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ference, are called its radii. If a complete circle bedivided by a line drawn through its centre, each part of thecircle is called a semicircle: any line drawn from the arc orcurve of the circle, immediately through its centre to theopposite point of the circumference, is called its diameter.
The circumference of every circle is presumed to be sus-ceptible of division into 3(10 equal parts, called degrees,(marked °,) whilst each degree is to be divided into GO equalparts, called minutes ('), each minute into seconds ("), thirds,fourths, or any other definite number of parts.
It should be observed, that the circle has from the mostremote antiquity been usually divided into 360 equal de-grees; although the moderns have believed it might be nowdivided into 500 or 1000 parts, for the sake of greaterfacility in subdivision; however, in this respect they havethought proper to retain it, and to pay a proper obedienceto the division already adopted by their predecessors. Thecircumference of a circle is said to be incommensurable to itsdiameter, because no exact proportion between them can beascertained. The ratio usually observed is 7 to 22, or 113to 325 ; thus, if the diameter be 12 feet, then as 7 is to 22,so is 12 to the circumference. Which proportion that greatgeometrician, Archimedes , first discovered; he also squaredthe parabola, and found out the proportion between a cone,a sphere, and a cylinder, of the same height and base, to beas 1, 2, 3; so that he directed these figures to be engravedon his tomb, which Cicero, whilst questOr of Syracuse , dis-covered, after it. had been long unnoticed by his countrymen,and indeed forgotten! (thus much also for patriotism!!!)being overgrown with briars and bushes, which the lloman,although of the land of his country’s enemies, had removedand restored to its pristine splendour. Cic. Tusc. Quest.v. 23.
The moderns have carried their calculations of this propor-tion, between the circumference and diameter further, and, itis said, nearer to truth: among those the most remarkable wasLudolf van Ceiden, a Dutch mathematician, about the be-ginning of the last century, on whose tomb-stone, in imita-tion of Archimedes , the proportion is engraven to 36 placesof figures: but since the discovery of fluxions, this proportionmay be carried to any assignable length.
Any part of the circumference of a circle, is called anarc, and as much of the circumference as it occupies, it issaid to be an arc of so many degrees.
Any straight line drawn from one end of an arc to thesame point on its opposite side, is called a chord; and any
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