained by the ignorant than a sufficient man. Some think that to be a great piece of cunning which in deed is either an error, or but a trifle. The benefit also to the skilful is so small, and the charge to be in such readiness as they ought so great, that they give over as wearied, leaving the matter to ignorant dispatchers, who stick not at any thing. If the learned and skilful, did use conferences, & devise ways, how these inconveniences might be redressed, true knowledge advanced, and ignorance depressed, as the learned in other professions do: great utility would ensue unto our common weal thereby. It is a lamentable thing that so great a mischief (as the ignorance of true landmeasuring bringeth) hath so long been spied, and that no remedy is therefore provided. Every man knoweth that land is our riches in the highest nature, and yet true surveying, and valuing thereof is shoufled up, as though it were a matter of small importance. If a receiver should in stead of an hundredth pounds usually receive either too much or too little, though it were under forty shillings, and the oversight but in money, his Lord, if he knew it, would think him very unskilful and negligent in his office, and quickly have an evil opinion of him therefore. But if ignorant measurers miss x. acres in an hunderth (whose value is commonly above forty pounds) they are not evil thought of therefore, though it be to the loss of so much inheritance. Ignorance beareth such sway, that for lack of good order these chances daily happen.  Peter 
How may a man when he lacketh a good surveyor, know him that is sufficient, from him that is insufficient?  Worsop 
Rules can hardly be given unto the ignorant of survey, how to choose one that is sufficient. If surveyors were in such order (as by good reason they should, the weightiness of their charge considered) then as the learned in other professions are known from the unlearned, so might they. Not any student of the Law can be admitted to the bar, except by the benchers he be thought sufficient. None can be admitted in the Universities to any degrees of learning but by the allowance of ancient graduates of the same profession. If the skilful in the parts Mathematical, Legal, and judicial would friendly, and singly join together to reform, and instruct each others, and to reduce survey to a perfect order: without doubt many which now understand but parts, and pieces rightly: but more things erroneously, or lamely, would in short space prove sufficient men. Also excellent good ways for the best instruction of young students thereof, would soon be had. They that enter themselves into the study of this science, and would persevere therein, are driven to go so blindly and confusedly to work, because they know not where to have right instructions, that they fall into many errors, and receive great discourages.  johnson 
Me thinks the number of surveyors in these days is too great. Gentlemen know well enough how to let their lands to the uttermost. They have cunning enough for that matter, they need no more help from skilful men.  Worsop 
Though some landlords deal over hardly with their tenants, the fault thereof is not to be attributed to surveyors. Good & skilful surveyors will reform those enormities, and not augment them. The common people for the most part are in great fear when survey is made of their land. If the survey be skilfully made, it reformeth over small measures, and excesses of rents. None can so well tell what is indifferent between Lord, and tenant, as the skilful sureveyor. Some part of his charge consisteth upon judgement, therefore seeing he is in some respects a judge: if he be godly, & justly minded, he will not exact upon the tenant, although the Lord please him for the survey taking: but will measure, and value, according to equity and indifferency, aswell for the discharge of his conscience, as the preservation of his credit. We are now come to the towns end, we will talk more of these matters an other time.  
FINIS.