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. XXIIII. Two squares or Circles being given, to substract the one out of the other, and to produce the re∣mainder in a third square.

FIrst, take betwixt your Compasses the side of the greater square given, and setting one foot in the side of the lesser given square, (counted on the side of the Quadrat) with the other foot cut the other side of the Quadrat; and where the Compasses so cutteth, there is the side of the remaining square, counted, from the center.

[illustration] diagram of the measurement of proportional lines (A, B, and C)

Let the two lines B and C be the sides of two squares, or the Diameters of two circles; and it is required to sub∣stract the square of B, out of the square of C, and to make a square equall to the remainder. First, I take 75 the line C (which is the side of the greater square,) be∣twixt my Compasses, and setting one foot in 60 the side of the lesser square, (counted on the side of the Quadrat) the other foot will reach unto 45, upon the other side of

the Quadrat; which 45 is the length of the line A, the side of the remaining square upon which if you make a square, it shall be equall to the remainder of the greater given square, when the lesser is taken out of the same, as was required.