...which is called a CIRCUMFERENCE : upon which all the ftraight lines falling, from oNE PoINT of thofe lying within the figure, are equal to one another....And the point is called the CENTER of the circle. 17. But a DIAMETER of a circle is any right line drawn through the center, and terminated both ways...

...KVK\OV Trepu^cpetai/] urai dXAt;A.ai9 turiv. 1 6. Kcvrpov 8t TOV KVK\.OV TO <rr)/jL(lov (caXcirai. 15. A circle is a plane figure contained by one line such that ail the straight lines falling upon it from one point among those lying within the figure are equal...

...rather than pure geometry. Theodosius defines the sphere as ‘ a solid figure contained by one surface such that all the straight lines falling upon it from...lying within the figure are equal to one another', which is exactly Euclid's definition of a circle with ‘solid' inserted before ‘figure' and ‘surface'...

...p. 13 (Chicago, 1902). H Circle. The ancient writers denned a circle substantially as Euclid did : A circle is a plane figure contained by one line such...those lying within the figure are equal to one another ; And the pornt is called the center of the circle. Euclid had already denned a figure as "that which...

...divides c, then ab divides c. (h) Show that Viand V3 are irrational. 8.7. Euclid defines a circle as "a plane figure contained by one line such that all the straight lines falling upon it from one particular point among those lying within the figure are equal." How does this definition of a circle...

...an extremity of anything. 14. A figure is that which is contained by any boundary or boundaries. 15. A circle is a plane figure contained by one line such...equal to one another. 16. And the point is called the centre of the circle. 17. A diameter of the circle is any straight line drawn through the centre and...

...other is called a perpendicular to that on which it stands. We omit what follows until we arrive at 15. A circle is a plane figure contained by one line such...the straight lines falling upon it from one point lying within the figure are equal to one another. 16. And the point is called the centre of the circle....

...knew in substance the Euclidean definition of the circle (Book I, Definition 15) : " A circle (kyklos) is a plane figure contained by one line such that...lying within the figure are equal to one another." 159 As a matter of fact this is the definition quoted, with certain variations in the wording, by Simplicius...

...an extremity of anything. 14 A. figure is that which is contained by any boundary or boundaries. 15 A circle is a plane figure contained by one line such...equal to one another; 16 And the point is called the centre of the circle. 1 7 A diameter of the circle is any straight line drawn through the centre and...

...name "common insights." Let us consider an example of each. The fifteenth definition runs as follows : "A circle is a plane figure contained by one line...among those lying within the figure are equal to one another."8 This definition explains how the term "circle" will be used, without asserting that circles...