A DISCOVERIE of sundrie errours and faults daily committed by Lande­meaters, ignorant of Arithmetike and Geometrie, to the damage, and preiudice of many her Maie­sties subiects, with manifest proofe that none ought to be admitted to that function, but the lear­ned practisioners of those Sciences:

Written Dialoguewise, ac­cording to a certaine communi­cation had of that matter.

By Edward Worsop, Londoner.

Euery one that measureth Land by laying head to head, or can take a plat by some Geometricall instrument, is not to be accounted therefore a sufficient Landmeater, except he can also prooue his instruments, and measu­rings, by true Geometricall Demonstrations.

AT LONDON, Printed by Henrie Mid­dleton for Gregorie Seton.

ANNO 1582.

TO THE RIGHT Honourable and his singular good Lord, Syr William Cecill, Baron of Burghley, Knight of the most noble order of the Garter, Lord high Treasourer of England, and one of the Lords of her Maiesties most Honourable priuie Counsell.

AMong the number of our worthie acts of Parlement (right Honoura­ble & my most singular good Lord) the statute of land measure is of great importance, and equitie. Certaine persons (wanting sufficient know­ledge for the executing of that sta­tute) notwithstanding intrude them selues into that weightie function as sufficient. Sundry of their false rules, and vntrue waies of mea­suring, as also sundry true rules (by some of them) falsely apply­ed, in this small treatise are discouered. Mine intention was not in the time of penning thereof, nor long since, to publish the same: but of late vpon great vrging, and persuasion of him (at whose request I did write this talke) and of certaine other my friends and acquaintances: I yeelded at their requests to the pub­lication thereof. The necessitie, and worthines of the matter re­quire learned and exquisite ordering, which I must resigne to be performed hereafter by the learned. By this treatise I may bee likened to a broyled founder, whose onely charge is to make mixture of mettals, and to roughcast them. The filing, gra­uing, and polishing, are done by other artificiall workemen, who goodly set out the same to the eye according to the riche­nes of the metall. I, a simple man among the common people, [Page] haue set forth this discourse to their behoofe, by the playnest waies I could deuise, and for their easiest vnderstanding: Sun­dry learned workes of the Mathematicals (for such as vnder­stand or affect learning) are extant in our vulgar tongue: as Euclide, the workes of Doctor Record, of Master Leonard Digges, of Master Thomas Digges, and of some others. But because these learned bookes can not bee vnderstoode of the common sorte, and that they be as iuels, and riches, sha­dowed or wrapped vp from their sight: I haue thought good by a plaine and popular discourse, to laie open vnto the vnderstanding of euery reasonable man, the necessities and commodities of those singular workes and knowledges, and the great abuse, inconueniences, and iniuries, the common weale susteineth by crediting and reteyning of ignorant doers, and neglecting of learned and skilfull writers, and practisio­ners. As wise and learned men, when they speake vnto a sim­ple and vnlearned man: frame their speache to his vnderstan­ding, which in the like cause they would vtter otherwise if they spake to one learned: so must some man to the behoofe of the common weale manifest those enormities popularly, that the hurt which ignoraunce bringeth in this weightie mat­ter may vniuersally bee knowen. I (although farre vnmeete to take so weightie a cause in hande) haue aduentured for the discharge of my conscience, and my duetie to the common weale: to manifest (as I best could) certaine great inconueni­ences which the common weale daily susteineth by vnlearned practisioners, humbly submitting my selfe where reformation is needeful, to the correction of the learned. And for because it is vniuersally knowen, that the continuall application of your noble hearte and minde, is to the furtherance of learned know­ledges, of equitie in causes, suppressing of ignoraunce, and to the commoditie of the weale publike (whereof your Honour [Page] is a principall piller) and for that your Honour hath been mine especiall good Lord, I doe presume (as enforced thereto by duetie) to dedicate vnto your Honour this small treatise: most humbly requiring pardon for such my great boldnes, as also that your Honor would vouchsafe to receiue the same into your noble patronage.

Your Honours most humble to command, EDWARD WORSOP.

The coppie of a Letter sent with this Booke.

TO perfo [...]rme my promise, and satisfie your request: I haue set downe in writing (as neere as I can call to remembrance) the communication had in our iour­ney, touching vntrue measuring of land, insufficient landmeaters, and why they are still permitted. For the further proofe of these matters, I haue drawen sun­dry figures like vnto some of those you sawe in my booke: which proofes the vnlearned in Geometrie may easily conceiue. I pray you reserue this booke for the satisfaction of your selfe, and your friendes. I would be loath it should come to the hands of learned Mathematicians, for they may iu­stly reproue sundry of my demonstrations, and declarations: because they are not penned as learning, and art require. If they were penned in arti­ficiall order, and termes: you could not vnderstand them, because you are ignorant of the Mathematicals. If you wil be instructed in Arithmetike, Euclide, Tectonicon, and Pantometria, according to your earnest prote­stations: and studie those bookes earnestly, because they are the best wri­ters, extant in our vulgar tongue touching the Mathematicall part of surueie: you shall then perceiue, what great pleasure, and commoditie, is receiued from learned, and artificiall writers, ouer that can bee had from them, which in their writings discend to the capacitie of the vulgar sort. Then also you will yeelde your selfe more beholding vnto me for writing this popular discourse at you request, to the diminishing, and aduenturing of mine estimation among learned Mathematicians: then nowe while you thinke it artificially done. Although my knowledge in Geometrie is verie small, yet I would not abase my selfe by penning any demonstrati­ons popularly: but to pleasure you, and your friendes, and for that I would many should vnderstand, the great hurtes the common weale su­staineth by landmeaters ignorant of Geometrie. When you haue at­tained [Page] knowledge, I hope you will deale with mee as good natured men deale with their nurses. Good natured men during their liues loue their nurses, because they receiued their first sustenance from them: al­though their stomakes would loath to suck their milke as they did in their infancie. When you shall finde your selfe learned in Geometrie, and that you can vnderstand the demonstrations of learned writers: you will repute my writing as cold and thin milk, in compa­rison of other meates, that are strong and of good nourishment. From London the two and twentie of September. 1581.

Your louing Friende 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."]

A DETECTION OF SVN­dry errours, committed in Landmeating.

Speakers.
M. Peter. Ihonson a Clothier. Worsop a Surueyor. M. Watkins. Steuen a Seruingman.
M. Peter.

THis séemeth to be rich pastureground, a tenant (in my iudgement) may safely giue a marke by yeare, for euerie acre thereof.

Iohnson

I would take a pasture ground with vs, and giue that price for euery acre, measured with the perche of xvi. foote, and an halfe, called statute measure, and ten shillings for euerie acre, if it be measured with the perche of xii. foote.

Worsop

An acre measured by the statute perche, conteyneth (almost) twise so much ground, as an acre measured by a perche of xii. foote. If the statute acre be rented at xiii. s. iiii. d, the acre mea­sured by the perche of xii. foote, will not come to vii. s. i. d, rate like. You should deceiue your selfe ii. s. xi. d. in euery such acre by that ac­count.

Iohnson

You are greatly deceiued, for by all reason, the acre measured with the perche of xii. foote, must be almost iii. quarters of the statute acre, because xii. foote, are almost iii. quarters of xvi. foote, and an halfe.

Peter

Howe much grounde of statute measure, are xi. acres of woodland measure, the woodland perche being xviii. foote?

Worsop

Aboue xiii. acres, & xiiii. perches, to my remembrance.

Peter

Your remembrance, or your casting haue fayled you. You are greatly deceiued in both your reckonings.

Worsop

I shalbe very sory, if I be deceiued in either of them: for I haue made sundry surueyes where occasion hath serued to [Page] reduce such acres as haue bin measured by the xviii. foote perche, & the xii. foote perche vnto statute acres. The xviii. foote perche for woodland is vsed in most places hereabouts: I haue not seene the xii. foot perch vsed 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 alway thought, and haue sundry times heard that xi. a­cres measured with the perch of xviii. foote, make xii. statute acres. And this reason hath alwaies induced me to thinke it true, because the xviii. foote perche exceedeth the statute perche by halfe a yarde, which is a twelfth part thereof: for the one perche is xii. halfe 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 opiniō) mea­sured with those perches, can not make any other difference.

Worsop

You do not knowe, or not consider, that when you talk of the diuersitie which vnequal perches make in land measure, that then you speake of the measure of planes and flattes. You think you are in the comparison of lengthes, when as in déede you are in an o­ther matter. Ye must vnderstand that Geometrie treateth of thrée sundry measures. The first of lengthes, which is called liniarie mea­sure, or the measure of lengthes, or lines. By this part, you may know howe farre any place is from the standing of your foote, also the distance betweene place and place, & howe much higher, or lower any place is, then the leuel of your eye, or foot. The second of length, and bredth, called superficiall measure, or the measure of planes, or flattes. By this part of Geometrie is measured, all maner of land, bord,, glasse, pauements, waynskottings, hangings, and such like. The third of length, breadth, and thicknes, called solide, or bodily measure. This part sheweth howe to measure all manner of timber, stone, vessels, and such like. M. Peter saide truth, that the perche of xviii. foote, and the perche of xvi. foote and an halfe differ in their lengthes, as xii. differ from xi. for the one is xii. halfe yardes long, and the other but xi. But ye must vnderstand, this difference is onely in respect of their lengthes, called liniarie measure. In lande measure (which respecteth length and bredth) the difference is other­wise: as I wil make plaine vnto you by an easie example. Suppose you haue two tables, or bords, the one iiii. foot euery way, ye other six. How much is the one longer then the other?

Peter
[Page]

By the one halfe.

Worsop

You say truth, and therefore you account the one table to be greater, then the other, iust by one halfe.

Peter

It must needes be so.

Worsop

I pray you howe many foote of wainscot doth a table conteine, that is iiii. foote euery way?

Peter

xvi.

Worsop

It doth so, and then by your account the other table of vi. foote euery way, must conteine xxiiii. for the halfe of xvi. is viii. which if you put vnto xvi. they both make xxiiii.

Peter

You say true.

Worsop

I pray you howe much is vi. taken vi. times?

Iohnson

Six and thirtie.

Worsop

By your reckoning it should be, but xxiiii.

Iohnson

We al know, that sixe times sixe, is sixe and thirtie, but how proueth this, such diuersitie in the acres?

Worsop

It sheweth vnto you at the first, that measures cast vp by their breadthes and lengthes, must otherwise bee considered of, then measures whose lengthes onely are compared together. A table that is iiii. foote broade, and vi. long, conteineth xxiiii. foote of bord, therfore a table that is vi. foot euery way, must needs conteine more.

Watkins

This standeth so by reason, that it must needes be as you say.

Worsop

I haue in my cloake bag certaine figures drawen in a booke, (which I must giue vnto a friend of mine) that will explane this error, and sundry others, which landmeasurers (vnlearned in Geometrie) often commit.

Peter

I pray you let vs see those figures.

VVorsop

You shall when we come to our Inne.

Peter

It will be late ere wee come thither, therefore wee shal haue small time then to talke of these matters: because men scatter when they are lighted. Also we must part company in the morning. Therefore I pray you let vs see them now, which if you vouchsafe, I, in some other matter, wil requite your courtesie. It standeth mee vpon to vnderstand the troth of this matter, by reason of a wood sale, that I, and an other should passe.

VVorsop

To pleasure you, I wil presently shewe them. Here is the booke: these iii. figures proue that which I haue spoken. [Page]

[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 deede that iiii. euery way maketh xvi. and that vi. euerie way maketh sixe and thirtie. and iiii. broade and vi. long make xxiiii. What meane you by this worde (Scale) which I see in so many places of your booke?

Worsop

The Scale is a measure vsed in platting, taken at the will of the plat maker, eyther greater, or lesse, to set foorth the plat measured in true proportion, and Symetrie, vpon paper, or any o­ther superfice.

Watkins

I vnderstand not this definition.

Worsop

Here (as ye sée) are sundry scales, and euerie of them is iust fiue inches long.

[Page]
[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 inche diuided into iiii. partes, the second in­to fiue, the third into ten, ye may apply these inches and diuisions, [Page] to what denomination you list. The Geographer applieth them to miles, or furlongs. The Surueyor, to perches, the Car­pentor, to feete, and so may any other arts man, in naming any o­ther measure greater, or lesse. Suppose I should describe a countrie, that lyeth in square forme, xviii. miles on euery side, vpon a peece of paper, that is lesse then v. inches square. In this case, the scale of iiii. will best serue my turne. For one inche being diuided into iiii. partes, doth represent the length of iiii. miles, therefore iiii. inches represent the length of xvi. miles, and ii. parts of the deuided inche added to them, must needes represent xviii. miles. But if I should describe a Shire, or Countrey, vpon the like paper, that lyeth thrée and fourtie miles square, in this case I must be driuen to vse the scale ten: that is to say, I must take in inches, and iii. parts of the ten, in the inche diuided into ten parts, which represent three and fourtie miles. For iiii. inches represent fourtie miles, and the three diuisions taken in the said inch diuided into ten parts, represent the three odds miles. The selfe same scales wil serue, if you should plat closes, with­in the like scantling of v. inches, the one being xviii. perches on eue­ry side, the other xliii.

Peter

I nowe perceiue what is meant by this worde scale. I re­member I haue séene the like lines, and compasses set inmappes, but I neuer vnderstood what they meant till nowe.

