Maitland Club > Works of Sir Thomas Urquhart

124. THE TRISSOTETRAS.
right to a large discourse apart, I will confine my pen upon this subject within those
prescribed bounds, and seeing the first basal, the first basidion, and first co-base, to-
gether with the datas whereby they are found out, viz. for the side, the first subten-
dentall, the first subtendentine, and the first co-subtendent, and for the angle the
prime cathetopposite, the next cathetopposite, and the first co-cathetopposite, the
datas being both for side and angle the same here that they were in the former mood,
then the subservient Ubamen, and its resolver Torp — Mu — LagCrf-Myr, with the
three peculiar problemets thereto belonging, Utopaet, Udobsed, and Vthophaeth, are
all and every one of them the same in this mood of Errelome, that they were in the
three foregoing moods of Ammanepreb, Enerablo, and Ennerable, these being the
onely foure moods which have a laterall prasnoseendal identity, the reader will not, in
my opinion, be so prodigall of his owne labour, nor covetous of mine, that either he
Mould put himselfe or me to any further paines, then have beene already bestowed
upon this matter by my selfe for his instruction ; and' therefore, leaving it for a sup-
posed certainty that the prasnoscendas or first bases, according to the nature of the
case, cannot escape the reader's knowledge, by what hath beene by me delivered of
them, I purpose here to give him notice that these foresaid first bases must concurre
with each its correspondent first subtendent, to wit, the first subtendentall, the first
subtendentine, and first co-subtendent, dignoscible by the characteristicks of t. £. £>.
for obtaining of the perpendicular, of which operation, Vchener being the subservient,
by whose resolver, Neg — To — NuC^Nyr, the problemets of Utsetca, Udaedca, and
Uthaethca are made manifest, as to the same effect it remaines couched in my com-
ment upon Ennerable, which is the onely mood that, with this of Errelome, hath a
subtendentine and basal catheteuretick identity.
The second work being thus perfected, the perpendicular thereby found out, is to
assist one of the rere subtendents in obtaining the illatitious terme of the maine quse-
situm correspondent thereto, discernable by the characteristicks or figuratives of c. t. 6.
or, more plainly to expresse it, the perpendicular must concurre, according as the
case requires it, with the second subtendentine, the second subtendentall, and second
co-subtendent, as you may see in the last mood, the datas of the resolutory partition
whereof are the same as here, to find out three bases which, by abstracting the first
from another base, then by abstracting another base from the second, and lastly, by
adding the third base to another, afford the summe and differences, which are the re-
quired bases.
For the performance of this operation, the same subservient and resolver suffice,
which served for the last ; so that Uchener subserveth it, by whose resolver, Neg —
To— NuO^Nyr, we are instructed how to explicate the subdatoquaeres of Wdcathced,
Wtcathuet, and Wthcathteth, or more orderly, Cathwdoed, Cathwtoet, and Cathw-
thceth.
All the three works being thus accomplished, the manner of conflating the last two