The description and use of the universall quadrat.: By which is performed, with great expedition, the whole doctrine of triangles, both plain and sphericall, two severall wayes with ease and exactness. Also the resolution of such propositions as are most usefull in astronomie, navigation, and dialling. By which is also performed the proportioning of lines and superficies: the measuring of all manner of land, board, glasse; timber, stone. &c. / By Thomas Stirrup, Philomathemat.

CHAP. XX. How speedily to finde the perpendicular of a Right Angled Triangle, the sides being given; as also to finde the segments of the base, cut by the perpendicular.

A Right angled Triangle, is that whose sides com∣prehending the Right angle falleth square or perpen∣dicularly one upon the other, thereby making the Angle contained betwixt them a Right Angle, or an Angle of 90 degrees.

To finde the perpendicular of such a Triangle, lay the threed upon the side of the Quadrat, & rectifie the bead to the lesser side of the Triangle given, then open the threed to the intersection of the contrary parallel of the greater side, with the Right Parallel of the lesser side; so shall the bead shew the contrary parallel of the perpendicular required.

[illustration] diagram of the measurement of a right-angled triangle (ABC)

Let the Triangle ABC, be a right angled Triangle given, whose perpendicular is required. First, laying the threed upon the side of the Quadrat, rectifie the bead to 45 the lesser side BC, of the given Triangle ABC; then opening the threed to the point of intersection, betwixt the contrary parallel of 60 the greater side AB, and the Right Parallel of 45 the lesser side BC; the threed lying upon this point you shall see it cut the contrary pa∣rallel of 36, which is the length of the perpendicular BD, which was required.

Or the bead being fixed as before, if you open the threed to the point of intersection, betwixt the contrary parallel of the lesser side BC, 45, and the right parallel of the greater side AB, 60; the bead shall fall upon the right parallel of 36, which is the length of the perpendi∣cular BD as before: or having two beads upon your threed, if you place the one to 45 the lesser side, and the other to 60 the greater side; and opening the threed as before, unto the point of intersection, betwixt the con∣trary parallel of 60 the greater side, and the right paral∣lel

of 45 the lesser side; the threed lying in this position, the bead which signifieth the greater side, shall shew the right parallel of 36, and the other bead shall shew the contrary parallel of the same, which is the perpendicular BD, as before.

And farther, the threed and beads lying still in this position, the bead which signifieth the greater side 60, shall cut the contrary parallel of 48, which shall be the greater segment of the base divided by the perpendicular, viz. AD; and the bead which signifieth the lesser side 45, shall cut the right parallel of 27, which is the lesser segment of the base, viz. CD.