Part 3 (1/2)

[Ill.u.s.tration: An arche.]

Nowe haue you heard as touchyng circles, meetely sufficient instruction, so that it should seme nedeles to speake any more of figures in that kynde, saue that there doeth yet remaine ij.

formes of an imperfecte circle, for it is lyke a circle that were brused, and thereby did runne out endelong one waie, whiche forme Geometricians dooe call an [Sidenote: An egge fourme.]

_egge forme_, because it doeth represent the figure and shape of an egge duely proportioned (as this figure sheweth) hauyng the one ende greate then the other.

[Ill.u.s.tration: An egge forme]

[Ill.u.s.tration: A tunne forme.]

[Sidenote: A tunne or barrel form] For if it be lyke the figure of a circle pressed in length, and bothe endes lyke bygge, then is it called a _tunne forme_, or _barrell forme_, the right makyng of whiche figures, I wyll declare hereafter in the thirde booke.

An other forme there is, whiche you maie call a nutte forme, and is made of one lyne muche lyke an egge forme, saue that it hath a sharpe angle.

And it chaunceth sometyme that there is a right line drawen crosse these figures, [Sidenote: An axtre or axe lyne.] and that is called an _axelyne_, or _axtre_. Howe be it properly that line that is called an _axtre_, whiche gooeth throughe the myddell of a Globe, for as a diameter is in a circle, so is an axe lyne or axtre in a Globe, that lyne that goeth from side to syde, and pa.s.seth by the middell of it. And the two poyntes that suche a lyne maketh in the vtter bounde or platte of the globe, are named _polis_, w^{ch} you may call aptly in englysh, _tourne pointes_: of whiche I do more largely intreate, in the booke that I haue written of the vse of the globe.

[Ill.u.s.tration]

But to returne to the diuersityes of figures that remayne vndeclared, the most simple of them ar such ones as be made but of two lynes, as are the _cantle of a circle_, and the _halfe circle_, of which I haue spoken allready. Likewyse the _halfe of an egge forme_, the _cantle of an egge forme_, the _halfe of a tunne fourme_, and the _cantle of a tunne fourme_, and besyde these a figure moche like to a tunne fourne, saue that it is sharp couered at both the endes, and therfore doth consist of twoo lynes, where a tunne forme is made of one lyne, [Sidenote: An yey fourme] and that figure is named an _yey fourme_.

[Ill.u.s.tration]

[Sidenote: A triangle]

The nexte kynd of figures are those that be made of .iij. lynes other be all right lynes, all crooked lynes, other some right and some crooked. But what fourme so euer they be of, they are named generally triangles. for _a triangle_ is nothinge els to say, but a figure of three corners. And thys is a generall rule, looke how many lynes any figure hath, so mannye corners it hath also, yf it bee a platte forme, and not a bodye. For a bodye hath dyuers lynes metyng sometime in one corner.

[Ill.u.s.tration: A]

Now to geue you example of triangles, there is one whiche is all of croked lynes, and may be taken fur a porti of a globe as the figur marked w^t A.

[Ill.u.s.tration: B]

An other hath two compa.s.sed lines and one right lyne, and is as the porti of halfe a globe, example of B.

[Ill.u.s.tration: C]

An other hath but one compa.s.sed lyne, and is the quarter of a circle, named a quadrate, and the ryght lynes make a right corner, as you se in C. Otherlesse then it as you se D, whose right lines make a sharpe corner, or greater then a quadrate, as is F, and then the right lynes of it do make a blunt corner.

[Ill.u.s.tration: D]

Also some triangles haue all righte lynes and they be distincted in sonder by their angles, or corners. for other their corners bee all sharpe, as you see in the figure, E. other ij. sharpe and one blunt, as is the figure G. other ij. sharp and one blunt as in the figure H.

[Ill.u.s.tration: E]

[Ill.u.s.tration: F]

There is also an other distinction of the names of triangles, according to their sides, whiche other be all equal as in the figure E, and that the Greekes doo call _Isopleuron_, [Sidenote: ?s?p?e???.] and Latine men _aeequilaterum_: and in english it may be called a _threlike triangle_, other els two sydes bee equall and the thyrd vnequall, which the Greekes call _Isosceles_, [Sidenote: ?s?s?e?es.] the Latine men _aequicurio_, and in english _tweyleke_ may they be called, as in G, H, and K.

For, they may be of iij. kinds that is to say, with one square angle, as is G, or with a blunte corner as H, or with all in sharpe korners, as you see in K.

[Ill.u.s.tration: G]