your Table made fast from the point of your standing draw a line into the next angle and measure the distance thither which measure set on the line drawne and then plant your Table againe in your third angle and in this order worke till you haue compassed the whole ground and if it fall out in the conclusion of your worke that the line and angle of your figure agrée with the line angle of the field then is your plat perfect if not you haue some errour And herein if I may aduise you begin your worke againe to finde your fault trust not to any helpe for the closing thereof wherein you shall but deceiue your selfe and happly of a small errour increase a greater for that you know not whether your saulte be in the lines or in the angles wherefore if your figures misse of closing aboue one pearche neuer trust vpon your worke And be sure when you plant your Instrument in one angle looke to the next that you so direct the sights that the visuall lines lye paralell to the hedge measured neither obseruing this paralelly is it materiall how far off the perimeter you place the Instrument alwaies prouided that you take your measure in the true direct place where the very hedge or bounds go for if you measure much within the hedge your lines fall too short if without too long therefore obserue the meane for in all things obseruare decorum is best This kind of measuring is principally and commonly vsed for woods for that in them a man cannot see the angles by any other me anes and may serue for all kind of other grounds and indéed commonly vsed of land meaters who hauing but this one Chapter and that rawly presume of the full knowledge of the vse of this instrument but how they performe it I leaue to those that shall try them which is but had as others before me haue reported CHAP. LVIII To draw the Plat of a field by placing the Instrument in euery angle thereof as in the last Proposition and yet measuring but one line in the whole Perimeter To draw the plâ—t of any field by going round about yet me asuring but one line FIrst place your instrument in that angle where you will begin which let be in such a place that the first line you go vpon may he of reasenable length then set vp a marke in the field in such a place as from thence you may see as many angles of the field as possible may bee which marke call your principall point and to that marke get the distance by your first and second station which let be in the first second angle in the field in order as before is set downe so shall you haue a point in your Table to represent that principall point in the field This done draw a line into the third angle and thereto remoue your instrument and hauing there placed it get the distance betwixt your two stations as you got your distance in the like case before which you shall performe thus Hauing first placed your Instrument by looking backe or by the néedle at his due situation lay your ruler either by the pricke on the paper that representeth the principall point in the field or by any point on the paper that you know representeth some marke in the field then turne your ruler about till you sée that marke in the field which the pricke by which your ruler lyeth doth represent and draw a line till it cut your stationary line and that point of interception sheweth the point on the paper where you stand in the field So in this order by placing your instrument in euery angle you may get the length of euery hedge seuerally with measuring but one in the whole and the conclusion will bee that in the end you shall make a figure with equall angles and lines proportionall to the plat of the field The premises bâ—â—ig well vnderstood and all things else well considered I will â—raue pardon and so cease further prosecution hereof presuming that there is sufficient said to open the whose scope of this chapter neither would I go about to fill the booke with many curious demonstrations and difficult questions to beguile the aspiring wit of the yong practitioner but onely set downe some such fewe things that were most requisite to bee knowne lest otherwise I should be held rather tedious then compendious and therefore I will hast to an end CHAP. LIX To take the plat of any Champion Field containing 2000. or 3000. Acres of ground by the plaine Table and yet neuer bee forced to change your paper YEt againe before I conclude I will giue you another way to séeke the plat of great Champion fields that containe 3000. or 2000. Acres by the Plaine Table which is not much differing from your worke by the Geodeticall Staffe You shall therefere place your Instrument in euery angle and so get euery angle and his sides To vse the plain Table and neuer change the paper not regarding the length of the conteining sides as you be wont then must you measure euery hedge and as you were wont to lay the same downe by your scale and compasse heere you shall but write the length of euery hedge vpon the lines drawne vpon your paper and responding thereunto so haue you finished and you shall neuer be forced to shift your paper nor haue the lines to runne off the same for that you may draw them as long or as short as you please Now when you come home vpon some shéete of paper protract all the angles one after another See the 3. chap. pro. 5. as you found them in the field allowing by your Scale and Compasse euery line his due length according as you finde the same note those figures vpon the said respondent lines and your conclusion will be to produce a figure like and proportionall to the field proposed This chapter is most excellent for the purpose before said and therefore worthy of note as they shall finde it that worke by the Plaine Table in countries that consist of great Champion fields CHAP. LX. What Chapter is most fit to vse in platting of ground as well such whose superficies is subiect to sight as others that be rough and full of wood as also to make choyce of the best instrument to performe the same as also to make a new kinde of particular YOu bee taught before to measure and plat any péece of ground whatsoeuer it resteth then for you to make choyce of such Propositions that are best as well in respect of the fashion of the field as in respect of the aptnesse of the Proposition Therefore for all grounds whose bounds and angles may all bée séene from one place vse the 51. Chapter and if you cannot trauers the same to measure it with your chaine by reason of pooles marshes or such like then is the 53. Chapter excellent as for the
