Maitland Club > Works of Sir Thomas Urquhart

98 THE TRISSOTETRAS.
The second disergetick axiome is Naverprortes, that is to say, the fine's comple-
ments of the verticall angles, in obliquangular triangles, a perpendicular being let fall
from the double verticall on the opposite side, are reciprocally proportionall to the
tangents of the sides ; the reason hereof proceedeth from Sbaprotca, the second general
axiome of the sphericals ; according to which, if we doe but regulate, after the custo-
mary analogical] manner, two quaternaries of proportionals of the former sine's com-
plements, and tangents proposed, we will find by the extremes alone, excluding all the
intermediate termes, that the sine's complements of the verticall angles, both fonvardly
and inversedly, are reciprocally proportioned to the tangents of the sides, and contrari-
wise from the tangents to the sines. The directory of this axiome is Allera, which
evidenceth that the moods of Allamebne and Erelomab depend upon it.
The third disergetick axiome is Siubprortab, that is to say, that, in obliquangular
sphericals, if a perpendicular be drawne from the verticall angle unto the opposite side,
continued if need be, the sines of the segments of the base are reciprocally propor-
tionall to the tangents of the angles conterminate at the base, and contrary ; the proofe
of this, as well as that of the former consectary, dependeth on Sbaprotca, the second
generall axiome of the sphericals : according to which, if we so diagrammatise an am-
blygonosphericall triangle, by quadranting the perpendicular, and all the sides, and
describing from the basangalary points two quadrantall arches, till we hit upon two
rowes of proportionall sines of bases to tangents of perpendiculars, then shall we be
sure, if we exclude the intermediate termes, to fall upon a reciprocall analogy of sines
and tangents, which, alternately changed, will afford the reciprocall proportion of the
sines of the segments of the base, to the tangents of the angles conterminat thereat,
the thing required.
The directory of this axiome is Ammena, which certineth that Ammanepreb and
Enerablo are founded thereon.
The fourth and last disergetick axiome is Niubprodnesver, that is to say, that, in
all loxogonosphericalls, where the cathetus is regularly demitted, the sine's comple-
ments of the segments of the base are directly proportionall to the sine's comple-
ments of the sides of the verticall angles, and contrary. The reason hereof is made
manifest, by the proportion that is betwixt the sines of angles, subtended by perpendi-
culars and the sines of these perpendiculars ; out of which we collation severall pro-
portions, till, both forwardly and inversedly, we pitch at last upon the direct proportion
required.
The directory of this axiome is Ennerra, which declareth that Ennerable and Erre-
lorne are its dependents.