Maitland Club > Works of Sir Thomas Urquhart

THE TRISSOTETRAS. 127
Alamebna. Say-Nag-Saf^-Nir. -n r Enerablo. Sei-Tag-Sef^Tir.
Allamebne. Nag-Mu-NaJK^Mur. ( \ Ennerable. Neg-Nu-Ne$??Nur.
Amanepra. Na-Say-Nag#2f Sir. C j Erelomab. Mu-Nag-Muffcft'Nir.
Ammanepreb. Ta-Tag-SefCf'Syr. J v. Errelome. Nu-Ne-NufC^Nyr.
These being the eight disergeticks, attended by their adaequat finall resolvers, it is
not amisse that we examine them all one after another, and shew the reader how, with
the help of a convenient logarithmicall canon, he may easily out of the analogie of
the three first termes of each of them frame a computation apt for the finding out of a
fourth proportionall, to every severall ternarie correspondent ; and so in order, begin-
ning at the first, we will deale with Say — Nag — SaC3=Nir, which is the adasquat finall
resolver of Alamebna, and composed, as it is appropriated to the first mood of the
disergeticks, of the sines of verticals and the antisines of cathetopposites, and so pro-
ceed therein, that by adding to the summe of the sine of a verticall and cosine of a
cathetopposite, the arithmetical complement of the sine of another verticall, we will
be sure, cutting off the supernumerary digit or digits towards the left, to obtaine the
cosine of the cathetopposite required, which cathetopposites and verticals are particular-
ised according to the cases of the mood.
The second is Nag — Mu — Nafc3°Mur, which, running upon the antisines of verti-
cals and the co-tangents of subtendent sides, sheweth, that if to the aggregat of a first
hypotenusall co-tangent and verticall antisine, we joyne the arithmeticall complement
of the antisine of another verticall, observing the usuall presection, we cannot misse of
the cotangent of the second subtendent side required, which, both second and first
subtendents, have their peculiar denominations, according to the cases of the mood.
The third resolver is Na — Say — NagO^Sir, which, being nothing else but the
first inverted, runneth the same very way upon the antisines of cathetopposites and
sines of verticals ; and therefore doth the unradiused summe of the antisine of a ca-
thetopposite, the sine of a verticall, and the arithmeticall complement of the antisine
of another cathetopposite, afford the sine of the verticall, illatitious to the angle re-
quired ; which verticals and cathetopposites are particularised according to the variety
of the cases of this Sindiforating mood.
The fourth generall resolver is Tu — Tag — SefcrSyr, which, coursing on the tan-
gents of the cathetopposites and sines of the bases, evidenceth that the summe of the
tangent of a cathetopposite and sine of a first base, added to the arithmeticall comple-
ment of the tangent of another cathetopposite, unradiated, is the sine of the second
base, illative to the segment required ; which bases, both first and second, and cathet-
opposites, are specialised conform to the cases of this Sindiforiuting mood.
The fifth resolver is Sei — Tag — SeG3*Tir, which, composed of the sines of the
second and first bases and the tangents of cathetopposites, giveth us to know, that if
to the summe of the sine of a first base and the tangent of a verticall, we adde the