lbert 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, then 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 fro