VVorsop

The knowledge, howe to apply the compasses to the scale, is commodious, for thereby when mappes, or carts, are peru­sed, it may be knowen howe farre any one Region, Citie, or place is distant from any other, eyther by land, or sea. Also, when a Sur­ueyor hath deliuered vp his plat, the Lord sitting in his chayre at home, may iustly knowe, how many miles his Manor is in circuite, and the circuit of any particular grounds, and wasts: and how ma­ny perches, or furlongs it is, from any one hedge, or corner of hedge, to any other hedge, or corner.

Iohnson

I perceiue also what you ment, when you said, ye may apply these diuisions, to what denominatiō you list. As if you would knowe by any cart, or mappe of England, how many miles it is frō Northampton to Sarisburie, then miles are the denomination: but if you would knowe by any platte of lande, howe many perches any ground is ouer, then perch [...]s are the denomination. And you call the opening and extending the compasses vpon the scale, the applica­tion of the compasses to the scale.

Worsop

You conceisse the meaning rightly.

Iohnson

What meane you by these seuerall words, in true pro­portion, [Page] Symetrie, and superfice.

VVorsop

To set forth a plat, in true proportion and Symetrie, are to say, to take, and set forth any plat in such sort, that you may readily tel thereby, euerie angle, bought, crooke, and straight line in the thing measured, and howe farre 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 vpper face of any thing, as in measuring of lande, paue­ments, hangings, & such like, we desire only to know the content of the outward plaine, or vpper face of the thing, not regarding thick­nes, weight, grossenes or depth: but only the mesure of ye vpper parts as in groundes: which consist onely of length, and bredth, whether they be flats, or leuels, hils, or valleis. It would be too tedious to de­scribe them at large: therefore I referre you to learned authors for your further instructions of their proprieties, and accidentes.

Iohnson

What is meant by this word, Parallel?

VVorsop

Parallel lines, are such lines, as (being drawen v­pon any plaine, or superfice) are equally distant ye one from the o­ther. If you draw them of neuer so great a length, yet will they ne­uer concur, or meet together. If they incline neuer so litle ye one to ye other, they are not parallels, but inclining lines, as you may see by ye

[parallel lines ab and cd; inclining lines ef and gh]

examples of these lines a. b. &c. d. which are parallels, and the lines e. f. & g. h, which are inclining.

Ihon.

Why write you such strange & far fetched words & termes, seeing you can write their meanings in plaine english, if you wold?

Worsop
[Page]

He for whom I haue written this booke, wil not think them strange, or far fetched, because he giueth himself to the studies of Arithmetike & Geometrie, and therfore acquainted wt words and termes of those arts. There is not any doctrine, or science, but hath of necessitie his peculiar termes: neyther doeth any learned man in any science, condemne an other learned man, in an other science, for a strange and farre fetching speaker, because hee vnder­standeth not many of his wordes and termes. Many of the profoun­dest learned men in the Vniuersities, vnderstand not a number of termes, pertaining to the common Lawes, which a young student of lesse then a yeres continuance, vnderstandeth very well. And con­trariwise, a great number of profound learned men in the lawes of the Realme, vnderstand not a great number of termes, vsed in Philosophie and Logike, which a young Logician vnderstandeth very well. The Ciuilian, vnderstandeth not many termes of Phi­sike, nor the Physition many termes appertaining to the Ciuill Lawes. The Greeke termes appertaining to Arithmetike, Geome­try, and other Mathematicall sciences, seeme stranger vnto al sortes of men, then the termes of other sciences, and therefore, of the igno­rant very much derided, who account them more curious then ne­cessarie. Yea some men that are learned in other sciences, but igno­rant in the Mathematikes, thinke them termes of hard and darke knowledges, and not greatly necessary, because they thinke much vanitie in them. Both these sortes of men, which condemne before they knowe, are in great error. The auncients, and best learned writers of Mathematicall sciences, were Grecians: the Latines, receiuing their knowledge from learned Greeke authors, neuer al­tered the Greeke termes, but vsed them aswell in workes of their owne making, as in translations. The Italians, Frenche men, and Germanes, finding them in the Latine, vsed also the Greeke terms, as followers of the Latines. Therefore the learned might iudge a great presumption, and lacke of discretion in vs, if we should tran­slate these Greeke termes, into our Englishe wordes: seeing the learned of other nations, retaine them still, though they can write more compēdiously, then we. We are not able to vtter Greek terms compendiously, but by circumlocution. I thinke one special cause, why learned writers in the best languages, vse the Greeke termes in all their workes, is, because readers of their bookes should com­pare [Page] them, with Greeke, and Latine authours, in whom they shall finde the selfe same termes, whereby the knowledge of these scien­ces, is much easier attained vnto. For if a man finde one thing in sundry languages, and diuers waies defined demonstrated, and ap­plied, he is very hard of capacitie, if he shal not be able to vnderstand some of them.

Ihonson

I thought verily before you tolde these causes, that you, and your friend for whom you haue written this booke, had deui­sed termes much like the deuise of Pedlers Frenche, because you would not haue your cunnings in land measuring knowen to any but to your selues.

Steuen

And I would haue thought them, words of coniurati­on, because being once in a place, and halfe a dossen others beside my selfe, where lay a booke that had many crosses in it, & a great num­ber of like figures, and circles, and as one of our company did reade such strange wordes, one other saide: my friend, you were not best to reade too farre in that booke, least you fetche one vp, that will aske what he shall doe, and if you can appoint him nothing, neither know howe to laye him downe againe, he will doe much hurt. And be­cause it was in a Priests his house, I may say to you, it so feared some fooles of vs, that we were glad when we were out of dores. I neuer heard that the Priest was suspected for coniuring, he coulde doe many pretie feates, for he made dials vpon walles, and in gar­dens, he could measure land, and tel howe wheeles, and other gins for milnes should be made. He hath told how things should be made and mended, concerning water workes, and milnes, that if the coun­trie had lacked his helpe, a great deale of money would haue beene spent in vaine by most mens sayings. I heard him say vnto lande­measurers, that they must néedes make wrong measure, if they pro­céeded by such way as they had cast their worke, and determined to procéed. One time (as I waited on my master when he went to the measuring of a meadowe that laye ii. miles from his house) there was great talke, and arguing by the way, whether it were possible to tel how far one place in view is distāt from an other: & how much one place is higher then an other, except it were first measured. Ma­ster Morgan answered that it was possible, & very easie to be done. Then Master Allen asked him if he could doe it by any of those in­struments we carried with vs. He answered that he could. Where­vpon [Page] M. Allen suddenly staying, sayd: I pray you tel me how farre it is from the place where I stand to yonder oke. I wil, sayd he, and immediatly he piched one of his instrumentes, and looked thorowe a fine knacke, or Iig, and measured a good pretie way from him, not towards the marke, but sidewise: and at the corner where his mea­suring ended, he looked againe through his Iig, and casting a little with his pen, he tolde iustly almost how many perches it was from his foote to the oke: for he missed not a perch in a length that was a­boue fiue furlonges. When we came to the oke, whose height from a certaine knot in a bowgh, downe to the ground was almost thrée and fiftie foote, he tolde within two inches the iust height by looking through an other Iig. One did clime the trée, and laide one ende of a wier line to the knot, and there helde it, and let the other end fall downe, by which meanes we made trial. We that sawe how néere he had tolde the length, and height, before they were measured, sayd it was pretely done. M. Allen asked if any good seruice, or commo­ditie to the common weale might ensue by these fine sleightes. Yea sayde M. Morgan, very much. For except a man can take lengthes and distances, he is insufficient to measure lande: because in lande measuring, the measurer many times through the impedimentes of thickets, waters, myers & such like, must be driuen to take lengths, & distances. Neither hils, nor dales, for the most part can truely be measured, except their heightes and depthes be taken. Also he that can exactly take them, can giue a very néere gesse, when he cometh on any ground whether it will cōtaine his generals army or not. He also can tell what quantitie of grounde the enemies campe ouer­spreadeth: and giue a néere gesse (if he sée the enemies in battaile raye) what number is of them. Also to know how to take lengthes, & heightes, be chiefe pointes in vndermining: namely if the vndermi­ning begin far from the place that should be blowen vp. The height of towers, stéeples, and wales, are knowen hereby, so that scaling ladders may be made fit: and it may be knowen howe much is be­twéene story and story in any house, without measuring them. Also how many foote high any trée dothbeare timber, and most requisite to batteries, & bowgeings, and to knowe how farre any péece bea­reth point blank. The degrees of longitude, and latitude, the eleua­tion of the poles, and the height of the sunne, thinges in nauiga­tion of greate necessitie: namely in long and farre viages, when [Page] they would knowe vnto what coastes, and countries they are néerest, are knowen, and founde out by geometricall instrumentes prepared for the taking of heightes, lengthes, and distances. The chief­fest péece of arte in the description of countries, is the taking of heightes, lengthes, and distances. The knowledge of them are in­cident to many other necessarie matters.

Peter

Call you these pretie feates, and fine sleightes, and such instrumentes, knackes, and Iigges? Mee thinketh hee that can doe these thinges, performeth matters of great weight in the com­mon weale, and ought as much to be accounted of, and aduanced for these knowledges, as learned men in other faculties for their knowledges.

Steuen

When the lande was parted betwéene my Maistres, and her thrée sisters, M. Morgane was a whole moneth with my maister, and measured for him. There were then certaine law­yeres, surueyors, and countrye measurers, and for thrée or foure dayes great controuersie was among them, and such a stur as I neuer sawe amongst wise men. Some would haue the lande mea­sured one way, some another: some brought long poles, some lines that had a knot at the ende of euerie perche, some lines that were sodden in rosen and waxe, M. Morgane had a line of wyers. They measured the poles, and lines with two foote rulers, & yardes, wher­of some differed from other, halfe an inche, which made great va­riance, for euery man iustified his owne ruler. If I durst to haue aduentured at the first, I could I haue gayned twentie nobles by laying on master Morgane his doings. There was such lustie bargaining on all sides, that crownes, and angelles were but try­fling layes. Maister Morgane layed little or nothing, but alwayes as he sayde, so it was agreed vpon: he could alwayes giue such rea­sons, and so well proue his doings.

Peter

Then he measured for them all.

Steuen

Nay, that he did not. The lande was to be deuided in­to foure partes. The sisters and their husbandes agreed that eue­ry of them shoulde bring their surueyours at the time appoin­ted: so that when any ground was to be measured, rented, and valued, it might bee agreed vpon by their generall consentes. [Page] Order was taken that a certaine meade should first be measured, & that euery measurer, should measure by himselfe, and that none of the other measurers should be with them: and that euery man when he had done, should deliuer vp his content of acres vnto Master Al­len, who went with them to receiue the same, and to sée that one should not tell another howe much hee made it, because it was thought good to see howe 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 halfe, an other xvi. and iii. roodes, and Master Morgane made it xvii. and almost a roode. Here­upon rose great contention and wagering, but at last all gaue place to Maister Morgane his measure. He that made it xvi. acres and iii. roodes, found that he misreckoned himselfe almost iiii. acres too litle, and afterwards he sware by Gods soule that he was glad thereof, because by that occasion his content came néerest to Master Mor­ganes.

Ihonson

I maruaile what may be the causes of their so great dis­agreeings, and differences in one, and the same so small a piece of grounde.

Worsop

No maruaile, for the common ignorant measurers by their generall rule are for the most part subiect to make groundes greater in quantitie then in troth they are.

Peter

I would very faine see howe it can be proued, that xi. a­cres by the xviii. foote perche, make of statute measure xiii. acres and xiiii. perches. When I am satisfied in that matter, we wil heare fur­ther of that partition.

Worsop

Number the square féete, conteined in these iii. figures. The figure A. sheweth the square féet conteined in the statute perch, which are CC. lxxii. and a quarter. The figure B. the square féete in the xviii. foote perche, which are C C C. xxiiii. And the figure C. the square féete, in the xii. foote perche, which are. C. xl. iiii. Your opini­ons are, that a measure made with the xviii. foote perche, is greater then a measure made by the xii. by the one halfe, because xviii. is xii. and the halfe of xii. But ye see it is farre otherwise, for C C C. xxiiii. the greatest square, conteineth C. xliiii. the lest square, twise, and xxxvi. ouer, which is the fourth part of C. xliiii. So that one acre measured by the xviii. foote perche, is equall vnto ii. acres, and a roode, measured by the perche of xii. foote. Such proportion as the [Page]

[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]

[Page] squares of perches haue eche to others: the groundes by them mea­sured haue also. But because you are ignorant of Geometrical pro­portions, that is to say, of Geometrical relations, comparisons, or respects, & that the proportiō of the square of the statute perch, to the squares of the other perches, fall so vpon the fraction, as I cannot expresse them by number to your vnderstandings: therefore I will set aside arte, and artificiall termes, in this our talke, and frame my speeche as I best can to your vnderstandinges. Yee all knowe that eight score perches make an acre, as eight score pennies make a Marke of money. Whether our coyne bee fine, or base, eyght score pennies euer make a Marke: so whether the perche bee litle, or greate, eight score perches euer make the acre. When yee talke of ii. vnequall perches of lande, yee must not thinke that yee talke of ii. suche vnequall poles, or lines, as Surueyors measure with, for they are instrumentes to laye out the sides of a perche of lande, and not perches of lande. If a man buye a piece of Dornixe of a yearde broade, to hang a roume withall, and when his hanging is made vppe, hee lac­keth a yarde of stuffe to perfourme the same: which hee buyeth. In this case the square yearde of bought s [...]uffe, perfourmeth the hanging, and not the yearde where with the stuffe was mea­sured. As a yearde of Dornixe cutte off from the peece, is conteyned within the boundes, and limittes of foure edges, or seluages, euery one beeing a iust yearde in length: for that quantitie of Dornixe is called a square yearde of Dornixe: so is that quantitie of grounde, called a perche of lande, which is conteyned within the limittes of foure perches beeing layde square. And as eyght score pennies, make a Marke of money, so eight score such parcels, or pieces of ground, make an acre. Ye haue told that C C C xxiiii. square féet are contained in the perche of eighteene foote, which summe eyght score times, maketh fiftie one thousand eyght hundred and fourtie. For one hundred foot eyght score times make sixteene thousand, then two ⟨3⟩ hundred eyght score times, must make eight and fourtie thou­sande. And eight score, foure and twenty times, make iii. thousande eight hundred and fourtie.

