A boke named Tectonicon briefely shewynge the exacte measurynge, and speady reckenynge all maner lande, squared tymber, stone, steaples, pyllers, globes. [et]c. Further, declaringe the perfecte makinge and large vse of the carpenters ruler, conteyninge a quadrant geometricall: comprehendinge also the rare vse of the squire. And in thende a lyttle treatise adioyned, openinge the composicion and appliancie of an instrument called the profitable staffe. With other thinges pleasaunt and necessary, most conducible for surueyers, landemeaters, ioyners, carpenters, and masons. Published by Leonarde Digges gentleman, in the yere of our Lorde. 1556.

Diuerse thinges conducible, to the arte of measu∣rynge. THE I. CHAPTER. (Book 1)

AS there are few craftesmen, whiche haue all the kyndes of Arithmetike rea∣dely:* 1.1 so I doo suppose none so ignorant but that they do, or maye easelye perceyue the simple significations of these Caracters or figures. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. and also theyr strength, in the firste, seconde, and thirde roumes placed.

Besides that, they must be familiar with these and suche like Fractions.

½ ⅓ 1/7 1/16 1/32 ¾ ⅘ 9/10 The firste leftwarde be∣tokeneth one secōd parte of an whole,* 1.2 be it Pearche, Inche, or any other measure: the nexte, one thyrde, then one seuenth parte: the other ensuyng, one sixtenth. So one thirty and two partes of an Inche. Thē folow thre fourthes: four fiftes. The last is nine tenthes of an Inch: that is nine partes of an Inch, diuided into ten porcions.

These I doo intend to put in my ensamples, and in my tables, and margines folowinge, to represente partes of Pearches or Inches.

As, if I woulde write halfe an Inche after this maner. ½. Thre quar¦ters of an Inche, thus. ¾ One eyght parte of a Pearche, on this wise. ⅛. So of the rest.

¶It is requisite also here to open what a Pearche, a Dayworke, a Roode, and an Acre is.

Althoughe there are diuers opinions engendred throughe longe custome in many places, of the length of a Pearch (vpon whiche our chiefe matter dependethe) yet there is but one true Pearch, by Sta∣tute apoynted to measure by. Wherin is ordey∣ned.

[illustration]

Breadthe.

Acre.

Lengthe.

3. barly cornes, drye, and rounde, to make an Inche: 12. Inches, a Foote .3. Foote, a Yarde .5. yardes and .½. a Pearche: 40. Pearches in len∣gthe, and .4. in breadth, an Acre.

So an Acre by statute ought to conteine. 160 pearches: the halfe Acre .80. pearches: a Roode, commonly called a quarter .40. pearches: a Day worke .4. pearches. Loe here the Acre expressed with his length and breadthe.

I must not omit here to tel you what thing is metest to measure land with.* 1.3 They vse commonly in the country, two peales, eyther of them the length of a pearch. They are very good.* 1.4 Yet for al kinde of lande, a corde .5. pearches in length, well seared with waxe & rosyn, knotted or marked at the ende of euery pearche, is more mete & rea∣dier. But in my fantasy, the Instrument Geometrical, which is put forthe in thende of this boke, passeth all them & other, for the exacte truth, & quickest spede. This instrument is so general & auaylable to so sundry thinges, that it alone requireth a large boke, if it shoulde be sufficiently set forthe.

Also I woulde not haue you ignorant what pece of lande is called a Triangle,* 1.5 which often shall hereafter be named. It is suche a fa∣shioned piece as hath, or is imagined to

[illustration]

haue thre sydes, and thre angels onelye: whether the sydes be equal or otherwyse as this figure sheweth.* 1.6 Againe, note that a lyne is sayde to fall squirewise, when it cutteth any thinge, or any syde of a Tri∣angle full crosse, lyke vnto a Squyre: As the hanginge pricked line, a. b. in .c. d. the base line of the Triangle. Loe, it cutteth the syde squyrewise, or full crosse, in the point b. and not as the other lyne a.* 1.7 e. dooeth. The Base of any tryangle is here called that syde, whiche is cut squyrewise of the hanging lyne.

Concerninge a Circle,* 1.8 knowe that the compasse of any circle,* 1.9 is named his circumference:* 1.10 the myddle point in him his Centre:* 1.11 the ryght lyne h.* 1.12 i. that goeth ouerthwart that

[illustration]

Centre, touchinge the circumference on bothe sydes, is his Diametre: the halfe of that line, the Semidiametre. Also an arcke is a pece of the circumference cut away, as ye se the arcke aboue the lyne f. g. Also f. g. and h .i. in this circle are named Parallels: for that they differ equally in al places, the one from the other.

Nowe because practyse and experience sheweth me, that there is almooste no lande, but it maye easelye be broughte by imaginati∣on, to a Triangle or Triangles, and so mooste truelye measured: therfore to be shorte, this order shalbe taken. I wyll fyrste fygure and set afore your eyes Triangled Lande, and other whiche by ima∣gination

shalbe brought into triangles. Then I shall teache the true measuring of them: I meane how to finde a length & breadth, with whiche ye shall enter the Table of accompt folowinge, where the a∣cres, and odde pearches, if there be any, shall appeare. As these fy∣gures are measured, so all tryangled land, and other, brought into triangles, of what fashion soeuer they be, shalbe measured, And be∣cause it is requisite for true measuring of all triangles, to finde a streigth hanging line, I shall shewe firste howe that Lyne is to be founde, imagined, or drawen.

Notes

• * 1.1

  Characteres numerall.
• * 1.2

  Fractions.
• * 1.3

  Instrumentes to measuce with Poales Corde knot∣ted.
• * 1.4

  Profitable staffe.
• * 1.5

  Triangle.
• * 1.6

  Line fallinge squirewise.
• * 1.7

  Base line.
• * 1.8

  Circle.
• * 1.9

  Circumferēce Center.
• * 1.10

  Diametre.
• * 1.11

  semidiametre Arcke.
• * 1.12

  Paralleles.