Maitland Club > Works of Sir Thomas Urquhart

THE TRISSOTETRAS. 117
angle be acute, and that one onely of the other two be an obtuse angle, the perpen-
dicular falleth outwardly.
Damforac, the tenet of the second case, signifieth, that if the given angle be obtuse,
and the other two acute, that the demission of the perpendicular is externall, as in
the first.
Thirdly, Dakinatam, the tenet of the third case, and variator of the first, sheweth,
that if the proposed angle be of the same affection with one of the other angles of the
triangle, as in the first case, the perpendicular may fall inwardly.
The cathetology of this mood being thus expeded, the praenoscendas come next in
hand to be discussed, which are the first bases, whose subservient is Vbamen, and its
resolver, Torp — Mu — LagfrS^Myr, upon which depend the three subdatoquaeres of
Vtopaet, Vdobaed, and Vthophaeth.
Thus much I beleeve is expressed in the very table of my Trissotetras ; and though
a large explication might be with reason expected in this place, of what is but summa-
rily mentioned there, yet because what concerneth this matter hath beene already
treated of in the last two moods of Enerablo and Ammanepreb, the whole discourse
whereof may be as conveniently perused as if it were couched here, I will not dull the
reader with tedious rehearsals of one and the same thing, but, letting passe the pro-
gresse of this first work, with the manner of which, by my former instructions, I sup-
pose him sufficiently well acquainted, will proceed to the catheteuretick operation of
this mood, and perpend by what datas the perpendicular is to be found out.
To this effect, the praenoscendas of Ennerable, to wit, the first basal, the first basi-
dion, and the first co-base, being, by the last work, already obtained, must concurre
with each its correspondent first subtendent, viz. the first subtendentall, the first sub-
tendentine, and the first co-subtendent, discernable in their severall natures by the
figuratives of t. 3. 6. for the perfecting of this second operation. The subservient of
this work, is Uchener, by whose resolver, Neg — To — Nu03=Nyr, the three subpro-
blems, Utaeta, Utaedca, and Uthaethca, are made manifest ; by vertue whereof, it is
perceivable how the same quaesitum is attained unto by the datas of three severall,
both first subtendents and first bases.
The perpendicular being thus obtained, must assist some other terme in the third
operation, for the finding out of the maine quaesitum ; which quaesitum, though it be
different from the finall one of the last mood, yet is the knowledge of them both at-
tained unto by meanes of the same datas ; the perpendicular and the three second
bases being ingredients in both.
It being certaine then, that the perpendicular must concurre in the last work of this
mood with the second basidion, the second basal, and second co-base, for obtaining the
second subtendentine, the second subtendentall, and second co-subtendent ; Enerul is
made use of for their subservient, by whose resolver, To — Neg — Ne£3°Nur, we are