Maitland Club > Works of Sir Thomas Urquhart

THE TRISSOTETRAS. 115
blems, both of this and the next preceding mood, you be pleased to have recourse to
the glosse upon the last mood, where this matter is treated of at large ; to the which,
for avoyding of repetition, I doe heartily recommend you.
The first work being thus expedited, we are to find out the perpendicular by the
second ; but so as that my direction to the reader for the performance thereof shall de-
taine me no longer here then the time I am willing to bestow in telling him, that the
whole progresse of this operation, as well as of the preceding, is amply expressed in
my comment on the last mood, from which, what ere is written of the subservient,
Ethaner, itsresolver, To — Tag — SeC^Tyr, or the under-problems, iEtopca, iEdobca,
and iEthophca, thereby resolved, may conveniently be transplaced hither, and re-
seated there againe, without any prejudice to either; Ammanepreb being the onely
mood, which, with this of Enerablo, hath a basal and opposite catheteuretick identity.
The perpendicular, by these meanes being found out, must be employed in the last
work of this mood, to concurre with the second basidion, or little base, the second
great base, and the second co-base, for obtaining of such cathetopposites as are, or
usher the maine quassitas, which, in the first case, is the complement of the fourth pro-
portionall, viz. the next cathetopposite, to a semicircle ; in the second case the prime
cathetopposite, and in the third the second co-cathetopposite. For the perfecting of
this operation, Erelam is the subservient, by whose resolver, Sei — Teg — ToCd^Tir, we
are instructed how to unfold its peculiar problemets, CEdcathob, CEtcathop, and
CEthcathops.
All the three operations being thus singly accomplished, according to our wonted
manner, the last two must be inchaced into one, and therefore their resolvers, To —
Tag — Seff^Tyr, and Sei — Teg — To0^Tir, must be untermed of some of their pro-
portionals; the which, that we may performe the more judiciously, let us consider
what they signifie apart ; the first importeth, as in the last mood I told you, that, As
the radius is to the tangent of one of the opposite angles, so the sine of one of the first
bases to the tangent of the perpendicular ; the second soundeth, As the sine of one of
the second bases to the tangent of the perpendicular, so the radius to the tangent of
an angle, which either ushers, or is the angle required.
Hereby it is evident how the radius is a multiplyer in the one, and a divider in the
other, and that the perpendicular, which, with the radius, is a multiplyer in the second
row, is in the power of the three first termes of the first row, whereof the radius is one,
by vertue of all which we must proceed just so with these last two operations here, as
we have already done with the two last of the moods of Alamebna, Allamebne, and
Ammanepreb ; and ejecting the radius and perpendicular out of both, instead of To —
Tag — SeC3°Tyr, and Sei — Teg — Tot3=Tir, set downe Sei — Tag — Sefr^Tir, that
is, As the sine of one of the second bases to the tangent of one of the cathetopposites,
so' is the sine of one of the first bases to the tangent of one of the other cathetoppo-
sites ; which proposition comprehendeth to the full the last two operations, and accord-