Iohnson

I vnderstande very well that this is true.

Peter

I haue tried it in multiplying 324 by 160, and finde it to [Page] agree that waies.

Worsop

Yee haue tolde also that two hundred three score and twelue foote and a quarter, are conteined within the statute perche, which summe eight score times, maketh xliii. thousand, D. [...] lx. squ are féete.

Peter

We haue cast this among our selues, and finde it to bee as you haue saide.

VVorsop

Take the lesser summe out of the greater, and note howe many remaine.

Ihonson

There remaine viii. thousande, two hundred and fourescore.

VVorsop

Ye say trueth, and ye perceiue that the one acre ex­céedeth the other, so many square feete of grounde. Can yee tell howe many times C C. lxxii. and a quarter are conteined in eight thousand C C. lxxx?

Peter

As wee haue cast, xxx. times, and C xii. foote and an halfe ouer.

VVorsop

Then yee perceiue that the acre measured with the perche of xviii. foot long, is greater then the acre measured with the statute perche, by xxx. perches of land and Cxii. foote and an halfe o­uer. How much is thirtie eleuen times?

Peter

C C C. and xxx.

Worsop

Howe much is C. xii. and an halfe, eleuen times?

Iohnson

xii C. xxxvii. and an halfe.

VVorsop

Howe many statute perches is that?

Peter

Foure statute perches, & an halfe, xii. foot, and a quarter and an halfe of a foote.

VVorsop

Thus ye haue found C C C xxxiiii. perches & an halfe, & a few od feet, which is ii. acres, xiiii. perches & an halfe. If you put them to xi. acres, then you haue xiii. acres, and aboue xiiii. perches, according to my former saying.

Iohnson

I pray you let vs trie the diuersitie, betweene the sta­tute acre, and the acre of xii. foote perche.

VVorsop

Ye see the xii. foote perche conteineth C xliiii. square seete: how much is that summe eight score times?

Peter

C xliiii. eight score times is, xxiii. thousand and xl.

VVorsop

How many times is C C lxxii. and a quarter conteined in xxiii. thousand and xl.

Peter
[Page]

Foure score, and foure times, and an halfe, xxxiiii foote, and seuen partes of a foote, the foote beeing diuided into eyght partes.

Worsop

Ye knowe that those lxxx. and iiii. times are so many statute perches?

Peter

We doe so.

Worsop

Howe much money is lxxx. and iiii. penies?

Iohnson

Vii. s.

Worsop

Yee see by your owne reckoning, that if the acre mea­sured by the xii. foot perche, did make lxxx. and v. statute perches, as ye see it doth not fully, that your rent could bee but vii. s. and a peny, after the rate of xiii. s. iiii. d. for the statute acre.

Ihonson

It is most true.

Watkins

These reckonings, and profes, are very finely, readi­ly, and plainely contriued. Till nowe I neuer heard ground cast vp to halfe a quarter of a foote, and so plainely proued to euery man his vnderstanding. And yet I haue heard that some will not misse an inche of ground when they measure.

Worsop

It is a small matter for one to cast vp any measure that he hath made within lesse then an inch, but to measure exactly within lesse then an inche is a greater matter then I euer knew a­ny would take vpō him to do. For albeit the art doth exactly teach ye way, yet are we not able (such is our imperfection) truly to execute the same. And where you thinke that this account hath beene finely, and readily cast vp: you much mistake it: for it hath beene very grossely done. The fiue waies are done by Arithmetike. I will by Arithmetike doe more in a line, then thus in a leafe: and in the space of ii. minutes, which this waies can skantly be done in halfe an houre. He that is a good auditor will quickely cast such a recko­ning with his counters. But because neither time nor place would permit me to vse any of those meanes, I was forced to proue this in such sort, as euery of yee might best vnderstand me.

Watkins

I thinke I vnderstande what you meane by these wordes, square feete, 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. Euery plaine, or superfice bounded with iiii. sides, hath iiii. angles, or corners, as yee may perceiue by these fi­gures, [Page] A. B. C. D. You may try by the scale of ten that euery 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)]

[Page] the figures A. and B. are xx. in length, and euery line is a streight line: and yet the one figure is greater then the other. The figure A. is the greater, because it is a square figure: and the figure B. is much lesse then the figure A. because it lyeth not in square forme. Like wise the figure C. is a long square, and therefore much greater then the figure D. which lyeth not square, and yet the sides of the one are equall to the sides of the other. Three kindes of angles are to bee considered of, by landmeaters: namely the right angle, the obtuse angle, and the sharpe angle. It can not be saide that any figure, or close lyeth square, except his corners be founde right angles. Who so is ignorant of certaine peculiar properties, and conditions apper­taining to these iii. kindes of angles, can not truely measure lande. It is not ynough for a measurer to knowe the sides of groundes, by laying his pole, or line, but he must knowe moreouer the contentes of the corners: for the square lying, narrownes, or broad opening of the corners in closes, make the contents diuers, although the sides be found equall by measure.

Watkins

Is he that knoweth the particular properties of those iii. kindes of angles, to be accounted a sufficient measurer?

Worsop

No more then hee is to bee accounted a sufficient Gramarian, that knoweth but iii. rules appertaining to the first part of speeche.

Iohnson

Notwithstanding your sayings, I like best the old ma­ner of measuring, by laying head to head, and side to side, taking their halfes, and that ways to cast vp the contents.

Worsop

That way is not true, but where the corners of the close be right angles, and the hedges streight. You shall not finde one close amongest an hundreth to lie in that sorte. The measurers eye, is not able to iudge exactely whether groundes ly square (though he haue great experience and good arte) if hee haue not some Geometricall instrument to direct him. If a grounde of foure sides, haue not at least two right angles, it may not be cast vp by laying head to head, for that kinde of casting will produce a false content. Tell mee I pray you, howe many acres a close of foure sides conteineth, if euerie side be iust xl. perches in length?

Iohnson

Fourtie times, fourtie pence, is xx. nobles, and xx. no­bles, is ten acres. [Page]

[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]

[Page]

[square A, each side measuring 40 units]
Worsop

This is a true content if the close lye in such fashion, as the figure A representeth: hauing all his sides streight, and an­gles right. But if it lye in fashion like to the figure B, then it is but eyght acres. The cause of this diuersitie is, the difference of the an­gles. By iudgement of your eye, you may perceiue, that the close A, is greater then the close B. All the sides of both the closes, or fi­gures, are equall in length, and euery of them lyeth streight. By the figure a. b. c. d. e. f. g. h. you may see the proofe of this diuersitie. E­uery side of the figure a. b. e. f. is xl. perches, as you may trie by the scale x: and because his angles be right angles, therefore his content [Page]

[parallelogram B, each side measuring 40 units]

[Page]

[diagram of parallelogram B superimposed on square A (from the figures on the previous two pages) to demonstrate the difference in area]

[Page] is iust ten acres. The figure h. d. e. f. hath also euery of his iiii. sides xl. perches, and yet a close lying in forme lyke to that figure, is but 8. acres. The figure a. b. c. g. is parcel of ye figure a. b. e. f. which figure a. b. c. g. is xl. perches one way, & viii. ye other. Fourty pence. 8. times, is ii. acres: which ii. acres, being taken from x. acres, there remaine viii. acres: which are included in the figure g. c. e. f. And ye may easily perceiue, that the figure h. d. e. f. is equal to the figure g. c. e. f. for the triangle c. d. e. is equall to the triangle g. h. f.

Peter

If the triangles. g. h. f. &c. d. e. be equall, then your mea­ning is, to put vnto the figure h. c. e. f. the figure g. h. f. in stéede of the figure c. d. e.

Worsop

You conceaue it right. For suppose I would cut of a péece of ground, from a close, or ortyeard, as here the péece 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 péece for it, in like fashion, and bignes, as the péece cut of, was, because I would haue the grounde lye in square forme, for the pleasure of myne eye: your rea­son giues you, that there is no difference in respect of quantitie of ground, betweene 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 néedes be as you say: but how can you proue that these two triangles c. d. e. and g. h. f. be equall?

VVorsop

The equalitie of these two triangles is proued by the fourth proposition of the first booke of Enclide his elementes. But because you vnderstand not geometricall demonstrations, I wil not proue it vnto you, as the art requireth, but by a grosse, and vnlear­ned way, for you shall so best conceaue the proofe. Ye may try by the scale, and compasses, that the side c. d. is equall 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 vnder 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 prickes, drawe finely thrée streight lines, and they wil include a triangular superfice equal to the figure c. d. e. then with a knife, or sisers, cut out the triangle drawen vpon the white paper, and lay it vpon the triangle g. h. f. and ye shal find, the one paper, iust as big as the other, without more or lesse. If the papers be equall in bignes, [Page] then your reasons must néedes giue you, that the figures h. d. e. f. & g. c. e. f. are equall. The selfe same troth that is in the measure of pa­per, is also in the measure of ground: one reasō serueth forboth. Thus ye see, that the figure h. d. e. f. is equall to the figure g. c. e. f. & there­fore much lesse then the figure a. b. e. f. And yet the sides of the figures h. d. e. f. are equall in length, to the sides of the figure a. b. e. f. and the hedges of the one, are as streight, as the hedges of the other.

Iohnson

If land may not be measured by laying head to head, how should it then be measured?

VVorsop

I am no more able to instruct you by one dayes talke, how to measure lande: then a learned Physition, is able to make you a good physition in the space of a wéeke. There is not any that can measure land as it ought to be, except he first be wel instructed, studied, and exercised in the sciences of Geometrie and Arithmetike. He that taketh vpon him to be a lande meater, and is ignorante in these sciences, is no other wise to be accepted for a good land meater, (although by happe he measure some fashioned groundes truely) then he for a good physition yt cureth some certaine disease by chance. I showe not these figures, and proofes of errors, that I thinke there­by, ye may be made good land meaters vpon a sudden: but that yee may perceaue, that your vnlearned measurers, which you alowe of, and suppose to doe well, doe vtterly abuse you, in deliuering vp false contentes. There be thrée erronious wayes in great vse, among vn­learned lande meaters. One is, to lay head, to head, another, to mea­sure a grounde rounde about, and to cast the measure of the whole circuit, into foure partes, or sides: and then to cast it vp, as though it lay square. Many vse this way in measuring of coppies, woods, and bushie groundes, when they can not sée how the hedges ly: but howe vntrue that kinde of measuring is, you may perceaue by the square figure. a. b. c. d. which is much bigger, then the figure inclu­ded within it, and yet the hedges of the included figure, are longer then the hedges of the saide square figure a. b. c. d. If you measure the crooked lines with fine thréedes, you shall finde them longer then the streight lines, as the crooked line a. b. is longer then the streight line a. b. by the length of the line b. e. In like sorte, you may trye the rest. Thus ye sée, whether they lay head, to head, or cast the whole cir­cuit into foure partes: yet either way they make the lesser grounde, containe more, then the greater. For those crooked hedges be­ing cast vp as though they lay streight, will yeelde a farre greater [Page]

[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]

quantitie of grounde, then 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 nookes, and corners. This were a good way, if they could lay out a square tru­ly, and also truely cast vp the corners. But seeing the learned in Geometrie, can not lay a square truly, but by the help of some geometrical instrument: ye vnlear­ned (being ignorāt how to vse such an instrumēt) can much lesse do it. I dare lay wt any of those good felows, xx. to one: yt they cannot lay out a piece of groūd per­fitly square, only by ye iudgemēt of ye eie: & other help, I neuer saw any of them vse. They also cannot measure the nooks and corners truly: because they know not howe to cast vp triangular superfices, by such rule as their fourme requi­reth. [Page] There be sundrie kindes of triangles, as well of right lines, as of spherall, spirall, and mixt, to euery of which appertaine pecu­liar rules, to the attaining of their contentes. In woods, rough grounds, and marshes couered with waters, they, which haue art, cannot for the most part lay out squares, but be driuen to measure, and to take their angles on the outsides, or vpon the bankes, or wals. If arts men can not laie out squares in such groundes, the ig­norant can much lesse doe it.

Watkins

It seemeth vnto mee, by that you haue shewed, and proued, that if all the hedges of a piece of grounde be cast into one summe, and diuided into foure equall parts, if then those iiii. hedges be laide square, that such a close, would conteine more grounde, then if it were laide in any other fashion.

