The trissotetras: or, a most exquisite table for resolving all manner of triangles, whether plaine or sphericall, rectangular or obliquangular, with greater facility, then ever hitherto hath been practised: most necessary for all such as would attaine to the exact knowledge of fortification, dyaling, navigation, surveying, architecture, the art of shadowing, taking of heights, and distances, the use of both the globes, perspective, the skill of making the maps, the theory of the planets, the calculating of their motions, and of all other astronomicall computations whatsoever. Now lately invented, and perfected, explained, commented on, and with all possible brevity, and perspicuity, in the hiddest, and most re-searched mysteries, from the very first grounds of the science it selfe, proved, and convincingly demonstrated. / By Sir Thomas Urquhart of Cromartie Knight. Published for the benefit of those that are mathematically affected.

Thus farre for the calculating of plaine Triangles, both right and oblique: now follow the Sphericals.

THere be three principall Axioms upon which dependeth the resolving of Sphericall Triangles, to wit, Suprosca, Sbaprotca, and Seproso.

The first Maxime or Axiom, Suprosca, sheweth, that of severall rectangled Sphericals, which have one and the same acute Angle at the Base, the Sines of the Hypotenusas are proportionall to the Sines of their Perpendiculars; for, from the same inclination every where of the one plaine to the other, there ariseth an equiangularity in the two rectangles, out of which we may confidently inferre the ho∣mologall sides (which are the Sines of the Subtendents, and of the Perpendiculars of the one, and the other) to be amongst them∣selves 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 proportionall to the Tangents of their Perpendiculars: which Analogie proceedeth from the equi∣angularity of such rectangled Sphericals, by the semblable in∣clining of the plaine towards them both. This proportion never∣thelesse 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 Perpendi∣cular, 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 onely say, that the Sines of the Bases, and Tangents of the Perpendiculars, and contrarily, are proportionall. Its Directory is Pubkutethepsaler, which sheweth, that Upalam, Uba∣men, Ʋkelamb, Etalum, Ethaner, epsoner, Alamun, and Erelam, are the eight Enodandas the reupon 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 Sphe∣ricall Triangles whatsoever; which is proved partly out of the proportion betwixt the Sines of the Perpendiculars substern∣ed under equall Angles, and the Sines of the Hypotenusas: and partly, by the Analogy, that is betwixt the Sines of the Angles su∣stained by severall Perpendiculars, demitted from one point, and the Sines of the Perpendiculars themselves. The Directory of this Axiom is Ʋchedezexam, whereby we know that Uchener, Edamon, Ezolum, Exoman, and Amaner, are the five Enodandas thereof.