degrées cut by the South end of the néedle which note downe and so procéed rightwards from angle to angle noting the degrées cut by the South end You are taught this chapter with a demonstration lib. 6. cap. 3. of the Geodeticall staffe vntill you haue gone round about the field of which degrées cut you shall make a little Table to the end you may remember how many degrées were cut at the first second third c. corner Next shall you cause one to mete with a chaine the true distance of the first corner from your staffe which note downe against the the first degrée cut in your Table then mete the distance of the second corner from your instrument which note downe in your Table against the number of degrées cut at the second corner and thus procéed vntill you haue gone round about the field laying downe the distance of euery angle from your instrument against his proper degrée cut which done fall to protracting thus Hauing prepared a faire shéet of paper as you be taught before about the middest thereof make a point which call your station then apply the edge of your instrument thereunto mouing him about vntill the South end of the néedle cut the degrées you noted at the first corner which done draw a line by the edge of the instrument from the point made in the paper out at length then moue him rightwards vntill the South end of the néedle cut the degrées noted at the second corner and then by the edge of the instrument draw another line as before so go forward vntill you haue finished all the degrées cut by the south end of your néedle noted in your Table then with your compasse take from your scale the distance of the first angle from your instrument which lay in the line first drawne from the point made in the paper towards the other end of the line then take the distance of the second corner from your instrument which apply to the second line drawne in the paper and so procéed from line to line according as you be taught in the third chapter of the Art of measuring ground The length of euery line laid downe in such order as is said then must you draw lines from point to point in each line so shall you drawe the limits and proportion of the ground according as in the foresaid third chapter of the art of measuring ground by the Staffe And by this meanes may you measure ground at two stations measuring but one line in the whole plat in such order as I set downe in the fourth chapter of the sixth booke of the Geodetical Staffe And since what is said before may giue sufficient light to performe both this way and many other I will omit further spéech least I rather seeme tedious to the wise then facile to the vnlearned And you shall heere note that by taking perfect notes in the field where one closse boundeth vpon another you may take the plat of many flelds lying together and so saue a great labour CHAP. LXXIIII The degrees of a field being taken to finde whether the plat will close the lines being truly taken To know if your plat will close NOte downe the quantity of euery angle at each seuerall station as well as you doe the degrées cut then adde vp all the quantities together then multiply 60. by a number lesse by 2 then the number of the angles and if your worke be right the product thereof shall be equall to the totall of the quantities Example Let the number of angles be 8. froÌ„ which take 6. which is a lesse then multiply 60. by 6. and the product will be 360. which agrâ—â—ing with the totall of all your quantities of angles added together is one argument that the plat will close CHAP. LXXV To reduce Hipothenusall lines vnto Horizontall after another way then in the 6 booke 8 Chapter of the Geodeticall Staffe onely by the sights in the old Circumferentor To reduce Hypothenusall lines to Horizontal lines PRepare a marke to bee carried before you the just height of your line of leuel from the ground when the iustrument is planted vpon his rest this marke must be placed in the angle whereunto you looke hee must stand perpendicular and when you take the degrée looke your instrument stand perpendicular and then moue the vane vpon the sight vntill you sée the top of the marke before planted through the hole in the vane and by the pins head then in the Hypothenusall diuisions cut by the vane vpon the sight for they will shew you how much that line you shall measure will differ vpon the 100 from that line you should measure if the ground were leuel therefore when you haue measured that line proportion him according to the parts cut Example Suppose the parts of the Hipothenusall diuisions cut to be 4 and the line measured to be 30 pearches now you are to finde a number to beare like proportion to 30 as 100 beareth to 104 which you shall find to be 28 1 5 1 1 so that the line measured by the cheine to be 30 pearches must be laid downe 28 1 1 1 3 pearches in your protracting But for asmuch as these calculations be tedious in the field your best way is to note the Hipothenusall parts cut and then reduce them when you come home CHAP. LXXVII To performe the same by a Quadrant made of purpose A new Quadrant to proportion lines YOu shal prepare a Quadrant and then diuide the limbe thereof in 30 equall degrees setting number therupon as the coÌ„mon order is then shall you diuide the lower side of the Quadrant the is betwixt the first degrée the center into 30 equall parts raising perpendicular lines vpon each diuision which will be paralell vnto the other side this done prepare an Index of the length of the semidiameter of the Quadrant with a center hole therein this Index is to be fastened to the center of the Quadrant with a brasse pin or such like which also must be diuided into 30 such equall parts as the semidiameter was the Quadrant thus prepared you shall fore shorten the lines thus First for the taking of your notes in the field you must work as in the last Chapter onely here you must note the degrée of a circle cut by the vane in stéed of the Hypothenusall diuisions and then procéed thus Put the Index to the different angles in the limbe then number the line measured vpon the Index and note the perpendicular there cut by the edge of the Index for that shall shew you the length of the Horizontall line which must be protracted Example Let the different angles from the Horizon be taken 18 degr and the line measured 20 perches first count 18 degrees in the limbe then thereunto bring the edge of the Index next count the line measured viz. 20. pearches vpon the Index fromwards the center so shall you there