Worsop

You must vnderstand that this is onely meant of clo­ses of foure streight sides. I can lay closes in diuers formes, whose hedges shall be streight, and but viii. score perches about, and euerie of them shal conteine aboue x. acres, and differ, one from another, in their contents.

Peter

I neuer heard in all my life, that more grounde then ten acres, could be conteined within the compasse of viii. score perches. Howe much grounde can you laie within that compasse?

Worsop

Twelue acres and almost three quarters of an acre: it shall not lack iiii. perches thereof.

Peter

In what fashion, must such a peece of ground lie?

Worsop

In a perfect round, like vnto this round figure.

Iohnson

In our Countrie we measure such a piece of grounde round about, and then cast it into iiii. sides, and we thinke it truely cast.

Wor.

You may perceiue yt to be erronious by ye circle and pricked square a. b. c. d. which giueth you 8. score perches in square, & also viii. score perches in rounde. You shall finde by the scale ten, that euery side of the square is iiii. inches, that is to say xl. perches, therefore al the iiii. sides are xvi. inches, which make viii. score perches. Also if you measure the circle, with a fine thred of xvi. inches long, from the streike in the toppe, rounde about, you shall finde the same also to bee iust xvi inches about, euen as the circuite of the square a. b. c. d. is. Your eye giueth you, that there is much more paper included within the circle, then within the square, and yet no more perches are in the circuite of the one, then in the circuite of the other. [Page]

[diagram of a circle]
Peter

I wil not ride any further, til I haue tried this, for I haue a silk thred in my bag. First I wil measure the iiii. sides of ye square, & cut of the thred at that length. Now I wil measure round about ye circle, frō the strike in the top. I do assure ye they agree to an heires breadth. It is very euident to the eye, that much more paper is conteined within the circle, then within the square: therefore common sense giueth, that if grounds be inclosed with hedges of like lengths, and fashions, that more ground must be conteined within the round [Page]

[diagram of square ABCD superimposed on a circle]

hedge, then within the square.

Iohnson

I neuer (in all the daies of my life) could haue deuised such a proofe as this, my head is so grosse. I maruaile much how you can lay viii. score perches in a rounde, without more or lesse. I take it to be a great piece of cunning. Can you doe the like vpon land, as you haue done vpon paper?

Worsop
[Page]

I can lay out grounds in any fashion, as wel vpon land, as vpon paper: but more time must be had, to the doing of the one, then to the doing of the other. Howe to transforme figures, accor­ding to their sides, or contents, to any other fashion, or kinde of fi­gure, ought (of necessitie) to be knowen vnto landmeaters. I finde ii. sorts of people of great contrarietie in their opinions, concerning the attaining vnto the knowledge of land measure. The one thin­keth it but a sleight, and learned by and by: the other dispaireth of his vnderstanding, thinking his senses ouer dull, and grosse, to at­taine the knowledge thereof. Both these sortes of people, are in wrōg conceits. He that thinketh it but a sleight, is of such courage, that he will (according to the common saying) leape ouer the style, before he come néere it. For saith he, If I might be but one weeke in the company of a cunning measurer, and haue but a litle instru­ction from him: I could learne all his cunning in that space. So sclender a knowledge is land measure in his silly conceit. If this iolly fellowe knowe howe to take a plat by any one instrument, and cast vp the same, by Multiplication, and Diuision, in whole numbers, taught in the vulgar Arithmetike, he thinketh himselfe to haue cunning sufficient. He will neuer trouble his head, with the vulgar fractions appertaining to those numbers, for they serue but vnto the parts of perches. Such a measurer may bee likened to one that will take vpon him to be a keeper of accountes, though his knowledge serue not further, then to cast such summes onely as bee in poundes: if there be shillings and pence, he will neuer trouble him selfe with them, nor beate his braines to learne howe to cast them. Such measurers know how to make their plat ioyne, although nei­ther last angle, nor last length be correspondent to their scale, and instrument. If the ii. last lengthes ioyne, eyther by in ward, or out­ward angle, they thinke their worke very good. I haue knowen some (when a plat hath beene well taken) so erroniously cast vp the same, through false rules in casting the triangles, and ignoraunce of the fall of ye perpendicular, that the measurer which worketh only by the perche, laying head to head, would haue giuen vp a truer con­tent then they. The ignorance of the time is such, that to talke by roate of measure, with making show of some instrumêts procureth great credit to such measurers. Whoso cannot prooue his instru­ment, his plat, and the casting vp ther of, by Geometrical demonstra­tion, [Page] is not otherwise to be accounted of for a good land meater, then he for a good Latinist, who can onely recite certaine sentences, be­ing vnable to perse one worde: or he for a good Orator, that is ig­norant of the parts of an Oration, and the Rhetoricall figures. As one that neuer read in the Bible, and yet wil take vpon him to be a Preacher, or one that neuer read Litleton, will notwithstanding take vpon him to be a Counseller in the laws, ought to be accounted insufficient for those functions: euen so ought he to be accounted insufficient for a land measurer, ye hath not red Euclides Elements, but is ignorant of his definitions and propositions: especially such, as concerne liniarie & superficial measures. As Euclide is a greek author, so is the name of his Elements greeke, to a great number of such land meaters, as holde their credit, by the signe of the instru­ment. Other tenure they can not pleade, then the signe of the instru­ment, and a grosse, and vnlearned order of platting, which they at­tained vnto by an imitation and exercise, and not by learning and vnderstanding, why it is so done. As in Diuinitie, Lawe, and Phy­sike, none are admitted to be practisioners, before they be so studied in the best authors, entreaters of those knowledges, that they are a­ble to proue their doings, by good doctrine, so should not any be ad­mitted to land measure, except he be so studied in Euclide his Ele­mentes, and other good writers of Arithmetike and Geometrie (whereof great plenty are extant in diuers languages) that he is a­ble to proue, and demonstrate his doings by their definitions & pro­positions.

Watkins

What is the cause why insufficient landemeaters bee suffered, and that order is vntaken, that none shall be permitted to measure lande, but such as can sufficiently doe the same: beeing thereunto admitted, by the learned in Arithmetike, and Geometrie, appointed by authoritie for that purpose. It seemeth vnto me (as I gather by your speaches) that the ignorant winne vnto themselues greate good opinions, and by showes and brags, cary away the doings from the learned.

Worsop

The abusing and contemning of the Mathemati­calles, is the chiefest cause▪ In the time of Poperie moste singular knowledges were shut vp. A Ciceronian, was accoun­ted an heretike. They could not abide the opening of learned know­ledges. They made darkenes, and ignorance, two of their pillers. [Page] They fedde the people with scumme and drosse, as well in humane sciences, as in diuine. For as in stead of diuinitie, they brought in superstition and idolatrie: so in stead of the pure Mathematicall knowledges, they vsed coniurations, sorceries, inuocations of spi­rits, enchauntments, and other vnlawfull practises, vnder the names of Diuinatorie and Iudiciall Astrologie.

Watkins

Coniurations, sorceries, inuocations of spirites, en­chauntments, witchecraft, and such like are cut off by our statutes, so that none vse them, but fellons, and reprobates. I vnderstand not what you meane, by Diuinatorie, and Iudiciall Astrolo­gie.

Worsop

Diuinatorie, and Iudiciall Astrologie (as a learned author saith) entreate of the reuolutions of the yeres of the worlde, of natiuities, of questions, of elections, of intents and thoughtes: it teacheth moreouer to foretell, to call backe, to auoide, or flie the endes of all things that may happen, and the secret disposition of Gods prouidence. An other saith, that the practisers thereof say, that they can tell of all things that are not come to passe, before they come to passe, by the course and mouing of the starres. By this they make their Prognostications, that tell of raine, and faire weather: sicknes, and health: warre, and peace: plentie, and dearth: with such like. By which also, they cast natiuities, tell fortunes, pretende to giue knowledge of things that be lost: and last of all, appoynt you daies, and times, good or ill, when to iourney by land, when by wa­ter, when to marrie, when to buie, and when to sell. Some of these doctrines, and practises, are vnlawfull. The Prophet Esay in his xlvii. Chapter saith, Let the heauengasers, and the beholders of starres, and mooneprophets, come on now, and deliuer thee, yea, & let them showe, when these newe things will come vpon thee. Be­hold they shall be like straw, which if it be kindled with fire, no man may rid it, for the vehemencie of the flame: and yet it giueth no syn­ders to warme a man by, nor cleare fire to sit by. Thus are they with whom thou hast wearied thy selfe. By this it appeareth, that heauen gasers, beholders of starres, and mooneprophets, can not by their prognostications foretell the secret disposition of Gods proui­dence. Therefore they are ill suffered to foretell of wars, of plagues, of famines, of vnseasonable weathers, to their owne destruction, as strawe consumed with fire, and to the deceiuing of the people, who [Page] can receiue no more good by their diuinations, then warmth and light, from the synders of burnt strawe. Ieremy saith in his tenth Chapter, Ye shall not be afrayde for the tokens of heauen, for the Heathen are afraide of such. Yea all the customes, and lawes of the Gentiles are nothing but vanitie. By these words they of the hous­hold of faith are taught, not to feare, howsoeuer planets threaten by aspects. In the eighteenth Chapter of Deuteronomie, among other prohibitions, it is forbidden that there be not any choser of daies, a­mong the Israelites: for the chosing of daies is an abhomination be­fore the Lord. It is one of the sins, for which God cast out certaine na­tions before ye Israelites. So abhominable are such elections in the sight of God. One of the ils which Manasses did in the sight of the Lord, euen after the abhominations of the Heathen, was, that hee maintained tellers of fortunes: and built altars for all the hoste of of Heauen, and worshipped all the host of Heauen, as it ap­peareth in the one and twentie Chapter of the fourth Booke of the Kinges. Therefore, the casting of natiuities, the tel­ling of fortunes by Palmestrie, and by such like waies, are also ab­hominations before the Lord. The Priestes of the Gentiles, (be­ing ignorant of the true God) deuised these abhominations. They brought the people in beliefe that certaine ingenious men, and women (after their naturall deathes) were stellified. They named certaine starres after the names of such men, and women, and made the people beleeue, that they were Gods, and Goddesses, and that they had placed themselues in the heauens, to behold the earth, and doings of men, and to order men, and humane things, according to their pleasures, and dispositions, when their turnes of regiment came about. The Caldeans, and Egyptians, hauing obserued cer­taine courses of starres, planets, and constellations, which God ap­pointed them in their first creation, say, that that planet shalbe lord of the ascendent for that yere, which is in the signe ascendent aboue our horizon, at the houre when the Sunne entreth into the first minute of Aries. And that all things that yere are gouerned here on earth, chiefely according to the disposition of that planet. Therfore they caused Temples to be erected in the honour of them, which they deuised for their gaine, and estimation, and for the better plea­sing, and ordering of the people. They fained a certaine man called Mars, (who in that age, was the most politike, valiant, and fortu­nate [Page] in martiall affaires) to be the God of battaile after his death, and that he was placed in the heauens to our sights, in the shape of a redde, and fiery starre, according to the nature of fierce warriours: appointed vnto him, for his habitation a large heauenly region. An other called Mercurie (because he had a deepe and readie witte, and was singular eloquent while he liued here on earth) after his death they brought the people in beliefe that he is the God of eloquence, & the messenger of the gods. Therefore Poets faine, that hee tyed wings to himselfe, when he went on any message, & painters paint him with wings, as they fondly paint Angels. To him also, they appointed an heauenly region. They fained a certaine woman called Ceres, to be the Goddesse of corne, because she first deuised the yo­king of oxen, the plough, and that order of tillage. The inuention of the art of whooring, is attributed vnto Venus, who therefore was reckoned in the number of the Goddesses, and called the Goddesse of loue. For she being vnchast, and occupied in al excesse of carnal plea­sures, taught the women of Cyprus, to please men with their bodie for monie. This so pleased ye priests & the people, yt they haue appoin­ted ye brightest planet (ye sun & moone excepted) in remēbrance of her, to the greater celebrating of her honour. Many other men and wo­men, they fained to be turned into Gods, and Goddesses, as Iupiter, Apollo, Saturn, Iuno, Pallas, and such others, some for their hu­mane vertues, and some for their vices: assigning starres, and pla­nets, and erecting Temples and Oratories in the honour of them. We reade in the Acts of the Apostles of Iupiter his Prieste, and of the Temple of Diana the great Goddesse of the Ephesians. These Caldean, and Egyptian Priestes, and fabling Poets, fained stars, planets, and constellations, to be the chiefe gouernours of men, and humane causes by turnes, much like the chosing of some kinde of of­ficers, one yere in, the next yere out, and within a fewe yeres af­ter, in againe. For one while Mars is Lord of the ascendent, an o­ther while Iupiter, an other while Saturne, and so of others. When Iupiter is Lord, they prognosticate a prosperous, and happie yere: But when Mars is Lord therof, they prognosticate chiefly of wars, and destructions, namely if Venus be retrograde, that is declining from him. But if she be in coniunction with him, the furie is not onely then qualified, but turned vnto pleasantnes: and in steade of great warres, they prognosticate great adulteries, insolences, and [Page] vnchastities. Thus these diuinors behight generally vnto the whol [...] worlde, an vniuersall spending of the yere, according to the dispositi­ons, and vsages of licentious persons. The vniuersall people at their appointmentes, must spend the whole yere, either prouident­ly, and vertuously: or dissolutely, and vitiously. If any bee desi­rous to vnderstand at large the vanities, contrarieties, lyinges, falsehoodes, heresies, and other abhominations, proceeding from abused Iudiciall, and Diuinatorie Astrologie, let them read the trea­tise of Iohannes Picus Mirandula, Cornelius Scepperus, and Cor­nelius Agrippa against such Astrologie: And also two English trea­tises, the one intituled, An inuectiue against Astrologie, the other, An admonition against Astrologie Iudiciall, and other curiosities. Abused Astrologie, is a greater hinderer and depressor of lawful A­strologie, and Astronomie, and the other singular and lawfull ma­thematicall knowledges: then rancke weedes of good corne. We may reade in the first Chapter of Genesis, wherefore God made the Celestiall bodies, where it is thus written. And GOD saide, Let there bee lightes in the firmament of heauen, that they may deuide the daie and the night, and let them bée for signes, and seasons, and for daies, and yeres. And let them bee for lightes in the firmament of heauen, that they may giue light v­pon earth: and it was so. And GOD made two greate lightes: a greater light to rule the day, and a lesse light to rule the night, and hee made starres also. And God set them in the firmament of heauen, to shine vppon the earth. And to rule the day and the night, and to make difference betweene the light and the darke­nesse. Here the worde of GOD sheweth for what causes the Sunne, Moone, and starres were made: namely to diuide the day and the night, and to bee for signes, for seasons, for daies, for yeres, to giue light vppon earth, to rule the day and the night, and to make a difference betweene light and darkenesse. Lawfull Astrologie, and Astronomie entreate not of the Sunne, Moone, and Starres, nor of their courses, and aspectes to further end then these. Who so goeth further, committeth as great euill, as hee that addeth to the worde of GOD, or maketh the worde of GOD a cloake to couer his wicked diuinings. All sensible people perceiue, that these lightes, gouerne, and deuide the day and the night, for when the Sunne is aboue our horizon, then is it [Page] day with vs: when vnder, then night. They be signes vnto vs of Gods great power, maiestie, and goodnes. By the courses which GOD hath giuen vnto these signes, wee knowe the ap­proching, present, and declining times of spring, Summer, Har­uest, and Winter. Nauigation into farre Countries can not conueniently be without taking the height of the Sunne and cer­taine starres, whereby men knowe in what parte of the worlde they are, and by the age of the Moone, they knowe when it is full sea, or lowe water in any hauen, or porte, whereby the safest times of bringing in their vessels is knowen vnto them. These and sundrie other greate commodities, receiue we by these signes. We see also that our seasons for plowing, sowing, setting, planting, shredding, cutting, felling, reaping, and gathering, are knowen by the courses and influences of these lights, and celestiall bodies.

