The Surveyor in Foure Bookes

centre to the former points B and C, then is that angle said to be in the centre of a circle, as the angle B-E-C. Which angle likewise subtendeth the same circumference B-D-C, and is always double in quantity to the former angle, drawn from the circumference. And the circumference B-D-C is also the measure of the quantity or greatness of the angle B-E-C in the centre.

A geometric diagram of a circle with center point E. A triangle A-B-C is inscribed within the circle, and lines connect center E to points B and C, forming an angle. Point D is marked on the lower circumference arc between B and C.

DEFIN. XIX.

Euclid, Book 3, Def. 9. Ramus, 16. 3.

As in the last DEFINITION, the figure B-E-C is the Sector of a circle, because it is contained under the two right lines E-B and E-C, drawn from the centre E, and under part of the circumference, namely, B-D-C, received of them.

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DEFIN. XX.

Euclid, Book 1, Def. 20.

As those which follow, being contained under three, four, five, or more sides, which take their names, as well of the number of their angles, as of their sides; so a figure contained under three lines, in respect of his sides, is called a three-sided figure; and in respect of his three angles is called a Triangle: and so of the rest. Where is to be noted, that every right-lined figure has as many angles as it has sides.

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DEFIN. XXI.

Euclid, Book 1, Def. 24. Ramus, 8. 8.

As a Triangle is the first of all right-lined figures (for under less than three right lines can no figure be contained:) So of all Triangles, the Equilateral Triangle is most simple and absolute, having equal lines and equal angles; containing every one of them a Sextans original: "Sextans" — meaning a sixth part, or 60 degrees of a Circle, which is 60 degrees. Triangles have their names, differences, and appellations, as well of their angles as their sides: As this Triangle A, in respect of his

A diagram of an equilateral triangle with the letter 'A' printed in the center.