Maitland Club > Works of Sir Thomas Urquhart

THE TRISSOTETRAS. 99
OF THE DISERGETICK LOXOGONOSPHERICALS THERE
BE IN ALL FOURE FIGURES : TWO ANGULARY
AND TWO LATER ALL.
The two angulary are Ahalebmane and Ahamepnare ; the two laterall are Ehena-
brole and Eheromabne.
The first angulary disergetick loxogonosphericall figure, Ahalebmane, comprehend-
eth all those problems, wherein two angles being given with a side betweene, either
the third angle, or an opposite side is demanded, and accordingly hath two moods, the
first whereof is Alamebna, and the second Allamebne.
Alamebna concerneth all those loxogonosphericall disergetick problems, wherein
two angles being proposed, with an interjacent side, the third angle is required ;
which angle, according to the severall cases of this mood, is alwayes one of the angles
at the base, that is to say, in the termes of my Trissotetras, a prime, or next opposite,
or at least one of the co-opposites to the perpendicular to be demitted. And there-
fore, conforme to the nature of the case of the datoquasre in hand, and that it may the
more conveniently fall within the compasse of the axiome of Nabadprosver, an angle
by the first operation of this disergetick is to be found'out, which must either be a
double vertical], a verticall in the little rectangle, or a verticall, or co-verticall, as
sometimes I call it, in one of the correctangles.
Thus much I have thought fit to premise of the praenoscendum of this mood, before
I come to its Cathetothesis ; because, in my Trissotetrall table, to avoid the confusion
of homogeneall termes, though the order of doctrine would seeme to require another
method, the first and prime orthogonosphericall work is totally unfolded before I speak
any thing of the variety of the perpendicular's demission, to which, owing its rectan-
gularity, it thereby obtaineth an infallible progresse to the quassitum ; but, seeing in
the glosse I am not to astrict my selfe to so little bounds as in my table, I will observe
the order that is most expedient ; and, before the resolution of any operation in this
mood, deduce the diversity of the perpendicular's prosiliencie in the severall cases
thereof.
Let the reader then be pleased to consider, that the generall maxim for the Cathe-
tothesis of this mood is Cafregpiq, the meaning whereof is, that, whether the side
whereon the perpendicular is demitted be increased or not, that is to say, whether the
perpendicular fall outwardly or inwardly, it must fall from the extremity of the given
side, and opposite to the angle required ; however, it is to be remarked, that, in this
mood, whatever be the affection of the angles, unlesse they be all three alike, the per-
pendicular may fall outwardly.
The generall maxim for the Cathetothesis of this mood, as well as for that of all the
rest, is divided into foure tenets, according to the number of the cases of every mood.