Maitland Club > Works of Sir Thomas Urquhart

THE
TRISSOTETRAS.
POSITIONS.
Every circle is divided into three hundred and sixty parts, called degrees, whereof
each one is sexagesimated, subsexagesimated, resubsexagesimated, and biresubsexa-
gesimated, in minutes, seconds, thirds, fourths, and so far forth as any computist is
pleased to proceed, for the exactnesse of a research, in the calculation of any orbiculary
dimension.
2. As degrees are the measure of arches, so are they of angles ; but that those are
called circumferential], these angulary degrees, each whereof is the three hundred and
sixtieth part of four right angles, which are nothing else but the surface of a plain to
any point circumjacent, for any space whatsoever about a point, is divided in 360
parts ; and the better to conceive the analogie that is betwLxt these two sorts of gra-
duall measures, we must know, that there is the same proportion of any angle to 4
right angles, as of an arch of so many circumferential degrees to the whole circum-
ference.
3. Hence it is that the same number serves the angle and the arch that vaults it,
and that divers quantities are measured, as it were, with the same graduall measure.
Angles and arches then are analogicall, and the same reason is of both.
4. Seeing any given proportion may be found in numbers, and that any two quan-
tities have the same proportion that the two numbers have, according to the which
they are measured ; if for the measuring of triangles, there must be certain proportions,
of all the parts of a triangle to one another, known, and those proportions explained
in numbers, it is most certain, all magnitudes being figures, at least in power, and all
figures either triangles or triangled, that the arithmeticall solution of any geometricall
question, dependeth on the doctrine of triangles.