And
20. If a right line drawne from the toppe of the triangle; cutting the base into two equall parts, be greater than either of those portions, the angle at the toppe is an acute angle: And contrariwise.
As in aei, let ao cutting the base ei into two equall parts, be greater than any one of those parts, the angle at the toppe is an acuteangle, as appeareth by the [7 e].
The ninth Booke, of P. Ramus Geometry, which intreateth of the measuring of right lines by like right-angled triangles.
The Geometry of like right-angled triangles, amongst many other uses that it hath, it doth especially afford us the geodæsy or measuring of right lines: And that mastery, which before (at the [2 e viij]) attributed the right angled triangles, shall here be found to be a true mastery indeed.
For it shall containe the geodesy of right lines; and afterward the geodesy of plaines and solides, by the measuring of their sides, which are right lines.
1. For the measuring of right lines; we will use the Iacobs staffe, which is a squire of unequall shankes.
Radius, commonly called Baculus Iacob, Iacobs staffe, as if it had been long since invented and practised by that holy Patriarke, is a very auncient instrument, and of all other Geometricall instruments, commonly used, the best and fittest for this use. Archimedes in his book of the Number of the sand, seemeth to mention some such thing: And Hipparchus, with an instrument not much unlike this, boldly attempted an haynous matter in the sight of God, as Pliny thinketh, namely to deliver unto posterity the number of the starres, and to assigne or fixe them in their true places by the Norma, the squire or Iacobs staffe. And indeed true it is that the Radius is not onely used for the measuring of the earth and land: But especially for the defining or limiting of the starres in their places and order: And for the describing and setting out of all the regions and waies of the heavenly city. Yea and Virgill the famous Poet, in his 3 Ecloge, Ecquis fuit alter, Descripsit radio totum, qui gentibus orbem? and againe afterward in the 6 of his Eneiades, hath noted both these uses. Cœliquè meatus. Describent radio & surgentia sidera dicent. Long after this the Iewes and Arabians, as Rabbi Levi; But in these latter daies, the Germaines especially, as Regiomontanus; Werner, Schoner, and Appian have grac'd it: But above all other the learned Gemma Phrisius in a severall worke of that argument onely, hath illustrated and taught the use of it plainely and fully.
The Iacobs staffe therefore according to his owne, and those Geometricall parts, shall here be described (The