the field where plant your Glasse and so take the quantity of that angle by the 23 Chapter then measure from that angle vnto the next angle noting it downe together with the first angle in some Table booke then take the quantity of that second angle and so measure from that angle vnto the 3 angle noting the same orderly downe so go round about the field stil taking the quantity of euery angle by the said 23 Chap. noting the same downe together with the quantity of their sides and when you haue finished vpon some plaine paper or vellam by the 25 Chapter protract euery seuerall angle laying downe the conteining sides thereof by your scale and compasse euen as you found the same by measure and as you be taught in the foresaid 25 Chapter The Arte of Geodetia fol. â—7 this requireth no example for that the angles being obserued the worke differeth naught from the 8 Chap. part 1. of my Arte of Geodetia CHAP. XXX To plat medowes plaine fieldes and pastures of no exceeding great quantity THis Chapter is best to be performed by plaÌ„ting your Instrument in some such place in the field from whence you may command the view of al the angles in the same field the quantity of which angles you must obserue by the 23 Chap. measuring the distance of each angle from your Instrument and so protract the same and lay their sides downe as in the 25 Chapter and this way I hold the best and truest in all such cases where the proposed field is not ouer great and if so be that the plat be not required but you put to measure the same your truest worke will be by this meanes to get the true plat thereof first and afterwards finde the contents by the 2 part of Geodetia and for that this chapter is also already performed in my first part of Geodetia Chap. 3. after the same methode as it is heere I will referre you therevnto for breuities sake And here note if you please hauing once planted your Planisphere in such order that the Diameter where the degrees doe take beginning may point into some one angle or other you shall not neede any more to moue the said Planisphere but onely keep him fixed moouing the Index from angle to angle round about noting the degrees cut by the Alhidada in the Planisphere at euery seuerall angle and so to protract the same by the 25 chapter These two kinds of waies remembred in this chapter and the last I do hold the best truest as for others many of them be vncertaine as the intersection of lines and such like but you may finde that remedied in the vse of the Psaine-Table the which if you can worke it there you néede not be to seeke here Many other pretty waies may you finde set downe in the seuerall vse of each Instrument which if you can performe in one you may soone performe the same in euery Instrument CHAP. XXXI To reduce lines Hypothenusall into lines Horizontall by the Topographicall Glasse COncerning ascending and descending grounds I told you in the first part of my Geodetia that it was not possible by one scale to lay downe the true plat and also by the same scale to render the true contents for that if the plat bee true the contents will bee false And on the contrary if the contents bee true the plat will be false the reason whereof I acquainted you with in the ninth Chapter of the sixth booke of the Geodeticall Staffe where I also taught you means to remedy the same and that diuers waies But forasmuch as wee shall not néede with this instrument to reduce these lines in the field but onely when we protract I will therefore deliuer a way which you may performe by this Glasse or by your Staffe In the very place where the ascent beginneth there plant your Glasse and in the top of the ascent a staffe of equall height with your Instrument Now turne the Index with the sights towards the staffe the planisphere being paralell and equidistant to the Horizon remoue the moueable sight in the demicircle vntill through that sight and the sight in 90. you sée the top of the staffe note then the degrées cut by the moueable sight for the angle of ascent then measure the distance betwixt your instrument and the staffe which increase by the signe of the complement of the angle of ascent part the product by the totall signe so haue you your desire For as the Secant is to the Radius so is the Radius to the signe of the Complement of the said Secant by the seuenth booke of the Geodeticall Staffe called Trigonemetria Example If the grounds descend as b d go to b and then worke as before But you shall not need to make this reducement in the fields vntill you come to protract And note further that if the ground ascend as a b and also descend as b d then must you in your protracting adde the Horizontall line a c and d c together and protract that in stead of the lines a b and b d so that by what is said before you may gather that the line which you measured in the field to be 40. pearches and rising 30. degrees high if you will worke truely should be laid downe not altogether 35. pearches CHAP. XXXII Certaine compendious Formes of working by my Tables in the seuenth booke of the Geodeticall Staffe called Trigonometria BEcause I haue taught you to performe many conclusions in this Booke by my Tables in the seuenth booke of my Staffe and for that there were some things omitted and some things also mistaken in the said booke I thought it not amisse heere to deliuer certaine compendious formes of working by the said Tables that is how to worke by any Triangle as you be taught for the auoiding diuision Compendium I. If the signe bee in the first and the Radius in the second or third how to bring the Radius into the first place for the auoiding of diuisiâ—n Regula â—or the signe that is in the first place put the Secant of the Complement thereof Et voti compos eris For as the signe is to the Radius so is the Radius to the secant of the Complement Compendium II. If the Tangent bee in the first place and the Radius in the second or third place to reduce the Radius into the first place for the auoiding of diuision Regula For the Tangent placed in the first place take the Tangent of the Complement Et negotium confectum erit For as the Tangent is to the Radius so is the Radius to the Tangent of the Complement Compendium III. If the Secant be in the first place and the Radius in the second or third how to bring the Radius into the first place for more ease in working Regula For the secant put in the first place take the signe of the Complement so shall you haue a true
