Maitland Club > Works of Sir Thomas Urquhart

114 THE TRISSOTETRAS.
heares the resolution of the cases of Ammanepreb, but that the habitude, which all the
termes thereof have to one another, proceedeth meerly from the reciprocall proportion
which the tangents of the opposite angles have to the basal segments, and contrariwise.
The third loxogonosphericall disergetiek figure, and first of the later, that is, the
first two termes of whose datas are sides, what ere the quaesitum be, is Ehenabrole,
which comprehendeth all those problems, wherein two sides being given, and an angle
betweene, either a cathetopposite angle, or the third side is demanded. This figure,
conforme to the two severall quaesitas, hath two moods, to wit, Enerablo and
Ennerable.
The first mood hereof, Enerablo, containeth all those obliquangularie questions,
wherein two sides, with the angle comprehended with them, being proposed, another
angle is required, which angle is alwayes one of the cathctopposites or angles at the
base, that is, either the complement to a semicircle of the next cathetopposite, the
prime cathetopposite, or the second co-cathetopposite ; to the knowledge of all which,
that we may with facility attaine, let us consider the generall maxim of the catheto-
thesis of this mood, which is Cafregpigeq, that is to say, that the perpendicular in all
the cases of Enerablo falleth from that given side, which is opposite to the angle re-
quired, upon the other given side, continued if need be ; and according to the variety
of the angle at the base, which is the angle sought for, there be these three especiall
tenets of the generall maxim of this mood, viz. Dacramfor, Damracfor, and Dasim-
quasin.
Dacramfor, which is the tenet of the first case, sheweth, that if the proposed angle
be sharp, and the required flat, the perpendicular must fall outwardly.
Damracfor, the tenet of the second case, signifieth, that if a blunt or obtuse angle be
given, and an acute or sharp demanded, the demission of the perpendicular must,
as in the last, be externall.
Lastly, Dasimquaein, the tenet of the third case, sheweth, that if the given and re-
quired angles be of the same nature, the perpendicular must fall inwardly.
Having thus unfolded all the intricacies in my Trissotetras of the cathetothetick
partition of this mood, I may, without breaking order, step back, to explicate what is
contained in the preceding partition ; and for the accomplishing of the first orthogono-
sphericall work of this mood, consider what its praenoscendas are, and by what datas
they are to be obtained ; but, seeing both the praenoscendas and the datas, together
with the subservient and its resolver, with all the three subdatoquaeres, and, in a
word, the whole contents of the first partition of this mood of Enerablo is the same
in all and every jot with the praenoscendas, datas, subservient, resolver, and proble-
mets, contained in the first partition of the last mood Ammanepreb ; I will not need
to tell you any more, then that the Trissotetras it selfe, though otherwise short
enough, shewing that Ubamen is the subservient to the praenoscendas, Torp — Mu —
LagG^Myr, its resolver ; and Utopaet, Udobaed, and Uthophaeth, the three subpro-