Maitland Club > Works of Sir Thomas Urquhart

THE TRISSOTETRAS. 119
that the datoquaere of Ennerable is bound for the veritie of its proportion, in all the
finall resolvers thereof, to the maxime of Niubprodnesver, because of the direct ana-
logic that, amongst its termes, is to be seen betwixt the sines complements of the
segments of the base, and the sines complements of the sides of the verticall angles,
which in all this treatise, both for plainesse and brevity sake, I have thought fit to
call by the names of first and second subtendents.
The fourth and last loxogonosphericall disergetick figure, and second of the lateralis,
is Eherolabme, which is of all those obliquangularie problems, wherin two sides being
given, and an opposite angle, the interjacent angle, or one of the other sides is de-
manded, and conforme to its two severall quassitas, hath two moods, viz. Erelomab
and Errelome.
The first mood hereof, Erelomab, comprehendeth all those loxogonosphericall prob-
lems, wherein two sides with an opposite angle being proposed, the angle between is
demanded, which angle is still one of the verticals, that is, the first verticall, the
second verticall, or the double vertical ; to the notice of all which, that we may the
more easily attain, we must consider the generall maxim of the cathetothesis of this
mood, which is Cafriq, the very same in name with the generall cathetothetick maxim
of Amanepra, and thus far agreeing with it, that the perpendicular in both must fal
from the angle required, and upon the side opposite to that angle, increased if need
be ; but in this point different, that in Amanepra, the perpendicular's demission is
from the angle required upon the opposite side, conterminat with the two proposed
angles, and in Erelomab, it falleth from the required angle, upon the opposite side
conterminat with the two proposed sides ; and according to the variety of the fourth
proportional], which, in the analogies to this mood belonging, ushers in the verticall
required, there be those three especiall tenets of the generall maxim of this mood, viz,
Dacracforaur, Damracforeur, and Dacrambatin.
Dacracforaur, which is the tenet of the first case, sheweth that if the given and
demanded angles be acute, and the third an obtuse angle, the perpendicular falleth
outwardly upon the third side, and the required angle is a first verticall.
Dambracforeur, the tenet of the second case, importeth, that if the proposed angle
be obtuse, and an acute angle required, the third angle being acute, the perpendicular
must likewise in this case fall outwardly upon the third side, and the angle demanded
be a second verticall.
Dacrambatin, the tenet of the third case, signifieth that if the proposed angle be
acute, and an obtuse angle required, the perpendicular falleth inwardly, and the de-
manded angle is a double vertical!.
I had almost forgot to tell you that Sindifora is the plus-minus of this mood, where-
by we are given to understand, that the summe of the top angles, if the perpendicular
fall within, and their difference, if it fall without, is the angle required ; and seeing
it varieth neither in name nor interpretation from the mensurator of Amanepra, the