together then be there certaine rulers of wood ioyned together with small brasse hinges which are made to fold as you may perceiue by this ensuing figure which beeing opened and stretched square serue iust to fall into the channel made about the 4 sides of the table these rulers in that place haue three vses principall the first is it ribs and binds the péeces of the table close together the next it holds the shéet of paper plaine and straight vpon the table vpon euery side lastly euery side respondently is diuided into a certaine number of equall parts which serue to drawe crosse paralel lines vpon the paper when you change your sheete as hereafter you may gather my meaning concerning the description thereof by the ensuing figure better then with many words Boxe Needle 3 To this Plaine Table there doth also belong a Boxe with a Néedle and a Card in the bottome thereof such a one as is described in the 1 Chap. This Boxe must be fixed to one of the sides of the Plaine Table a d or b c in such sort that the line in the boxe m n lie paralel thereto so shall k l lie close with the side of the table a d then is there an appendix growing to this boxe through which go two holes for passage that two screw pins may fixe the said boxe to the body of the Plaine Table as you may gather amongst the shadowed lines in the insuing figure ✚ N ↓ m 4 To the backe side of this Instrument there is fixed a socket of brasse with two screw pins as you may perceiue by this figure and in the midst of this socket there is a scrue pinne which serues to wreste against the Staffe that is put into this hollow socket prouided alwaies that you haue a thin péece of brasse within the socket for the scrue pin to force against the staffe being put therein 5 Also you must prouide a thrée footed staffe that is 3 legges or feete to be fixed in a head of box like a thrée footed paire of compasses set the head of your staffe that goeth into the hollow socket bewrapped in a plate of brasse so shall not the brasse pin crush the same being forced here against If you make the ruler and sights in brasse they were best to be made to fold vp and downe as the order is in such things Thus much of the description of the Plaine-table and his parts which I haue the rather wrote for their sakes that affect the same for whose sake also I will somthing prosecute the vse thereof CHAP. XLV Of the absurdities that many vse that affect the plaine Table and of reforming many inconueniences therein Why the plaine Table is affected by the vulgar THis Instrument is so plaine by reason of the ocular spectation of the worke still demonstrated before the eye that it hath thereby begot it selfe a wonderfull affectation of the vulgar whereby they vainly thinke no worke doth relish well vnlesse it bee serued vpon this plaine Table But this opinion is no lesse ridiculous then full of many doubts that I haue heard diuers plaine Table men propound Ignorance of some practizers Saith one I thinke the grounds you teach for the casting vp of péeces of ground be false for take a square and measure the same by your scale and compasses and note the contents and then reduce the same square into triangles and so againe measure the same by the doctrine of triangles and the contents produced by the square measure will differ from the triangular measure for you must note that he was a witty fellow that wrought by the doctrine of a curious small scale and a goodly blunâ—â—â—â—re of compasses as you may gather by the error he was in for get the contents of any square by multiplying the one side in the other as is taught and note the product then square one of the equall sides and double the offcome the square root where of is the diagonall Lib. 6. cap. 16. pro. 1. Bac. Geod then finde the perpendiculars by the 21. Chapâ—â—â— of the foresaid 6. Booke and so working according to the doctrine of triangles you shall finde the product of the two triangles to agrée with the formes square But to returne to the supplements of the wants in this Instrument Inconueniences in the plaine Table reformed First the paper of this instrument by occasion of wet is oftentimes blotted and blemished insomuch that the points lines and other obseruations bee in many places taken away and so by reason of hasty taking of the Table vp the paper is by the wet so stretched and disfigured that many errors grow vpon a small scale To auoyd all which and such like I thought good to giue this admonition First let your table be couered as you bee wont with a faire shéet of paper vpon which shéet let there be placed another shéet well oyled on both sides with Lin-séede oyle so may you worke notwithstanding the raine deaw or miste only draw the lines something more heauy vpon the vpper shéet that they may also pierce the lower apparantly And this thing note further in the Table that when you take plats oftentimes they will not all bee contained in one or two shéetes therefore you must drawe a number of paralell lines crosse wise at right angles that thereby you may ioyne the shéetes together truly which the diuisions vpon the foure rulers performes and as you measure the circumference of any plat by this Table oftentimes cast crosse angles Diagonal lines ouer the plate which will kéepe you the truer to your worke This holds not in hilly ground without reducing of hypo lines to horizontall for indéede a small error heerein produceth a great absurdity in the closure and you may now and then try if the chaine measure of your Diagonals agrée with your scale which if it doe not is a true argument of errour You must further haue a speciall care in reducing the lines hypothenusall to lines horizontall as you be instructed in the sixth booke I haue seene some plaine table man when he was set to measure a banke ascending round about go vnto the top thereof and so produce lines from euery corner vnto one center measuring it thereby one station and hee thought it was a rare deuice and had laid it downe in Plano truly But surely by how much the higher the ground was by so much the greater was his error But small banks and ridges as some suppose this respects not for that hee laid it downe in a greater compasse then it should insomuch that if he had laid the plaine adiacent sides precisely downe by that scale likewise the want of closure would haue contained a reasonable large péece of ground for you must néedes confesse that the lines he protracted vpon the paper were visuall or horizontall and the lines measured hipothenusall Other things should be reformed in
