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. XLI. To finde the superficiall content of any part or segment of a circle:

EVery part of a circle, whether it be semicircle, Qua∣drant, or any other sector of a circle, is neere equall to that right angled parallelogram or long square, whose length and breadth is, the one equall to the semidiameter, the other to the one halfe of the arch line, or to the whole Diameter, and one quarter of the arch line. And there∣fore may be measured by the 26, or 27, or by this last Chapter.

For if you would measure the semicircle ABDC in the 39 Chapter you may take the semidiameter AB, or AC for your breadth, and the one halfe of his arch line BDC, which is BD, or CD 20 3/7 for your length.

Or if you would measure the Quadrant ABD, you may take the semidiameter 13 for your length, and halfe the arch BD 10 3/14 for your breadth: the like holdeth for any sector of a circle whatsoever.

But if you would measure the segment FDGH, you must first measure the plain of AFDGA, by the for∣mer rules, and then the Triangle AGF by the 28 or 29 Chapter or by the 41 Chapter, taking the perpendicular for the breadth, and halfe the base for the length of a right angled parallelogram; the content of which Trian∣gle being added to the content of AFDGA, giveth the content of the segment FDGH.

And if you would measure the segment FGE, you

must first measure the sector EGAF, and from the con∣tent take the content of the Triangle AFG, so shall the remainder be the content of the segment FGE, as was required.