When the Sunne is in the tropike of Capricorn, then is it with vs winter season: when in the Equinoctiall, spring time: when in the tropike of Cancer, sommer. These & al other seasons are know­en to skilfull Astronomers by the courses of the celestial bodies. The knowledge of the day naturall (which is the space of foure and twentie howres) and of the day artificial, which is the time betwene Sunne rising, and Sunne setting, is of great necessitie in our hu­mane affaires. In like manner to knowe in what space of time the yere is accomplished, is a thing of greate commoditie vnto vs. C C C lxv. daies, vi. houres, and a small portion more of time, make the yere: which Astronomers haue found out by obseruing the course of the Sunne through the whole zodiake. If the reuolu­tions and courses of the celestiall bodies, should not yerely be exactly obserued by Astronomers, they could not set forth almanakes, and if we had not almanaks, great losses, inconueniences, and confusions in humane affaires would immediately ensue. Philip Melanch­ton saith in an Epistle of his, that it is a greate, and manifest profitte to keepe a true, and certaine account of the yere. How great would the confusion be of present buisines, of contracts, of bargains, of iudgements, & how great disorders would there be, if there were not a distinction of yeeres and moneths? If the numbring of yeares were taken awaye, what greate obscuritie woulde there bee in Hystories? The beginning of the Worlde coulde not bee thought on, neyther the begynninges of [Page] religions discerned, nor the alterations of kingdomes distinguished. It is euident, that the knowledge of these things are greatly neces­sarie to diuinitie, and to many partes of our life. Wherefore the in­gratitude, or rather the peruersenes of many can not sufficientlie be maruelled at, which reproue this doctrine of the heauenly motions, and description of the yere. The greatnes of the profite, & the iudge­ments of the wisest Princes, and of the best learned, who with great labour, searche, and diligence, haue set the yere in order: ought to moue the ignorant to detest the hearing, and vsing, of such doltishe and scoffing reprofes, as are vsed against good artes, so excellently set out, as it were by diuine inspiration. The worthiest princes, magistrates, and philosophers, haue had a great care rightly to des­cribe the yere: that times may be discerned, & the memorie of things set forth, and conserued. We must needs grant that our first fathers the Patriarks and Prophets, who excelled in wisedome, and godli­nes (as it were by diuine inspiration enforced) haue obserued, and set forth, the distinction of yeres. We reade the Patriarke Abraham taught the Egyptians Astronomie, and Geometrie. And godly Iob nameth certaine starres by proper names. Great reasons, profes, & authorities, as well from Diuinitie, as from Philosophie, and na­turall reason, might be brought, howe worthie and needefull the Mathematicall knowledges are. Therefore they are greatly too blame, and much ouershoote themselues, in bewraying their igno­rance, and ill disposition, which scoffe at Mathematicians, calling them fantasticall, and vaine fellowes. They which haue no vnder­standing in Mathematicall arts, when they see a fellow with a run­ning head, or light braine, especially if he be studious, and giuen to solitarines, say in way of scorning, he hath a mathematicall head. They thinke they speake finely and aptly, but they make themselues more ridiculous vnto the learned by vsing this newe terme, then the simple man, that calleth an arbitrement, a bikerment, and him verie vnrude, whom they would condemne for carterlines. In their imagination, a running or fantasticall head, and a mathematicall head, are of one signification, which is farre otherwise. Tullie saith, If art, and nature meete in an Orator, the excellencie therof is such as he cannot expresse the same. In like maner, if a man haue a Ma­thematicall head, & mathematical art, yt man is to be reputed a most excellent and most necessarie member of the common weale. For [Page] most certainely such a man can perfourme great, and weightie acti­ons, to the benefite of his Prince, and Countrie. Howe vngratefull, I may rather say how dishonest, and despitefull are they which mock at the makers of Almanakes: terming them fantastical, and mathe­maticall heads, & keakers on the newe Moone: when as themselues continually carie an Almanake about them, and set one vp in their houses, as a most necessarie instrument to their priuate affaires. E­uidences are daily brought vnto lawyers, that the expirations of leases, and of prescriptions, and the continuance of discents, and pe­digrees may be knowen. Men thinke a fee well bestowed vpon their Counseller, to be truely informed in any of these cases. Astronomers haue so reduced the yeres of our Lord, and the reignes of Kings, that the expirations of termes, may readily be knowen. These reducti­ons are extant in our vulgar tongue, in three, or foure varieties, and euerie of them of small price. Yet Astronomers, are not onely vnre­compensed for their paines taken to pleasure the common weale, but are called vaine fooles for their labours.

Iohnson

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 mathematicall sciences, is cal­led a Mathematician. And those learnings, or sciences, which may plainely be proued by true demonstration, apparant to sense, are cal­led sciences mathematicall. Philosophie, Logike, and certaine other worthy doctrines, are not learned by most certaine demonstration, but perceiued by reason, and studious searche. Most men wrongful­ly conceiue, that certaine vnlawfull practises attributed to Astrolo­gie are parts of the Mathematicall sciences, which chiefely bringeth such great discredit, and contempt of Mathematicians, and of the pure, and single mathematicals. Some professing Astrologie, impu­dently vsurpe the name of Mathematicians, as popish, and supersti­tious Priests, the names of Diuines. As Papists abuse the worde of God by ioyning Psalmes, Epistles, Gospels, and other partes of the Scriptures to their superstitious, and idolatrous abhominati­ons: so haue certaine abusers of Astrologie, intermingled their false, and vaine doctrines with mathematicall operations. They make the mathematicals cloakes to couer their wicked doctrines, as Pa­pists doe the Scriptures to couer theirs. Diuines, and other lear­ned [Page] men (ignorant of Mathematicall sciences) and in manner all sensible men, perceiuing howe directly against the worde of God, and howe vtter false, their prognostications of drowthes, fluddes, warre, peace, sicknesse, health, plentie, scarcitie, and such like are: and also the vntruthes, vanities, and superstitious curiosities in electi­ons, and settings of figures: neglect, and condemne the mathemati­cals in generall, because they thinke these vanities proceede from them, which is nothing so. It is daily seene, that euill disposed persons conuert and abuse good things to wicked actions. As good wine to drunkennes, good meates to surfetting, a weapon to mur­der, and roberies, mariage to debate, monie to vsurie, the lawe to briberie, the word of God to heresie. Yet wine, meates, weapons, mariage, monie, lawe, and the word of God, may not bee reiected and contemned, because lewde disposed persons abuse them. In all ages Arithmetike, Geometrie, and Astronomie, haue beene ac­counted liberall sciences: and must they now be disdained, and reiec­ted, because some vsurping the name of Astrologers haue abused them? It behoueth our Vniuersitie graduates (who are, or ought to bee seene in the Mathematicals) to vpholde as much, as in them is, the seuen liberall sciences. They knowe Plato forbad any to come within his schoole that was ignoraunt of Geometrie. Hee called Arithmetike, and Geometrie the two wings with which hee raysed himselfe into the heauens. Hee knewe, that hearers ignoraunt of those sciences, could receiue small profitte by his lectures of Astronomie, or of sundrie partes of Philosophie, and Logike. I haue heard some Masters of Art say (which haue beene but meanely studied in Euclides Elementes) that they should ne­uer haue vnderstoode Aristotle his meaning in sundry places, if they had continued ignoraunt of certaine his propositions, and demonstrations. A Doctor in Diuinitie, who was vniuersally knowen amongest our learned men, to bee a singular Grecian, and schooleman: confessed to the like effect, after hee vnderstoodē by instruction the two and thirtie, and seuen and fourtie propositi­ons of the first booke. He would oftentimes say, that Logike, and Philosophie, could not rightly, and perfectly bee vnderstoode, ex­cept some reasonable vnderstanding of Arithmetike, and Geome­trie, were first had. And that those things which are of most diffi­cultie [Page] to schoolemen, would be vnto them as easie as the easyest, if they had any reasonable vnderstanding in those sciences. Plato willeth that children should bee exercised in numbers, and num­bring. If that course were taken with them, they should (when they came to yeres of discretion) passe their affaires more vnderstan­dingly, and with a greater facilitie then nowe they doe. Some iudi­ciall Astrologers please well the fansies of many, because they will prognosticate good fortune vnto them. Many Genethliakes (to please the vaine, and incredulous parentes) behight good fortune to their children. When any at yeres of vnderstanding, is so fonde that he will haue his natiuitie cast: such Genethliakes will learne by one meanes, or other, the course, and some speciall chances, of his passed life. The declaring of them winneth such credit, that the foretelling of the other part to come is beleeued, and expected. Certaine cou­sening mates are dispersed in many parts of this Realme, called of the people cunning men, or wise men. Some others as foolishly (though they thinke they speake wisely & aptly) call them Astrono­mers or Mathematicians. Silly maidens, & foolish wiues, daily run vnto these couseners, to know how many husbands, & children they shal haue, & howe long their husbands shal liue, & whether they shall leaue them rich, or not. These companions will take vpon them, to tell, and direct folkes howe they shall get againe into their posses­sion such goodes as they make account to bee lost, or stol­len from them. Yea, they will appointe vnto hazarders, and theeues, fortunate times, and houres to make their attemptes. They say if theeues make their attemptes when certaine Pla­nettes are in suche and suche aspectes: that they shall not onely obtaine their purposes, but also it shall neuer bee knowen that they were the robbers. Many of these wise or cunning men are so vnlearned, that they know not any one definition, or principle of Astronomie, Astrologie, or of any other parte of the mathematicals. They knowe Astronomicall characters of Planettes, aspectes, and certaine constellations: and perhaps so much of the vulgar Arith­metike as a quicke witted youth will learne in xiiii. dais. They haue commonly an Ephemeris calculated by some learned Astrologer which is a necessary book for many good purposes. The Ephemeris is an almanacke, or register, in which is shewed among other things [Page] what aspects the Sunne, Moone, Planets, and constellations eue­rie day in the yere haue eache to others, as the vulgar Almanakes shewe where the signe is, and the age of the Moone. He that can tel when the Moone changeth, or where the signe is, by looking in the common Almanakes, may as well be called an Astronomer for that small cunning, as they for telling the aspects of Planets, and con­stellations onely by looking in the tables of Ephemeridis. They haue also certaine 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 onely vpon their obser­uations (for they can not proue their iudgements by naturall reason, nor by Mathematicall demonstration) take vppon them to foretell by the constitution of the heauens, otherwise saide by the aspects of Planets, & constellatious: aswel what shal euery yere generally befal in humane causes, as to euery mā particularly. The strange names of these Heathen authours, cause the more credit to bee giuen to their blasphemous doctrines, and fables, according to these ver­ses:

If one affirme he learnd it of a Iewe:
The sillie people thinke it must be true.