point vpon the paper which represented c and thereupon lay the fiduciall edge of the rule mouing the other end vntill through the sights you seâ— c so wilt the edge of the ruler in the line vpon the paper representing â— d thâ—â— kâ—â—ping the â—uler â—pon that point d I moue the other 〈◊〉 vntill it pâ—â—oâ— to 〈◊〉 shall the fiduciall edge of the rule intersectâ— witâ— the â—â—â—e 〈◊〉 the papâ—â— represenâ—â—ng a b from the point of which intersection to the point a is b the termes of the line a b which being measured by your scale and compasses is found 133 pearches CHAP. XLIX To take the distance of any two townes or such like COnsider well the premises and this labour is already effected therefore plant your Instrument at a Latitudes as you were directed in the 29 chapter and let the latitude required be d c noâ—â—raw lines from a to point to d and c and also to b your second station now obseruing the former directions I â—emoue my instrument to b and so draw lines from b to point againe to d and c then doe I note the concurse or intersection of the said lines which I measure by the scale and compasses as before so will the stationary line a b bee 316 perches and the distance required d c 131 perches A note for many distances And here note if you had sought more distances as the distance of f e e d d c c. the labour is no more but to draw lines at euery station to point â—nto the distances required and then to note the intersection of matchy lines vpon the paper which after measure by your scale and compasses so shall you haue your stationary line g h 10 score the distance f e 12 score c. whereby you may plat any field and come not within the same as in the 8 chapter CHAP. L. To finde the Horizontall distance of any place from you standing by a new way vpon the Plaine-Table To finde any Horizontall distance after a new way IN the 44 chap. at twice I told you of 4 certaine rulers or ribs that were belonging vnto the Plaine-Table euery one being diuided into a 100 equall parts or more by these rulers ordered in their due place vpon the Plaine-Table shall I teach you to séeke the Horozintall distance of any place thus Lay the ruler with the sights vpon the very edge of one of the sides of the Plaine-table turning the Table about vntill through the sights you espy the marke whose distance is required but with this prouiso that the corner of the Table where the diuision take begining be neerest vnto you this done take the ruler with the sights the Table vnmoned and place the same vpon the right side the Table as before and then looking through the sights espy your second station in a knowne distance from your first station Next shall you beare your Instrument to your second station situating the Instrument by helpe of the Needle and backe sights here in all respects as it was at the first which being done lay the ruler ouer the corner or both sides of the Instrument remoouing the same vntill through the sights you espy the marke whose distance is required lastly note the equall parts vpon the ribs cut by each end of the ruler or sight hauing regarde to those parts that doe responde to the statinary line and also to the distance required for as the parts respondent to the stationary line are to the line it selfe being measured and knowne so are the parts respondent to the distance vnto the distance required therefore worke by the golden rule in this worke the line of distance and stationary line alwiaes cut at right angles this needeth no example for as it is most exact so it is most plaine easy The premises béeing considered and the doctrine before well vnderstood you may produce infinite wates to performe many rare conclusions but we cannot stand to set downe a demonstration to suite to euery proposition that may happen in the field chiefly for that let the demand stand howit will you may resolue the same by due regarding the prescript Now I will briefly touch the order of taking a plat of a field mannor c. by the plain Table according as we haue dealt with the Geodeticall staffe and other instruments before ayming to performe some such propositions here that were omitted in the other bookes for it would increase the volume ouer much to set downe euery kind in the vse of euery instrument since wee understanding what is said of the one may also be performed in the other and that much after one kind of method as I haue said before but indeed I haue here set downe such propositions that will best agrée with the Plaine Table and are aptest to be wrought thereon setting aside all impertinent demonstrations And you shall note for diuers good respects that I shall omit one thing that standeth firme and is ordinarily vsed in demonstrations of this nature that is lines to represent the Instrument the lines also drawne thereupon my reason is because I will not confound the worke with multitude of lines as also to saue the cutting of many figures whereby such that serued in the Glasse likewise serue in the Plaine Table CHAP. LI. To draw the plat of a peece of ground at one station where all the angles of the field may be seene from that place of standing At one station to get a plat FIrst goe round about the field and in euery angle set vp some marke then plant your table couered with paper in such a place as from thence you may sée all the angles of the field that done in a place conuenient of your table make a pricke or point to represent the place of standing from the point to each marke draw a visuall line by the edge of your Ruler then from your place of standing measure exactly with your wire line the iust distance in pearches to each seuerall mark and set those distances by the scale each vpon his own line which was drawne to those markes noting these seuerall points where these measures end Lastly from point to point by the edge of your Ruler drawe lines which shall include a figure proportionall to the field to be measured and the lines so drawne shall represent the hedges of the field as in this demonstration Your station is i the lines drawne from i to point to euery angle are i a i b i c i d i k i e i f i g and i h which are measured as is noted vpon each line as i a 27 pearches i b 9 ¾ pearches c. then from a to b I drawe a line and so go round so haue I made a figure proportionall which was required CHAP. LII To drawe the plat of any field by the rule taught in the last Chapter where you cannot from one place of the field see
