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and applied as the line A-B are called Chords, or chord lines, of those Arches which they so subtend; or Subtenses, because they subtend both segments. THEOR. 73. PROB. 34.
DEFIN. XIV.
Equal Circles are such as have equal Diameters, or whose lines, drawn from their Centres, are equal.
Euclid, Book 3, Def. 1.
As these two circles A and B are equal, their diameters being equal, namely, C-D and E-F, or their Semidiameters (which, according unto this DEFINITION, are lines drawn from the centres unto their circumference) as A-C or A-D and B-E or B-F.
A geometric diagram showing two circles placed side-by-side. The left circle is labeled 'A' at its center and has a horizontal diameter line with endpoints 'C' and 'D'. The right circle is labeled 'B' at its center and has a horizontal diameter line with endpoints 'E' and 'F'.
DEFIN. XV.
A right line is said to touch a circle, which touching it, and being extended or produced, does not cut the circumference thereof.
Euclid, Book 3, Def. 2.
As the right line A-B, being drawn by the point C, does there only touch the circle, and being produced unto B, cuts not the circumference thereof. This line is commonly called a Tangent, or Contingent line: whereof there is great and infinite use, in many Conclusions, Geometrical and Astronomical, especially in the mensuration and resolution of Triangles, as well right-lined, as spherical, by the Canons and Tables of Sines, Tangents, and Secants, in that behalf calculated.
A geometric diagram showing a circle with its center labeled 'E'. It has a vertical diameter line with endpoints 'C' at the top and 'D' at the bottom. A horizontal line, labeled 'A' and 'B' at its ends, passes through point 'C', touching the circle at that single point.
DEFIN. XVI.
An angle of a Section, or Segment, is that which is contained under a chord line, and the arch line of the same Section.
Euclid, Book 3, Def. 6.
As the angles A-B-C and B-A-C in the lesser segment of this circle, are angles of a Section, because they are contained under the chord line A-B and the arch line A-C-B. Also the angles D-B-A and
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