Maitland Club > Works of Sir Thomas Urquhart

THE TRISSOTETRAS. 105
neall, and that the concurse of the proposed and required sides is at an acute angle,
that then the perpendicular must be demitted outwardly, and one of the proposed
angles becomes a second verticall.
The third tenet is Dadiscramgatin, whereby we learne, that if with the various
affection of the angles given, the concurse, mentioned in the preceding tenet, be at an
obtuse angle, the perpendicular falleth inwardly, and that one of the foresaid angles is
a double verticall. This is the onely case of Allamebne, wherein the perpendicular is
demitted inwardly, save when the three angles are qualified all alike, of which case,
because it falleth in all the moods of the loxogonosphericall disergeticks, and that in
Alamebna I have spoke at large thereof, I shall not need, I hope, to make any more
mention hereafter.
Having thus unfolded the mysteries of the perpendicular's demission in all the cases
of this mood, as I must doe in all those of every one of the other loxogonosphericall
disergeticks, because such obliquangulars, till they be reduced to a rectangularity,
which, without the perpendicular, is not performable, can never logarithmically be re-
solved, I may safely go on, without any let to the reader, to the three several! ortho-
gonosphericall operations thereof, as they stand in order.
The qusesitas of the first operation, which are alwayes the praenoscendas of the
mood, are in this mood the same that they were in the last, to wit, the double verti-
call, the first verticaline, and the first covertical, and are likewise to be found out by
the same datas, both of side and angle here, that they were in the former mood ; that
is, for the side by the first and great subtendent, the first but little subtendent, and the
first co-subtendent ; and for the angle, by the prime cathetopposite, the nearest cathet-
opposite, and the first co-cathetopposite : so that the datoquaere sounding thus, the
subtendent and an oblique angle being given to find the other oblique, the subservient
of this computation must needs be Upalam, and its resolver To — Tag — NuC3°Mir,
which sheweth that the subducing of the logarithm of the radius from the summe of
the logarithms of the sine complement of one of the first subtendents, and tangent of one
of the angles at the base, residuats the logarithm of the tangent complement of one of
the verticals required, and consequently involveth within so much generality the parti-
cular resolutions of the sub-problems of Upalam, viz. Utopat, Vdobaud, and Vtho-
phauth, diversified thus according to the variety of their praenoscendas, whereon, to
speak ingenuously, I intend to insist no longer ; for, besides that the peculiar enoda-
tion of all the three apart is clearly set downe in my glosse on the last mood, they are
in both the first partitions of the moods of Ahalebmane to the full expressed in the
table of my Trissotetras.
The verticall angles, according to the diversity of the three cases, being by the
foresaid datas thus obtained, must concurre with each its correspondent first subten-
dent, notified by the characteristicks of r. 8. 0. for finding out of the perpendicular re-
quisite for the performance of the second work in every one of the cases of this mood.
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