of the field a is my first station b my second and so working by the doctrine of the 31 Chapter I obtaine a line like proportionall to the field which was required CHAP. LVI To draw the plat of a field by many stations and and yet to measure but one line in the whole FIrst set vp marks in euery angle then point out your first station where your instrument being placed draw from the pricke of your station lines to as many angles as you can conueniently see then appoint out your station in such a place from whence you may see all those marks to which you draw lines at your first station to which station draw a line and measuring the distance betwixt those two stations vpon that line set your distance by your scale and then remoue your Table to your second station where plant it in his due situation and then from the center of that situation draw lines againe to each angle whereunto you drew lines at the first and note the interception ech with his match line and then draw lines from point to point which shall represent somuch of the hedges of the field as you haue gotten by these two stations Now your instrument standing thus at your second station vntemoued from the center of your second station againe draw lines to as many new angles as you sée that is from whence you haue not drawne lines before then chuse out a third station from whence you may sée all those angles whereunto you drew lines last before and then draw that station line and then againe remoue your Table and hauing placed it in his due forme to find the center of this your third station doe thus lay the edge of the ruler to any point in the paper which doth represent some marke in the field and remoue your ruler to or fro till through the sight thereof you sée that marke in the field which the point on the paper doth represent by which the edge of the ruler doth lye and then draw a line towards you till it cut the station line and note the interception for that point representeth the pricke of your third station And from the pricke or center of your second station to that point sheweth the distance betwixt the second and third station viz. that point on the paper sheweth in what part of the field your instrument is placed Now from that center draw lines to all the angles which you drew to your second station where they intercept or crosse each his match lines make prickes or points there and so from point to point draw lines which shall represent so much of the hedges of the field as there you could see and draw lines vnto This done and the Table vnremoued from that point or center of your standing or third station draw lines to as many angles as you can sée which haue not lines drawne to them already Then chuse out a fourth station in such sort as you did chuse out your third and to this get your distance as there you did and then intercept those lines as before is taught and in this order make so many stations as neede shall require till you haue ended your whole worke and at last you shall produce a figure with lines proportionall and equal angles to the plat of the field Example My first station is a whence I obserue the angles d e f k l m my second station is b whence I draw lines to point to as many of the angles I obserued at my first statioÌ„ as you can see as b d d e b f. and so noting the intersection of matchy lines draw the lines d e and e f which is so much of the hedges that you haue obserued now the Instrument vnremoued at b I espy as many more angles from b as I well can as g h and i and so draw lines to represent b g b h and b i. Lastly I espy some other place whence I may see all these three former angles but the way to finde your third station c is thus vpon some point on the paper representing some angle in the field as e laying there the edge of your ruler mouing the other end vntill you obserue through the sights the angle e then note where the edge of your rule and the line b c intersecte as at c so shall you finde the true place where your instrument stands your instrument resting situate at c in all respects as at the other stations draw lines to point from c to g h and i and so note the intersection of these lines with their matchy lines drawn froÌ„ b so haue you another part of the perimeter by drawing lines from one intersection to another as g h and h i and for that you may see from c to all the rest of the angles k l and m obserued at a therefore I draw lines to point from c to k to l and m and so noting the intersections as before and drawing lines I haue included a figure proportionall and like to the proposed figure Note I draw no figure vpon a b or c to represent the Table because I will omit the multitude of lines and letters and this kind of intersection of lines being duely ordered of all other is the best because by apt chusing of your stations you may auoide acute angles CHAP. LVII To draw the plat of a peece of wood ground where for the thickenesse of the wood a man cannot place his Instrument but onely in the angles of the perimeter IN this manner of worke you shall vse 4 men to helpe you whose labour shall he thus two measure with the line the distance from angle to angle one man to go before you into euery angle and the fourth man to be left standing in the place where you planted your Instrument because you must for the more precise planting your Instrument at euery remoue looke backe to him Being thus furnished you shal begin your worke as followeth First plant your Instrument in any angle and appoint for your place of standing some pricke in your paper then draw a line into the next angle which line measure on the ground and set those measures by the scale on the line drawn then place your instrument in the angle say the ruler along the line drawne theÌ„ turne the Table about til you sée the angle or the man left in the angle froÌ„ whence you came last where screw fast the Table and for your more assurance you may behold your néedle The singâ—lar vse of the backe sight which in this kind of platting will stand you in great stéed For looke what degrée your néedle did cut your first standing the same degrée must it stand on at your other standing wherefore it were good at the first placing of his instrument to write downe the degrées cut by the néedle for the helpe of memory in the rest of the angles I say this done and
