Plutarch's Platonic questions (5.2-5.3)

urn:cts:greekLit:tlg0007.tlg133.perseus-eng2:5.2-5.3

Refs	`{'start': {'reference': '5.2', 'human_reference': 'Chapter 5 Section 2'}, 'end': {'reference': '5.3', 'human_reference': 'Chapter 5 Section 3'}}`
Ancestors	`[{'reference': '5'}]`
Children	`[]`

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Or is a right line in Nature prior to circumference; or is circumference but an accident of rectilinear? For a right line is said to bend; and a circle is described by a centre and distance, which is the place of a right line by which a circumference is measured, this being everywhere equally distant from the middle. And a cone and a cylinder are made by rectilinears; a cone by keeping one side of a triangle fixed and carrying another round with the

base,—a cylinder, by doing the like with a parallelogram. Further, that is nearest to principle which is less; but a right is the least of all lines, as it is simple; whereas in a circumference one part is convex without, another concave within. Besides, numbers are before figures, as unity is before a point, which is unity in position. But indeed unity is triangular; for every triangular number[*] taken eight times, by adding unity, becomes quadrate; and this happens to unity. Therefore a triangle is before a circle, whence a right line is before a circumference. Besides, no element is divided into things compounded of itself; indeed there is a dissolution of all other things into the elements. Now a triangle is divided into no circumference, but two diameters cut a circle into four triangles; therefore a rectilinear figure is before a circular, and has more of the nature of an element. And Plato himself shows that a rectilinear is in the first place, and a circular is only consequential and accidental. For when he says the earth consists of cubes, each of which is contained with rectilinear superficies, he says the earth is spherical and round. Therefore there was no need of making a peculiar element for round things, since rectilinears, fitted after a certain manner among themselves, do make up this figure.

Besides, a right line, whether great or little, preserves the same rectitude; but as to the circumference of a circle, the less it is, the crookeder it is; the larger, the straighter. Therefore if a convex superficies stands on a plane, it sometimes touches the subject plane in a point, sometimes in a line. So that a man may imagine that a circumference is made up of little right lines.

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3	1	w	783
6	1	w	785
10	1	w	788
15	1	w	791
21	1	w	794
28	1	w	797
36	1	w	800
45	1	w	803
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