It is not long since certaine rogues (pretending to be Iewes, or E­gyptians) tooke vpon them to tell all sortes of people their fortunes by looking in their handes. The people were too simple to let some rogues holde them by the hands, whiles others of their company cut their purses, and pickt their pockets. Those roges tolde fortunes as truely, as such Genethliakes can. The forenamed authors, and o­thers their auncient sectuaries, giue such differing, and contrarious Astrologicall iudgements vpon euery particular constitution of the heauens, that our Astrologians knowe not which of them to be­leeue, or folowe. The chiefest cause why our prognostications are so contrarious, is, for that some of our prognosticators write after the opinions of some one of those ancient writers, and some of an o­ther. And they writing different, or contrarie the one to the other, of necessitie some must hit right. Their iudgements are as the blinde man casteth his staffe, peraduenture hit, but most commonly misse. Seeing vnlawfull Diuinatorie and Iudiciall Astrologie, are so di­rect [Page] against the worde of God: such seducers of the people from sted­fast trust, and full depending in, and vpon the deitie: such sclander, & discredite, to the pure, and single mathematical sciences, to the great hurt of our common weale: because such excellent, and most neede­full actions as Mathematicians (if they were duely esteemed) would perfourme to the behouse of the same, are neglected, and left vn­done: it is to be wished, and we ought daily to pray, that it would please God, to stirre the Queenes Maiesties heart, and the heartes of her honourable Counsell, to appoint the learned Diuines, and Mathematicians of her Realme, to cull, and separate, these ill doc­trines, from the good, and lawfull mathematicall sciences. The last Parlement a worthie statute was enacted, which forbiddeth all diuinations, erecting of figures, and such like practises, tending to her Maiesties most royall person. It were greatly to the honour of God, and benefite of the Realme, if they were cut off altogether. The Mathematicals being greatly applied to sundry vaine, and vn­godly practises, and litle thought on, or regarded, to bee applyed to such weightie causes in the common weale as most requisitely they ought: may be compared to a swéet, healthsom, & plentiful fountain, standing néere a Citie greatly distressed through the want of such a spring, and yet the Citizens rather let it run into soule ditches, and marshes, in which it doth no good, then they wil conueie it into their Citie, to their great pleasure, and health. We greatly esteeme ar­tificiall strangers, for their deuises; and workemanshippes: but wee respect not the causes why their doings be more excellent then ours. The instructions, that such artificers, or Mechanitians, receiue from Mathematicians; is the chiefest cause why they exceede vs. He is called a Mechanitian, that can make certaine Geometricall fi­gures, and doe certaine Mathematicall conclusions, by practise 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 Frenchemen write themselues the Kings Mathematicians, because they haue office, and stipend, from the King to maintaine their charge, and studies. Others write them selues publike professor of the Mathematicals of such an Vniuersi­tie. Also euery Citie in Fraunce, Germanie, and Italie, hath one Geometer at the least, who hath office in the same, and stipend from the chamber thereof. Some great Cities haue three or foure such [Page] Geometers at the least. Masons, Carpenters, Ioyners, Paynters, clockmakers, In ginors, and such others: vnto whose faculties most needefully appertaine the knowledges of making squares, roundes, triangles, and many other figures, with their transformations ac­cording to any proportion assigned: resort vnto these professors and Geometers, to learne certaine grounds, & chiefe mechanicall rules. Such of them as enter so farre into speculation, as that they vnder­stand Euclids elements, proue most excelent men. Few, or none such come into this countrie. Mechanitians wil serue our turne, yea we think them most singular men, we are so grosse, & vnskilfull in arts. As a man hauing but one dimme eye, is of blinde men thought to bee wel sighted: so most of vs thinke Mechanitians greate cun­ning men. Ignorance as I saide, and the abuses and contemptes, of the Mathematicals, are the chiefe causes, why insufficient land­measers hee suffered to carie awaye the doinges by showes, and brags.

Watkins

Diuinatorie, and Iudiciall Astrologie, and euery part of them, (as I gather by your talke) should be abrogated as vnlaw­full.

VVorsop

You gather ouer largely of my talke. I spake not against lawful Astrologie: but against such as attribute vnto Astrologie, & Astronomie, sundry actions contrary to the word of God. Astrologie (not contrary to the worde of God) is a commendable knowledge. Philosophie prooueth sundrie influences, proceeding from the cele­stiall bodies, to the terrestriall, (first obserued by Astrologers) against which, I will not rashely speake: But referre you rather to lear­ned Melanchton that famous Deuine, who calleth them Epicureos Theologos that impugne the lawfull science of Astrologie. These matters are so farre aboue common vnderstanding, that wee will cease to talke any further of them: referring reformation where oc­casion serueth, to magistrates, and tho godly learned. Master Iohn Dee in his mathematicall preface, learnedly sheweth what Astro­logie is. In that preface you shall finde, howe some ouer reache: that is, vnlawfully attribute more vnto that science, then duely ap­pertaineth thereunto.

Iohnson

You founde faulte with mee of late, for saying mine head was so grosse, that I should neuer haue deuised such a proofe as you made, when you prooued that a close entrenched within a round [Page] ditch of viii. score perches, was greater then a close entrenched with­in ditches of the like number of perches, laide square. You seeme to dislike that men should eyther showe their cunning, or confesse their ignorance.

Worsop

I found not fault with you for confessing your ignorāce, but because you shewed your selfe dispaired of conceiuing yt, which e­uery reasonable creature may conceiue, if he wil studie Arithmetike, and Geometrie. Neither do I find fault with the other sort for show­ing such cunning as they haue: but for taking vpon them more then they are able to perfourme: namely in so weightie a matter as lande measure. Ye must not think that these comparisons of figures, & these proofes are my deuises. My learning extends not to adde a deuise vnto Geometrie. I haue gotten my smal knowledge by instruction, & studie of learned authors. Who so maketh any mathematical deuise ought to prooue the same in al parts, by Euclids elements: if he can not so do, his deuise is but a gesse, & therefore not to be allowed. But if he can prooue it by mathematicall proofes, then you may easily perceiue that the like hath bin heretofore deuised, because he findeth rules for al ye parts of his deuise. As a Grāmarian yt is able to proue by the rules of Grammar that his Latine is true, must needes grant that ye like Latin hath bin spoken in times passed, because he findeth rules therefore: so if a man haue deuised any thing in Geometrie yt he can proue by the elements of that science, he must needes graunt that the like deuise hath bin heretofore, or else those rules could not be extant. Most men when they see heights, depths, lengths, or dist­ances truly taken, ingins deuised yt with smal strength draw vp, & hold things of huge weight: manifest proofes why a close lying in such a fashion, conteineth more ground then if it lay in such a fashion, al­though their circuites be equall: with many such like: haue in great admiration the wit of him that performeth such actiōs. They think men attaine vnto these knowledges onely by their owne deuise, and ingeniousnesse: and not by mathematicall studies, and practises. They referre all to naturall witte, they haue no respect to arte, nor thinke thereon. Euerie sensible man that will studie Euclydes elementes, and giue himselfe to practise, may with as great ease vn­derstand the Mathematicals, as any of the other sciences liberal. The grounds, & reasons of Mathematicall operations be so plain, so simple & so easie to be perceaued after some reasonable instructiō, & practise: [Page] that not any sensible man hath iust cause to dispaire yt he shal not at­tein those knowledges, for children about ye age of xii. yeres, by those meanes may easily learne them, they be so plaine. After a man is some what entred, he doth greatly maruaile to see such weightie ef­fects, proceede from such plaine and simple rules. Euerie first en­trance into the studie of any of the sciences liberall is hard. How drie, hard, and vnsauerie seeme the rules of Grammar vntil ye come to construction, and proouing by the Grammar rules▪ euerie worde of the sentence to be in congruence. But when you can prooue the congruence, then great pleasure is receiued from that, which before seemed so hard, and vnsauerie? Euen as a man must know, and vn­derstand those drie rules before he can attaine the knowledge of the Latine tongue, so must he knowe, and vnderstande, the definitions, and propositions in Euclides elements, and howe to applie them to his workings, before he should be allowed a sufficient practisioner of the mathematicall part, or charge of Astronomie, Perspectiue, Cosmographie, Geographie, Nauigation, Martiall exploits, suruey of lands, mensuration of solides, architecture, ingins, drenings or mountings of water, and many other faculties. If in the practise of these forenamed sciences, the mathematicall part be defectiue: such practise may bee compared to a naturall liuing bodie, that hath some principall member or members, as armes, or legs, so benum­med, taken, or shrunk vp, that they stand not in any stead, but hang on like deade things. The mathematicall part is the head, or chiefe part of some of these sciences. If the powers of the head bee stopped, or taken away, the bodie serueth to small purpose.

Peter

I perceiue that Euclides elements is a booke of mathe­maticall rules, and that by the knowledge of those rules mathema­ticall operations are perfourmed, euen as the Latine tongue is at­teined by the knowledge of the Grammar rules, or reading by the knowledge of the alphabet, and the other accidentes appropriate to that science.

Worsop

You say truth. The elements of a science are the first, chiefe, and principall rules of that science: whereof all the operations of that science take their beginnings.

Iohnson

Are there not other authors that haue written those rules, as learnedly as Euclide, because still you nominate him?

Worsop
[Page]

There is not any comparable to him. For all his pro­positions are so fully, plainely, truely, orderly, and learnedly proo­ued: that all singular, and learned writers of the Mathematicals since his time, haue beene content to be tried by his elements, so excellent an author he is, and so plaine, pure, and simple is the subiect of his matter, that he leaueth not any thing doubtfull, or referreth you to a quere. These be the causes why learned Mathematicians, make the proofes of their doings by his propositions: and rely vpon him as vpon a most sure foundation. There is not any writer of hu­mane causes of whom so boldely a man may say, (Ipse dixit) as of Euclide, so free is he from errours and controlments.

Watkins

In what age liued Euclide? You saide hee is a Greeke author. Chiefe officers in martiall affaires, measurers of lande, ma­sters of ships, ingenors, dreyners, mounters of water, and diuers o­ther arts men, of whose faculties (by your saying) the part mathe­maticall is a principall member, vnderstand not for the most parte the Greeke tongue. Fewe vnderstande the Greeke tongue but Vni­uersitie men: would you not haue any chiefe professors of these fa­culties but graduates?

Worsop

Euclide was liuing about xl. yeres before the Reigne 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. yeres of age to learne Geometrie of Euclide. Some of Socrates his scholers gaue themselues chiefely to the stu­dies of morall, and naturall Philosophie: as Plato, Xenophon, and Antisthenes. Other some to the Mathematicals, as Aeschines, Phe­don, Euclide, and Aristippus. I haue seene Euclides elementes in the Latine tongue, in ten sundrie translations at the least. They are also extant in Frenche, Italian, Spanish, high Almane, & Dutch. But in the English tongue farre exceeding all other impressions, most learnedly are they extant. Therefore our professors of facul­ties may learne and vnderstand him sufficiently to discharge their functions, although they vnderstand not the Greeke. Graduates that perfectly vnderstand the Greeke tongue, and the other sciences (by which they receiue their degrees) are without doubt fittest to be publike readers, and instructors of the Mathematicals (although they should teach in the English tongue) and although the Greeke termes are expounded in the English translation. They can best [Page] shewe the etymologie, and deriuations of words, and termes, the methode, and other parts of learning.

Peter Who translated him into our tongue?

Worsop

Master Henrie Billingsly one of her Maiesties c [...] ­mers for the port of London.

Peter

The translation is made by a verie honest Gentleman.

Worsop

Euen from his childehoode I haue heard from others, and noted to my selfe, such his great paines taken in studie, his dis­cretion, and such his vertuous inclination, and impressions, that my minde alwaies gaue me, some notable benefite to his country would proceede from him.

Peter

How long hath this English impression bin extant?

Worsop

Euer since the yere 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. Iohn Dee, who is accounted of the learned Mathematicians throughout Europe ye prince of Mathema­ticians of this age: as Cicero named Cratippus ye prince of Philoso­phers in his age. This M. Dee hath put vnto these englished elemēts, many scholies, annotations, corollaries, and expositions which giue great light, and facilitie to the vnderstanding of them. Also his ma­thematicall preface vnto these elements, is a worke of such singu­laritie and necessitie to all students of the Mathematicals, that I wish them to make it a manuel.

Iohn.

I pray you let vs see some figures representing streight hed­ged closes iust viii. score perches about, that shal conteine more then x. acres. You said you could lay closes in diuers fashions that should conteine more then x. acres, and yet but viii. score perches about We haue seene it proued in the roūd, now we would see the like proofes in some with streight hedges.

Wor.

I wil shew you some examples, by certaine regular figures. I cal those figures regular, whose sides are equall the one to ye other, and whose angles also are equal the one to the other. Euery side of the fiue sided figure a. b. c. d. e. is xxxii. perches in length, as ye may try by ye scale x. fiue times xxxii. make 8. score. It is manifest to your eye that the said figure is greater then the pricked square f. g. h. i. Euerie side of the square is xl. perches, and therfore as ye haue seene by for­mer proofes, it conteineth x. acres: but this equilater, and equiangle pentagon, or figure of fiue sides, conteineth eleuen acres, and fiue perches.