line from that point along the edge of the instrument then kéeping the edge still at that point moue the instrument vntill the South end of the néedle cut the degrées noted at your second obseruation then draw another line by the edge of your instrument whereupon lay the line measured betwixt both your stations counted from the point first made towards the end of the said line and where that number ends there make a point which let represent your second station where place the edge of your instrument turning him about vntill the south end of the néedle cut the degrées you noted at the second station then by the fiduciall edge of the instrument draw a line note where it intersecteth with the first line for that is the place of the marke whose distance is required the distance of which from either of your stations may you measure by the Scale that you expressed the length of your stationary line by CHAP. LXXI To take an altitude onely by the old Circumferentor To take an altitude YOu must first get the horizontall distance vnto the thing whose length is required then plant your instrument perpendicular and moue the vane vntill through the hole therein you sée the top or the summitie of the altitude note then the equall parts cut by the side of the vane for such proportion as they beare vnto 100. the like doth the altitude vnto the distance multiply therefore the distance by the parts cut and diuide by 100. the quotient she weth the height which is correspondent to the leuell of your eye The ground of this worke is borrowed from the Iacobs Staffe as may appeare in the ninth Chapter of the fifth booke of the Geodeticall Staffe An inconuenience like to that in the Theodelitus But in taking of altitudes you shall haue it oftentimes so fall out that the altitude will be so high that you cannot bring the vane so low as to sée the top of the altitude by the hole and pins head When it so happens you must place the center of the Index vpon the wire in the shorter sight looking through the sight hole in the Index vntill by the wire and through the said sight you sée the summitie of the altitude then note the equall parts cut by the fiduciall edge of the Index vpon the right edge of the instrument for as those parts are in proportion to 60. the like proportion hath the distance vnto the height And so that proportion as those parts cut haue to the parts cut in the Index the very proportion hath the distance to the visuall line Therefore multiply the horizontall distance by 60. and diuide by the parts cut on the right edge of the instrument the quotient will shew the height Againe multiply the horizontall distance by the parts cut in the Index and diuide the same by the parts cut in the edge of the instrument the quotient sheweth the visual or hipothenusall line As you séeke altitudes so must you sinde profundities as I haue said often in the Geodeticall Staffe but the errour is great if the instrument be not exact paralell CHAP. LXXIII To take the plat of a peece of ground by the old or new Circumferentor DIuers wayes may bee set downe to fetch the plat of a péece of ground by this instrument To measure woodland or any other ground but I hold that most easie which is to be protracted by the Instrument it selfe because you shall not bee troubled to séeke the quantitie of angles which in this Instrument is ouer tedious Hauing therefore a péece of ground giuen you shall begin at some one corner and there plant your Instrument looking vnto the next corner and note what degrée the south end of your néedle cuts then with a chaine measure from the first corner to the second and note downe the degrées cut by the south end of the néedle and the length of the line measured Next go to the second angle and there conuey your sight to the third angle paralell to the hedge then measure the distance from the second corner vnto the third noting downe the degrées cut by the south end of the néedle the length of the line at your second obseruation Then go vnto the third angle and note the degrées cut and the length of them and so procéede from angle to angle noting the degrées cut and the length of euery line answering thereunto vntill you haue gone round about And if you being at any one angle and from thence can sée two or three angles more you shall not néed to remooue your instrument to any of them but onely from that angle obserue all the rest onely measuring the hedges With these notes you shall resort vnto a faire shéete of paper and there protract it downe thus In some place of the paper make a point and there place the fiduciall edge of your Instrument turning it about vntill the south end of the néedle cut like degrées as he did at your first obseruation then drawe a line by the fiduciall edge of the instrument whereupon from the said point to wards the other end lay downe the length of the first measured line which you must take with your compasse from your scale where that number ends in the said line there make a point where place the edge of your instrument mouing him about vntill the South end of your néedle cut like degrées hee did at your second obseruation then drawe a line by the fiduciall edge thereof whereupon lay the length of your second line and where that number ends make a point where as before place the edge of your instrument mouing him vntill the South end of the néedle cut like parts hee did at the third obseruation then drawe a line by the edge thereof whereupon lay the third line and where that number ends make a point as before placing there the edge of your Instrument turning him vntill the South end of the néedle cut like parts as at the fourth obseruation and so procéed laying downe the parts cut and the length of the lines vntill you haue gone round about by which meanes you shall lay downe the plat of the péece of ground in true forme then for the casting vp thereof resort vnto my booke of the art of measuring ground CHAP. LXXIIII To take a plat at one station from whence you you may see all the angles in the field by the old or new Circumferentor To take a plat at one station THis kinde of working is performed with as much ease as the former You shall therefore repaire into the field and finde some such place from whence you may behold all the corners in the said field where plant your instrument and then begin at some one angle whereunto direct your sight noting the degrées cut by the South end of the néedle then direct your sight vnto the second corner vpon the right hand and there againe note the
