Part 4 (1/2)
[Ill.u.s.tration: The globe as is before.]
Howe be it you must marke that I meane not the very figure of a tunne, when I saye tunne form, but a figure like a tunne, for a _tune fourme_, hath but one plat forme, and therfore must needs be round at the endes, where as a _tunne_ hath thre platte formes, and is flatte at eche end, as partly these pictures do shewe.
_Bodies of two plattes_, are other cantles or halues of those other bodies, that haue but one platte forme, or els they are lyke in foorme to two such cantles ioyned togither as this A.
doth partly eppresse: or els it is called a _rounde spire_, or _stiple fourme_, as in this figure is some what expressed.
[Sidenote: A rounde spier.]
Nowe of three plattes there are made certain figures of bodyes, as the cantels and halues of all bodyes that haue but ij.
plattys, and also the halues of halfe globys and canteles of a globe. Lykewyse a rounde piller, and a spyre made of a rounde spyre, slytte in ij. partes long ways.
But as these formes be harde to be iudged by their pycturs, so I doe entende to pa.s.se them ouer with a great number of other formes of bodyes, which afterwarde shall be set forth in the boke of Perspectiue, bicause that without perspectiue knowledge, it is not easy to iudge truly the formes of them in flatte protacture.
And thus I made an ende for this tyme, of the definitions Geometricall, appertayning to this parte of practise, and the rest wil I prosecute as cause shall serue.
THE PRACTIKE WORKINGE OF +sondry conclusions geometrical.+
THE FYRST CONCLVSION.
To make a threlike triangle on any lyne measurable.
Take the iuste l?gth of the lyne with your cpa.s.se, and stay the one foot of the compas in one of the endes of that line, turning the other vp or doun at your will, drawyng the arche of a circle against the midle of the line, and doo like wise with the same cpa.s.se vnaltered, at the other end of the line, and wher these ij. croked lynes doth crosse, frome thence drawe a lyne to ech end of your first line, and there shall appear a threlike triangle drawen on that line.
[Ill.u.s.tration]
_Example._
A.B. is the first line, on which I wold make the threlike triangle, therfore I open the compa.s.se as wyde as that line is long, and draw two arch lines that mete in C, then from C, I draw ij other lines one to A, another to B, and than I haue my purpose.
THE .II. CONCLVSION
If you wil make a twileke or a nouelike triangle on ani certaine line.
[Ill.u.s.tration]
Consider fyrst the length that yow will haue the other sides to containe, and to that length open your compa.s.se, and then worke as you did in the threleke triangle, remembryng this, that in a nouelike triangle you must take ij. lengthes besyde the fyrste lyne, and draw an arche lyne with one of th? at the one ende, and with the other at the other end, the exple is as in the other before.
[Ill.u.s.tration]
THE III. CONCL.
To diuide an angle of right lines into ij. equal partes.
First open your compa.s.se as largely as you can, so that it do not excede the length of the shortest line y^t incloseth the angle. Then set one foote of the compa.s.se in the verye point of the angle, and with the other fote draw a compa.s.sed arch fr the one lyne of the angle to the other, that arch shall you deuide in halfe, and th? draw a line fr the gle to y^e middle of y^e arch, and so y^e angle is diuided into ij. equall partes.
[Ill.u.s.tration]