[Page]
[diagram of a pentagon superimposed on a square]

[Page]

[diagram of a hexagon superimposed on a square]

The figure k. l. m. n. o. p. is an equilater, & equiangle hexacon (yt is to say a figure of vi. e­qual sides, & of vi. equal angles. Euery side thereof is 26. perches, & two third partes of one perche. A close lying in such fashion, conteineth xi. acres, an halfe, & 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.

[Page]
[diagram of an octagon superimposed on a square]

The figure v. y. x. z. a. b. c. d. is a regular octogon, euery of his sides are xx. A close lying in such fashion conteineth 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 moe sides a regular close hath, the greater is his content. For the moe sides the neerer he draweth to a circle: and euerie circle conteineth more area within him, then anyother figure of many streight sides can conteine, if their circuits be equal in mea­sure.

[Page]
[diagram of an irregular six-sided close superimposed on a square]

[Page] As all regular figures of moe sides then iiii. must alwaies conteine aboue x. acres, if their perimetrie or circuit be iust viii. score perches: so if they be irregular, that is to say, if their sides and angles or any of them be vnequall, they may conteine lesse then x. acres, as this close i. k. l. m. n. o. which is but ix. acres & an halfe, & therfore lesse then the square p. q. r. s. which conteineth x. acres, but much lesse then the former equilater, and equiangle sixe sided figure, whose content is xi. acres, an halfe, and viii. perches. The neerer any figure commeth to regularitie, the greater is his content. Ye nowe euidently see that land cannot be truely measured if the measurer be ignorant of Geo­metrie: for if his knowledge extend not further then to lay head to head, and side to side, or to measure the whole circuite, and to cast the same into foure equal parts: or to make crosse measures making the one the head, and the other the side, most of his contentes will bee false.

Watkins

We see euidently that the proofes which you haue 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 Geometricall figures, but onely of length, and breadth, most men thinke that we are to respect our statutes, & to follow them: and not to follow the new begun professors of Geo­metrie: as though they were wiser, and knew better what belongeth to landmeasure, then the wise, learned, and experienced men of the Parlement in those daies. It seemeth by the ancient, huge, and sump­tuous buildings, and by the acts for al maner of measures, and assi­ses, that as skilful Mathematicians were in those daies, as in these. The statute saith when an acre of land cōteineth x. perches in length, it shal conteine xvi. in bredth. When xx. in length, then viii. in bredth. When xl. in length, then foure in breadth. Therefore if I measure ye side, and the head, which are the length, and the breadth, I measure according to the statute, and other kinde of measure then the statute apointeth the people desire not.

Worsop

That statute is wel, and rightly penned, but of many (ignorant of the Mathematicals) it is misvnderstoode. Though ye finde not termes of art therein, but vsual words, yet those exact ap­pointments, and reductions of breadths to euerie length in that sta­tute nominated, could not be done but by a Mathematician. And al­though some of those breadths be vntruly set downe, yet they of vn­derstanding [Page] perceiue 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 certaine easie reductions are printed fals­ly. The varieties of lengthes, and breadths in that statute expressed, tend to driue men to learne, and consider, what the measure of an a­cre of land is. I told ye not long since yt viii. scorrsquare perches make an acre. If ye haue a peece of ground, that is xx. perches long, and 8. broad, lying square like to the figure a. b. c. d. such an inclosure 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 iii. roodes, though euery 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 euery of the sides e. f: g. h: r. s. and v. t. equall to the side a. b. or c. d. For euerie of those vi. heads are 8. perches broade, & euerie of the vi. sides xx. perches long, as ye may trie by the scale of foure. The in­ward inclination or bending of the sharpe angle e. h. g. abateth two perches in the breadth of the figure i. k. g. h. which figure i. k. g. h. is e­quall to the figure a. b. c. d. and therefore that figure e. f. g. h. is equall to such a figure as is vi. perches broad, and xx. long: namely to the fi­gure m. l. g. h. which is but iii. roodes. For vi times xx. make vi. score, and vi▪ score representeth iii. roodes. The line q. o. is the breadth of ye figure e. f. g. h. and not [...]. h. as the ignorant of Geometrie erroniously suppose. And the line v: x. is the breadth of the figure r. s. t. v. one de­monstration serueth to them both. Breadths must bee measured streight, and vpright, called of Geometers, perpendicular, or rectan­gular measure▪ as al ye lines in the figure a. b. c. d. are perpendicular lines, for they stand vpright vpon the line c. d. neyther bending in­ward making a sharpe angle as the line [...]. h. doeth with the line h. g. nor falling outward making an obtuse angle as the line r. v. doth wt the line v. t. The line n. o. in the figure e. f. g. h. lyeth not vprightlie as lines of breadth should: but slopingly, for if it were laide or measu­red vprightlie, it would reach to the line i. k. as ye may try by the vp­right line o. p. which is equale in length to the saide slope lines. n. o. or. e. h. The eye of the conningest Geometer that is, cannot exactly iudge when he measureth lande, vpon what partes of hedges per­pendicular measure, that is to saye measures of breadthes must fall, but by the helpe of some geometricall instrument. Ye may by the example of the three figures whose heades are viii. and sides xx. trye and finde that the like, and as great errors may befall in euery of [Page]

[diagrams comparing the areas of rectangles and parallelograms]

[Page]

[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 ye square a. b. c. d. must haue euery of those sides to be in length xii. perches and an halfe, ii. foot, iii inches and an half, and the fiftieth part of an inch. These▪ iiii sides added together make▪ fifty perches and an halfe, xi. inches, & the twelfth part of an inch and somewhat more, as ye may try by the scale of foure. That length cast into a rounde close, like vnto this circle▪ e. f. g. h. and measured from Easte, to Weaste, here represented by .e g. and from south to north represented by .f.h. (as many erroniously vse to doe) taking ye one measure for the length the other for the breadth: they shal produce by that way of measuring one acre, and an halfe, and halfe a rood, which circuite in square forme maketh but one acre. Such a round close by true measure is one a­cre, one roode, and three perches. Therfore such a round close by that maner of crosse measure is made one rood and xvii. perches more thē it ought to be: and by casting such a round circuit into a square, they [Page]

[circle EFGH superimposed on square]

make the land lesse then they ought, by one roode, and three perches. The words, and meaning therefore of the statute certainely is: that in what fashion soeuer grounds do ly, that iust viii. score square per­ches must alwaies make the acre. We must not thinke so wor­thy a stat [...] for so weightie▪ a matter to be made vppon so weake a foundation or consideration: that the meaning was to alowe of mea­sures so greatly disagreeing eache from other, and so greatly swar­uing from the troth sometime by excesse, and sometime by want. There can be but one true content of a peece of ground, which cannot allowably be found by any measurer, but by such a one as can proue the same by the elements of Geometrie.

[Page]
[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 paire of shoes in his shoppe made al vpon one paire of lasts, For some feete his shoes must needs be too large, for others too litle, for some by chance they may be fitte. Suppose there bee a square close, hauing eyther of his sides xii. perches long, and eyther of his heads vi. perches broade like to the figure a. b. c. d. Howe much ground doth such a close conteine?

Peter

Sixe, twelue times, is lxxii. that is vi▪ s. If it were viii. perches more, it were halfe an acre.

Worsop

Suppose there be an other close, the one side w [...]reof is xxi. perches long, the other but xii. and eyther of the heade [...] [...] per­ches broad, lying in fashion like to the figure e. f. g. h. How much doth such a close conteine?

Iohnson

Xxi. and xii. added together make xxxiii. The halfe [Page] thereof is xvi. perches, and an halfe. These xvi. and an halfe I take for the length, & taking vi. for the breadth, I finde that xvi. d. ob. sixe times, is viii. s. iii. d. which representeth halfe an acre and xix. perches. If it were but one perche more, it were halfe an acre, and halfe a roode. I see that iii. sides of the one figure are equall to three sides of the other: and that their difference is onely in one side: for the heads a. c. and b. d. of the one figure are equall 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 then the side a. b. by ix. perches, for the one is xxi. and the other but xii. therefore the longer sided close conteineth more ground then the shorter by half a roode and vii. perches. For if ye take lxxii. perches, the content of the figure a. b. c. d. from foure score and xix, the content of the figure e. f. g. h. there will remaine xxvii. perches, which is halfe a roode, and vii. perches. Ye see before your eyes that the figure e. f. g. h. is on the one side almost as long againe as the figure a. b. c. d. if it were iii. perches longer, it were ful twise so long as the other.

VVorsop

Measurers ignorant of Geometrie deliuer vp such con­tents. Sundry buyers, par [...]eners, exchangers, lessees, and takers of land as ignorant as they, content themselues with such measures. When the blinde leadeth the blinde, they fall both into the ditch. Ye haue great respect howe much the close e. f. g. h. is longer then the close a. b. c. d. but ye respect not howe much the saide close a. b. c. d. is broader then the other. The shorter close a. b. c. d▪ by reason of his square lying conteineth vii. perches more then the longer. But for the easter proofe I will admit it to be but vi. perches, as may be [Page]

[diagram with trapezoid superimposed on rectangle to demonstrate the calculation of area for each]

proued by this figure a. b. c. d. e. f. g. h. i. The pricked square a. b. c. d. in this figure, is equall to the other figure a. b. c. d. And e. f. c. d. in this figure is equall 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 equall 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 equall to the two triangles e. g. c. and h. f d. Therefore also the figure g. f. i. c. is equall to the figure e. f. d. c. The figure g. f. i. c. is xvi. perches and an halfe in length, and foure in breadth, which make v. s. vi. d. but the figure a. b. c. d. being twelue in length, and sixe in breadth, commeth to vi. s. therefore the figure e. f. c d. is lesse then 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 equall to v. s. vi. d. and to the halfe thereof which is ii. s. ix. d. Those two summes cast into one, make viii. s. iii. d. You saide if the side of xxi. perches in length, had beene xxiiii. that then it had beene double to that of xii: and you suppose that a ground so sided, would be greater then that, whose side is xxi. wherein you are greatly deceiued. It is impossible to include any su­perfice or quantitie of ground within a close hauing either of ye 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. laide vnto them driueth the other iiii. sides to a streight line: not suffering them to make any angles, so yt they be as it were ii streight hedges the one standing vpon the other, not including any quantitie of ground. Two right lines cannot include a superfice by [Page]

[diagram of a trapezoid]

the sixt petition of the first of Euclides Elements. The close a. b. c. d. hauing all his angles right, is greater then any other close can bee, if any one side of his length be made more then xii. For the obtusenes or declination of angles diminisheth quantitie of ground, as ye haue seene by the other figures, and more plainely may see by this figure m. n. o. p. which hath thrée of his sides equal to three sides of the figure a. b. c. d. but the fourth side is xxiii. perches and an halfe.

[Page]

Measurers ignorant of Geometrie, committe the like errours in measuring of triangular, or three cornered closes. Most men thinke that a three cornered close whose sides are xxx. xl. and lxv. perches, doth containe more ground then an other three cornered close whose sides are but xxx. xl. and l. because the side lxv. of the one figure, is longer then the side l. of the other figure, by xv. perches. But the longer sided close, namely the triangle p. q. r. is lesse then the triangle s. t. v. by one acre, halfe a roode, and three perches. For s. t. v. the shor­ter sided close, conteyneth three acres, and three roodes, where the longer sided namely p. q. r. conteineth but two acres, and an halfe, & xvii. perches.

Watkins

I am now fully resolued that they which measure with the pole, or line, (if they be ignorant of angles) doe they knowe not what, and that they greatly abuse them for whom they deale.

Iohnson

The worlde was merier, before measurings were v­sed then it hath beene since. A tenant in these daies must pay for eue­ry foote, which is an extreme matter. I knowe surueyors that vse not measuring when they make their surueies, which fashion I like best.

