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.

Howe to measure all maner Triangled Lande. THE III. CHAPTER. (Book 3)

IF thou be an Arithmetrician multiylie this streigth hā∣ginge lyne,* 1.1 drawen as aboue as shewed, in halfe the nū∣ber of pearches of that syde which it cutteth squirewise. For want of that knowledge, take the aforenamed pear ches (I meane of the hanginge lyne, and halfe the syde which he cutteth) and with that Length and breadthe enter youre table of accompt, as there is set forth. So shall ye perceaue the nū∣ber of Acres, Roodes, Dayworkes. &c.

Ensample.

FOr the perfect measuring of triangles afore fygured, and all other, suppose the secōd of these laste. 9. fygures on thother syde, hauing written about it. a. b. c. d. to be a pece of land, whereof I would haue the true measure. I fynde by a corde or otherwyse, the pricked hanging lyne a. d. to be. 23. Pearches: the syde b. c. whiche it cutteth squirewise. 44. Pearches, whose halfe is. 22. With these. 22. & 23. the conuenient length and breadth, I enter the table of accompte. There I fynde by that table, at the corner where bothe the lynes of conunient length and breadth do mete .3. Acres, 6. Dayworkes, and 2. Pearches to be in that Triangle. Thus of all before fygured.

Here note,* 1.2 your Table must euer be entred with al the pearches of the hanging Lyne, and with halfe the side that he cutteth squire∣wyse: Or with the halfe hanging lyne, and the whole syde cut.

A figure of a double Triangle.

[illustration]

THis fygure e. f. g. h. is but two Triangles: and therefore measured as aboue in two partes: Or thus. The hangynge lyne, e. g. is .33. Pearches: the syde. f. h. that he cut∣teth squirewyse .20. Pearches, the halfe of the whiche is .10. Nowe enter your Table as afore, with 33. and .10. the conueniente lengthe and breadthe. So shall ye fynde, 2, Acres, 2, Daye∣workes and, 2, Pearches, the true contente of this fygrue, e, f, g, h,

An other ensample.

ADmit. i. k. l. m. lande to be measured. Because it is no maner Triangle, it must be brought by imagination, as I haue saied, into a Triangle or triangles.* 1.3 Which imagination is here signi∣fied

[illustration]

by the lyne dashed. i. l. Then as aboue is declared, it ought to be measured (accordinge to the rule of Triangles) in two partes, be∣cause there are two triangles in that lande. So by profe ye shal finde in the vpper. i. m. l. one Acre .3. Rodes and .5. Dayworkes: in the other i. k. l. one Acre. Thus I gather the whole content of that lande to be 2. Acres .3. Roodes, and .5. Dayworkes.

None otherwyse of the adioyned. n. o. p. q. and all other fygures fo∣lowynge, and other whatsoeuer they are, that by any meanes may be brought into triangles.

Furthermore knowe, that the fygure. i. k. l. m. is redely thus mea∣sured. Adde the pearches of bothe the hangynge lynes together: so haue ye. 23. Wyth this number, and wyth halfe the pearches of the syde. i. l. whiche he cutteth squyrewyse, beynge. 20. pearches, enter your table: so is founde as afore.

These two fygures folowynge may also be thus measured, other∣wise then by the rule of Triangles. Enter your table wyth theyr conueniente lengthe and breadthe. So shall ye fynde the contente of all suche.

[illustration]

These three fygures folowinge, althoughe they may be measured by the rule of Triangles: yet for quicker spede, they haue also theyr proper measuringe as ensueth.

Laye together the two sydes whiche are parallels of the fyrst fy∣gure a. that is .6. and 18. makinge .24. the halfe is .12. the breadthe .5. Enter with .5. and .12. your table. So haue ye one rode, and fyue day∣workes. For the other two b, c, and suche lyke, ioyne the heades or endes in one: and enter your table with halfe of those pearches, and with the whole number of the middle lyne.

[illustration]

How by supputation to measure all Triangled Lande.

* 1.4IOyne all the sydes together: take halfe: out of that halfe pulle euery syde, nothing difference. Then multiply the ••ifferen∣ces the one in the other: and the thirde difference augment in the product. That which encreaseth multiply in the halfe of all the sydes ioyned. Then the Radix of the surmontinge summe is the content of that Triangle.

* 1.5Nowe reste foure rules to be treated of. The fyrste for all maner regular square Superficies. The seconde for Rounde lande, and her partes. The third for Steples, Columnes, Globes, and theyr parts. The laste for Mountaines and Ʋalleyes. Here they shall in order followe.

Notes

• * 1.1

  Euclide the firste boke, 41. pro.
• * 1.2

  This Table foloweth.
• * 1.3

  Figures of many Angles.
• * 1.4

  To measure triangled lāde bi supputatiō
• * 1.5

  Foure rules folowing.