Here might I note the error of good _Albert Durer_, which affirmeth that no perpendicular lines can be paralleles. which errour doeth spring partlie of ouersight of the difference of a streight line, and partlie of mistakyng certain principles geometrical, which al I wil let passe vntil an other tyme, and wil not blame him, which hath deserued worthyly infinite praise. And to returne to my matter. [Sidenote: A twine line.] an other fashioned line is there, which is named a twine or twist line, and it goeth as a wreyth about some other bodie. [Sidenote: A spirall line.] And an other sorte of lines is there, that is called a _spirall line_, [Sidenote: A worme line.] or a _worm line_, whiche representeth an apparant forme of many circles, where there is not one in dede: of these .ii. kindes of lines, these be examples. [Illustration: A twiste lyne.] [Illustration: A spirail lyne] [Illustration: A touche lyne.] [Sidenote: A tuch line.] _A touche lyne_, is a line that runneth a long by the edge of a circle, onely touching it, but doth not crosse the circumference of it, as in this exaumple you maie see. [Sidenote: A corde,] And when that a line doth crosse the edg of the circle, thẽ is it called _a cord_, as you shall see anon in the speakynge of circles. [Sidenote: Matche corners] In the meane season must I not omit to declare what angles bee called _matche corners_, that is to saie, suche as stande directly one against the other, when twoo lines be drawen a crosse, as here appereth. [Illustration: Matche corner. Matche corner.] Where A. and B. are matche corners, so are C. and D. but not A. and C. nother D. and A. Nowe will I beginne to speak of figures, that be properly so called, of whiche all be made of diuerse lines, except onely a circle, an egge forme, and a tunne forme, which .iij. haue no angle and haue but one line for their bounde, and an eye fourme whiche is made of one lyne, and hath an angle onely. [Sidenote: A circle.] _A circle_ is a figure made and enclosed with one line, and hath in the middell of it a pricke or centre, from whiche all the lines that be drawen to the circumference are equall all in length, as here you see. [Illustration] [Sidenote: Circumference.] And the line that encloseth the whole compasse, is called the _circumference_. [Sidenote: A diameter.] And all the lines that bee drawen crosse the circle, and goe by the centre, are named _diameters_, whose halfe, I meane from the center to the circumference any waie, [Sidenote: Semidiameter.] is called the _semidiameter_, or _halfe diameter_. [Illustration]