Maitland Club > Works of Sir Thomas Urquhart

THE TRISSOTETRAS. 85
the side can be had, Xemenoro praesubserves it for an angle, and Danarele becomes its
possubservient for the side required. The reason of both these operations is founded
on the second axiom, the last characteristick of whose directory inrolleth Shenerolem
for one of Eprosos enodandas.
The fourth figure is Erelea, which, being Monotropall, hath no mood but Pserelema.
This Pserelema encompasseth all those planobliquangulary problems, wherein the
three sides being proposed, an angle is required. This datoquasre not being resolvable
by the logarithms in lesse then two operations, because the segments of the base, or
sustaining side must needs be found out, that, by demitting of a perpendicular from
the top angle, we may hit upon the angle demanded ; the resolver for the segments
is Ba — Gres — Zes(fc?"Zius, whereby we learne, that, if from the logarithm of the
summe of the sides, joyned to the logarithm of the difference of the sides, we subtract
the logarithm of the base, the remainder is the logarithm of the difference of the seg-
ments, which difference being taken from the whole base, halfe the difference proves
to be the lesser segment. This theorem being thus the prsesubservient of this mood,
its possubservient is Vbeman, whose generall resolver V — Rad — EgCS'Sor, is parti-
cularised for this case Uxiug — Rad — IugcCS*Sor, which sheweth, that, if from the
summe of the logarithms of the totall sine, and of one of the segments given, we subduce
the logarithm of the hypotenusa conterminall with the segment proposed, the re-
mainder will be the logarithm of the sine of the opposite angle required ; for the de-
mitting of the perpendicular opens a way to have the theorem to be first in generall
propounded thus, as the subteudent to the totall sine, so the containing side given
to the sine of the angle required ; or, in particular, thus, as the cosubtendent adjoyn-
ing the segment given is to the radius, so is the said segment proposed to the sine of
the angle required.
THUS FARRE FOR THE CALCULATING OF PLAINE
TRIANGLES, BOTH RIGHT AND OBLIQUE:
NOW FOLLOW THE SPHERICALS.
There be three principall axioms, upon which dependeth the resolving of spherical]
triangles, to wit, Suprosca, Sbaprotca, and Seproso.
The first maxime or axiom, Suprosca, sheweth, that, of severall rectangled spheri-
cals, which have one and the same acute angle at the base, the sines of the hypotenusas
are proportionall to the sines of their perpendiculars ; for, from the same inclination
every where of the one plaine to the other, there ariseth an equiangularity in the two
rectangles, out of which we may confidently inferre the homologall sides, which are
the sines of the subtendents, and of the perpendiculars of the one and the other, to be