Worsop

There is greater cause of good mirth, and ioye, in these daies, then was in those you speake of. We haue the light, and frée­dome of the Gospel, so that our soules may ioy in the true saluation. We haue a wise, and mercifull Prince, who as God his good instru­ment hath all the time of her Reigne preserued vs from warres, spoyles, and heauie taxes. If your meaning bee that smalnes of rents, and cheapenes of victuals make the mery worlde: then was that worlde merier when the statute for lande measure was first made, and duely executed: then it hath beene at any time since the neglecting of the same. We may finde in our Chronicles, that in those daies a fatte oxe was commonly sold for a noble, a sheepe for vi. d. a quarter of wheate for ii. s. Most tenants that take land after the common measuringe pay for more then they should. Therefore if the tenant had true measure, he might liue meryer then he doeth. Seeing most Landlords couet to let their grounds to the vttermost, and most tenants seeke to sell their wares at the hyest prices: it is verie requisite for both sides, that the land be truly measured. True measure is not extremitie, but good iustice. By the Lawes of our Realme, and by common reason, such like equalitie, and troth of [Page]

[diagrams of triangles PQR and STV, separately and overlaid]

[Page] measure in landletting ought to be betwéene Lorde and tenant: as is be­twéene buyers and sellers of cloth, silkes, graine, liquors, stone, tim­ber, or of any other commodities for which our statutes haue ap­pointed standerds, and assises. I know sundry honest gentlemen pro­fessors of surueie, that many times omitte measuring. Surueie con­sisteth vpon three principal parts: that is to say the Mathematicall, the Legall, and the Iudiciall. Vnto the Mathematical part belongeth true measuring, which is Geometrie: true calculation of the thing measured, which is Arithmetike: and true platting, and setting forth of the same to the eye, in proportion, and symetrie, which is Perspec­tiue. To the Legall part belongeth the knowledge of kéeping courts of surueie, of the diuersities of tenures, rents, and seruices, likewise how to make terrors, rentals, particulars, sute rols, customarie rols, & also how to engrosse books, wt many other things appertaining to yt part, as may appeare in the statute, called Extenta Manerij, but more at large in the treatises of M. Fitzharbert, and Valentine Leigh touching surueie. The Iudiciall part consisteth vpon the considerati­on, and knowledge of the fertilitie, vesture, situation for vent, health somenesse, commodiousnesse, discommodiousnes, and such like of e­uery kinde of ground, building, and encrease, in his owne nature, & kind. Some make apportionation, & valuing a member of this part, other think them more worthie the name of a principal. I suppose thē to be in common to al the iii. parts. It is impossible for a surueyor to make a true value of lands, except he first know ye tenure, rents, cu­stōs, & seruices to thē appertaining in their proper natures, & kinds. He must haue great respects to the part legall when he valueth. And also as great respects to qualitie, and quantitie, which are the partes Iudicial, and Mathematical. Qualitie, and quantitie be inseparable companions, they must of necessitie be ioyned together in apportio­nation, & valuing. Who can tel, what a cloth, or a peece of veluet is worth if he be ignorant how much they conteine by measure? A skil­ful man knoweth by colour, finenes, making, strength, & other points Iudicial what euery yard of them is worth: but he can not value thē, except he also know how many yards either of them conteineth. So is it of graine in heape, & of liquors, of which the value of a bushel, or of a gallon may iudicially be rated, but ye value of ye whole cannot be knowen, til true quantitie, that is, the number of bushels & gallons be also knowen. Some surueyors vse not to measure, because they are ignorant of the parts mathematical: but refer the measuring to such, as take vpon them the knowledge therof. They shew thēselues [Page] honest, in not taking vpon them beyond their skil. Many are skilfull in the part Legal, and in many points of the part Iudicial, which vnderstand litle in the parts Mathematical: and therfore they deale not further then their knowledge extendeth. Sometimes also the Lorde desireth not further information then in the parts Legal, and Iudi­cial: because by his euidences, records, and accustomed nomination what number of acres euery ground conteineth hee is satisfied tou­ching the quantitie. In cases of partitiō, 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 exchāge. The one hath CCC. acres lying very néere vnto ye mansion house of ye other. Lands of like value (which ly not passing 4 miles from those CCC. acres) should be giuen for them. They haue desired me to find meanes how this exchange may indifferently bee made. In lesse then ii. daies it would be dispatched. If I may haue your help, you shal haue good chéere, be very welcome to them both, and pleased for your paines. We wil al beare you company, and help you the best we can.

Wor.

When oportunitie on al sides serueth, I wil 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 haue diuers times measured about CCCCC. acres in a day, so in some other dais, hauing had ye like time, & help, and as faire weather, & taking as great or greater labour I could not ouer come xl. The formes & fashions of grounds are ye chiefe causes why measures are either long or spéedie in doing. Many grounds yt lie long, & narrow, by an indenting, crooking, and winding brook side, cannot truly be mea­sured, without great labour, & much expence of time. Many such grounds haue I measured (the ritchnes wherof hath bin such) yt ma­ny men would haue giuen aboue xx. pounds for the inheritance of e­uery acre therof. When the weightie buisinesses of partitions, exchā ­ges, & sales fal betwéen mē: it behoueth yt the measurer haue good skil, and yt he vse great diligence, exactnes, & circumspection in his measu­rings. If he shold misdo one acre in xx. in such kind of groūds: it were aboue xx. li. losse to ye one side, & an vnlawful gaine to the other: which is a weightie matter to the soule, & conscience of him yt either ignorātly; or negligently shou [...]eth vp such weightie buisin [...]sses. It is impos­sible for measurers ignorant of Geometrie, truely to measure such crooked groundes. They can not misse so litle as one in twentie. [Page] Many men (rather then they would wrongfully loose halfe an acre of their inheritance) would spend an hundreth pounds in the lawe for the maintenaunce of their right. Many times through the ignorance of vnskilfull measurers, they loose scores of acres: yea sometimes in great grounds hundreths. But that which the eye seeth not, the heart rueth not. The blinde eate many flies they knowe not of. Many thinke that a Geometer can measure lande in shorter time, then a common measurer that measureth onely with the pole. Vn­skilfull, and vnlearned measurers (for the most part) make more hast then good spéed. The ignorant thinke if a Geometer but once looke through the sights in his instrument, that thereby he knoweth pre­sently howe many acres the grounde conteineth. True Geometri­call measure asketh longer time then onely running ouer a grounde with a perche, or a line. Great cheere, and company keeping, binder much in the time of surueying. A good surueyor will auoide them. Diligent and exact surueying so fully occupieth both the bodie, and minde of the whole man, as he can haue small leysure for talke, or recreations.

Iohnson

I knowe some that will iustly tell, how many acres e­uery parcel of grounde conteineth onely by the viewe of them: not v­sing either pole, or instrument.

Worsop

Diuers surueyors by their great experience, and by the helpe of deedes, terrors, particulars. Iurors, and report of the inha­bitants, can giue a great gesse at the true contentes of landes: and thereupon will set downe their iudgementes, which maner of sur­ueying differeth from exactnes. He that is much exercised in the tals of mony can giue neerest gesse howe much bagges, and heapes con­teine vpon the viewe of them. Likewise they which are greatly ex­ercised in buying of peeces of veluets, silkes, and cloths: can by their bulkes giue sometimes neere gesses at their contents: but yet their gesses are vncertaine, and most commonly vntrue. The records of such coniecturall surueyes, ought not to be produced as good, and sufficient euidence for proofe of the quantitie.

Iohnson

Is then a Mathematician the best surueyor, ought not any to be admitted vnto suruey but he?

Worsop

He that vnderstandeth all the parts of suruey, best de­serueth to be admitted to that function. There be diuers Mathema­ticians that vnderstand. Geometrie, Arithmetike, and Perspectiue [Page] sufficiently for the Mathematical part of surueie: that vnderstand li­tle in the parts Legal, and Iudicial. Also there be diuers that vnder­stand the parts Legall, and Iudicial, that vnderstand litle of the Ma­thematicals. Therefore when partitions, exchanges, buyings, and sellings by the acre, are to be made, they to whom these matters ap­pertaine, if they will haue their businesses exactly done: should get such a one as vnderstandeth all the parts of surueie, or els two who by their knowledges ioyned together are able to make a perfect sur­ueie. If defection be in any of the three parts, the residue of the suruey is litle better then labour lost, such great errors will ensue thereof.

Peter

I would faine be acquainted with some that vnderstand al the parts of surueie perfectly. You know many such.

Worsop

I knowe verie fewe such. Ye haue heard of M. Thomas Digges, he is verie skilful in all the three parts. All surueiors are greatly beholding vnto him, for setting forth three bookes of Geo­metrie, in which hee learnedly teacheth Geometricall measurings. For the part mathematicall all good surueiors owe vnto him great reuerence, because he is a lanthorne vnto them, aswel in the specula­tion, as the practise. He and M. Leonard Digges his father haue bin the first, and chiefest that haue giuen light, and tast of this necessarie part of surueie in our vulgar tongue. M. Thomas Owen one of the Counsellours of the Citie of London (of any learned man towardes the Lawe) best vnderstandeth al the parts of surueie as I haue heard from them that be skilful, and for ought that euer I could perceiue o­therwise. He wel vnderstandeth diuers tongues, and is so wel furni­shed of the best authors in diuers languages, that hee hath gotten much and rare knowledge from them. M. Iohn Hils an Auditor (of any man whose learning and practise I knowe) in my iudgement is the perfectest, and readiest man in all the parts thereof. He vnder­standeth Arithmetike, Geometrie, and perspectiue, both speculatiue­ly, and practically singularly wel. His knowledge and daily exercise of Auditorie, mixt with the studie of the common Lawes, & his great search and practise of the part Iudiciall, haue brought him to a pro­found iudgement and knowledge. M. Fardenando Malyn, and M. Iohn Malyn his brother can surueie singularly wel. They vnderstād the Mathematical parts perfectly, and are of good studie, and great practise in the other. M. Fardenando is the readiest man in the field yt euer I saw. M. Deuhurst, M. Grent, & M. Godfrey can surueie ve­rie [Page] well. M. Godfrey hath verie good knowledge in Perspectiue. I assure my selfe that many others are verie skilful, and can do verie wel in al the parts thereof: but I can not report the skil of any vpon mine owne knowledge, sauing of these.

Peter

Me thinks many should giue themselues to be skilful pro­fessors of surueie: and to vnderstand the knowledge, and practise of al the parts thereof. What be the causes why there are so fewe suruey­ors, that can sufficiently surueie?

Worsop

Such sufficient skil as a surueyor should haue, before he ought to execute that office, can not bee attained but by a longer studie, and a greater practise, then is commonly thought to bee had thereto. It is also one of the chargeablest studies, that one can enter into. There are fewe that wil take the paines to giue perfect instru­ctions to young beginners, & to set them in the right course of study and practise, which is a great cause of much vaine expences. The Mathematical part séemeth so drie, and hard, at the first entraunce, that some (as wearied) giue ouer before they haue passed halfe way. Also measurers ignorant of Geometrie make quicker dispatch, then the learned and skilful can: which so pleaseth the ignorant because it diminisheth present charge, that they therefore litle regard him, that maketh true measure, which in troth is penie wisedome, and pound foolishnes. Also through lack of good order in this weightie matter, braggers that by showe of their instrument win credit, are sooner reteyned by the ignorant then a sufficient man. Some thinke that to be a great peece of cunning which in deede is eyther an error, or but a trifle. The benefite also to the skilful is so small, and the charge to be in such readinesse as they ought so great, that they giue ouer as wearied, leauing the matter to ignorant dispatchers, who sticke not at any thing. If the learned and skilful, did vse conferences, & deuise waies, how these inconueniences might be redressed, true knowledge aduanced, and ignorance depressed, as the learned in other professions do: great vtilitie would ensue vnto our commō weale therby. It is a lamentable thing that so great a mischiefe (as the ignorance of true landmeasuring bringeth) hath so long bin spied, and that no remedie is therefore prouided. Euerie man knoweth that lande is our riches in the hyest nature, and yet true surueying, and valuing thereof is shoufled vp, as though it were a matter of small importance. If a re­ceiuer should in stead of an hundreth pounds vsually receiue either [Page] too much or too litle, though it were vnder fourtie shillings, and the ouersight but in monie, his Lord, if he knewe it, would thinke him verie vnskilful and negligent in his office, and quickly haue an euill opinion of him therefore. But if ignorant measurers misse x. acres in an hunderth (whose value is commonly aboue fortie poundes) they are not euill thought of therefore, though it bee to the losse of so much inheritance. Ignoraunce beareth such sway, that for lack of good order these chances daily happen.

Peter

How may a man when he lacketh a good surueyor, knowe him that is sufficient, from him that is insufficient?

Worsop

Rules can hardly be giuen vnto the ignorant of suruey, how to choose one that is sufficient. If surueyors were in such order (as by good reason they should, the weightines of their charge consi­dered) then as the learned in other professions are knowen from the vnlearned, 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 Vniuersities to any degrees of learning but by the allowance of ancient graduates of the same profession. If the skilful in the parts Mathematicall, Legal, and Iudicial would frind­ly, and singly ioyne together to reforme, and instruct each others, and to reduce surueie to a perfect order: without doubt many which now vnderstand but parts, and peeces rightly: but moe things erronious­ly, or lamely, would in short space proue sufficient men. Also excel­lent good waies for the best instruction of young students thereof, would soon be had. They that enter themselues into the studie of this science, and would perseuere therein, are driuen to go so blindely and confusedly to work, because they know not where to haue right in­structions, that they fall into many errors, and receiue great discou­rages.

Iohnson

Me thinks the number of surueyors in these daies is too great. Gentlemen know wel ynough how to let their lands to the vttermost. They haue cunning ynough for that matter, they néed no more help from skilfull men.

Worsop

Though some landlords deale ouer hardly with their te­nants, the fault thereof is not to be attributed to surueyors. Good & skilfull surueyors will refourme those enormities, and not augment them. The common people for the most part are in great feare when surueie is made of their land. If the surueie be skilfully made, it re­formeth [Page] ouer small measures, and excesses of rents. None can so wel tel what is indifferent betwéene Lord, and tenant, as the skilful sureueyor. Some part of his charge consisteth vpon iudgement, therfore séeing he is in some respects a Iudge: if he be godly, & iustly minded, he will not exact vpon the tenant, although the Lord please him for the surueie taking: but wil measure, and value, according to equitie and indifferencie, aswell for the discharge of his conscience, as the preseruation of his credit. We are now come to the Townes end, we wil talke more of these matters an other time.

FINIS.

This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Text Creation Partnership. Searching, reading, printing, or downloading EEBO-TCP texts is reserved for the authorized users of these project partner institutions. Permission must be granted for subsequent distribution, in print or electronically, of this EEBO-TCP Phase II text, in whole or in part.