Maitland Club > Works of Sir Thomas Urquhart

S6 THE TRISSOTETRAS.
amongst themselves proportionall. Its directory is Uphugen, by the which we learn,
that Uphanep, Ugemon, and Enarul, are its three enodandas.
The second axiom is Sbaprotca, whereby we learne, that in all rectangled sphericals
that have one and the same acute angle at the base, the sines of the bases are propor-
tionall to the tangents of their perpendiculars ; which analogie proceedeth from the
equiangularity of such rectangled sphericals by the semblable inclining of the plaine
towards them both. This proportion neverthelesse will never hold betwixt the sines of
the bases, and the sines of their perpendiculars ; because, if the sines of the bases were
proportionall to the sines of the perpendiculars, the sines of the perpendiculars being
already demonstrated proportionall to the sines of the subtendents, either the sine of
the perpendicular, or the sine of the base, would be the cord of the same arch, whereof
it is a sine ; which is impossible, by reason that nothing can be both a whole and a
part, in regard of one and the same thing ; and therefore doe we only say, that the
sines of the bases, and tangents of the perpendiculars, and contrarily, are proportionall.
Its directory is Pubkutethepsaler, which sheweth, that Upalam, Ubamen, Vkelamb,
Etalum, Ethaner, Epsoner, Alamun, and Erelam, are the eight enodandas thereupon
depending.
The third axiom is, that the sines of the sides are proportionall to the sines of their
opposite angles, the truth whereof holds in all sphericall triangles whatsoever, which
is proved partly out of the proportion betwixt the sines of the perpendiculars substerned
under equall angles, and the sines of the hypotenusas, and partly by the analogy that
is betwixt the sines of the angles sustained by severall perpendiculars, demitted from
one point, and the sines of the perpendiculars themselves. The directory of this axiom
is Vchedezexam, whereby we know that Uchener, Edamon, Ezolum, Exoman, and
Amaner, are the five enodandas thereof.
THE ORTHOGONOSPHERIC ALL TABLE CONSISTETH
OF THESE SIX FIGURES :
Valamenep, Vemanore, Enarulomc, Erolumanc, Achave, and Esheva.
The first figure, Valamenep, comprehendeth all those questions wherein the sub-
tendent and an angle being given, either another angle or one of the ambients is de-
manded.
Of this figure there be three moods, viz. Upalam, Ubamen, and Uphanep. The
first, to wit, Upalam, containeth all those orthogonosphericall problems wherein the
subtendent and one oblique angle being given, another oblique angle is required ; and
by its resolver, Torb — Tag — Nuft^Mir, sheweth, that the summe of the sine com-
plement of the subtendent side and tangent of the angle given, the logarithms of these