any altitude is leuell with your eye c. 19. p. 58 To search out lengths in heights c. 20. p. 59 To reduce parts of the right side the Geometricall quadrant into parts proportionall of the left side c. 21.61 To find lengths in heights by the Geometricall quadrant in the Glasse c. 22. ibid. To know how much one hill is higher then another 23.64 To know if water will run to the appointed place c. 24.67 To take the quantitie of any stationary angle c. 25.70 To make a protractor scale c. 26. ibid. To protract an angle and lay downe the ends c. 27. p. 71 To obserue an angle of position and protract it c. 28.73 To take the plat of a great chāpion c. c. 29. p. 74 To plat meadows plain fields pastures c. c. 30.75 To reduce lines hypothenusall into lines horizontal 31.76 Cōpendious forms of working by the Geod staffe 32.77 To square lands and to reduce irregular formes to regular c. 33.80 To search the perpendicular in any triangle c. 34.81 To reduce many plats or obseruations into one map 35.82 To diuide an Empire kingdom or continēt into Prou. 36.85 Reasons why the suns altitude hath bin hitherto falsly obserued 37.87 Paralaxes of the sunne ib. 88. A table of the sunnes paralaxe ib. 90 Correcting the taking of the starres altitude 38.91 To take the altitude or Almicanther of the sunne or any starre and to find their Azimuth 39.92 To take the amplitude of sun or starre 40.93 To get the houre of the day the houre of sunne rising or setting by the Topographical Glasse 41. ib. To find the houre of the night likewise hie water 42.64 Additions to the planisphere in the Glasse ib. 95 To vse the Topographicall Glasse as the Plaine table 43.97 A description of the plaine table 44.98 Absurdities vsed of many who affect the plain table 45.102 Things belonging to the vse of the plaine table c. 46.104 To take any horizontall distance by the plaine table c. 47. ib. Part of the distance of any thing giuen to find the rest ch 48. p. 107 To take the distances of two townes c. c. 49. p. 108 To find the horizontall distance from you by a newe way c. 50. p. 110 To draw the plat of a peece of ground at one station where all the angles of the field may be seene 51.112 To drawe the plat of any field where you can not see all the angles c. 52. p. 113 To drawe the plat of a field by once placing the instrument in an angle of the field and measuring the field round about c. 53. p. 115 To take the plat of a field by the rule of the foregoing Chapter where all the angles cannot be seene from one angle c. 54.116 To draw the plat of a peece of ground by two stations and measuring but one line c. 55.117 To draw the plat of a field by many stations and yet measure but one line in all c. 56. p. 118 To drawe the plat of a peece of wood-wood-ground which for thicknesse one cannot set an instrument in c. 57.120 To drawe the plat of a field by setting his instrument in euery angle yet measuring but one line c. 58. p. 122 To take the plat of any champion field by the plaine table yet neuer change paper c. 59. p. 123 What chapter is fittest to vse in platting of ground what instrument to vse c. 60.124 A description of the circumferentor and the parts thereof c. 61. p. 126 Of the Sights longer shorter c. ib. p. 127 The Circumferētor his appellation and things generally to bee considered therein c. 62. p. 129. To take the Almincanther and Azimuth of the sun 63.130 To know in what part of the horizon any thing seene lieth c. 64. p. 131 To finde the houre of the day by sight of the sun c. 65. p. ib. To find the houre of sun rising and setting c. 66. p. 132 To find the amplitude of rising sun or starres c. 67. p. ib. Of the opposite degrees and how to find them c. 68.133 To find the quantitie of an angle c. 69. p. 134 To take the distance of any marke by the old Circumferentor c. 70. ib. To performe the last Chapter by protracting the Circumferentor ch 71. p. 135 To take an Altitude onely by the Circumferentor 72.136 To take the plat of a peece of ground by the old or new Circumferentor c. 73. p. 137 To take a plat at one station by the circumferentor 74.139 Degrees of a field being taken to finde the closing of the plat ch 75. p. Ibid. To reduce hypothenusall lines into horizontall c. 76. p. 141 To performe the same by a Quadrant ch 77. p. 142 To take Altitudes by such a Quadrant ch 78. p. 143 To take the declination of a wall chap. 79. p. ib. Suruey of a Mannor ib. p. 144 To make a Map and sea Carde ibid. p. 146. To discouer the true plat of a parke forrest c. c. 80. p. 148 To cast the contents of a parke chap. 81.153 To plat any field by intersectiō of lines c. 82. p. 159 To seeke the distance of a Turret c. 83. p. 158 To finde the length of any hypothenusal c. 84. p. 160 To finde the distance of two Towers c. 85. p. 162. To finde the distance of any thing from you 86. p. 165 To know whether a ship come to you or goe from you chap. 87. p. 167 A ship pursuing another when it will ouertake the former chap. 88. p. Ibid. How to take the platforme of a house Castle c. 89. p. 168 To discouer how Mines and Trenches run ch 90. p. 169 To place barrels of powder vnder Castles c. ch 91. p. 170 Whether a mine bee aboue or vnder the Horizon chap. 92 p. 171 To know which way it declineth ch 93. ibid. To build and situate a Cittie ch 94. p. 173 To build and situate a Mannor chap. 95. p. 174 To sinke a wel and conuey water pipes c. 96. p. 177 To draw the plat of a building or other thing not seene ch 97. p. 179 To make an excellent ruler for reducing plats chap. 98. p. 180 To burne any thing farre off with the Sunne beames ch 99. p. 182 To make a Glasse to discerne any small thing halfe a mile off as to reade a letter c. c. 100. p. ibid. How to buy annueties or money due afterwards ch 101 p. 183 The measuring of Solids and Plaines THe best time to fell Timber and to season boords chap. 1.186 To measure solid timber 2.187 To find the square of any tree growing 3.188 To find the square of a tree vnsquared 4.189 To find the square of a squared peece 5.190 To find the square of any flat peece 6.191 To find the square of a peece like a diamond 7.192 To find the square of peeces of 3 5 6 7 or 8 sides looke the 8 and 9 chap. p. 193 To find how much timber will make a foot square 10.195 To measure all sort of timber 11.196 Of surfaces and solide figures 12.197 Measuring contents superficiall and solide 13.200 To measure the aire or any plaine surface 14.202 FINIS You may haue any of the Instruments in this booke made of wood in Hosier lane neere Smithfield in London by Iohn Tomson The Glasse is made in brasse in blacke Horse-ally neere Flecetebridge by Elias Allin