On the Threefold Minimum and Measure (1591) - Page 10

OF CHAPTERS.


To show materials entirely equal, or to repeat the same thing twice, is impossible (p. 66)	### III. THE DISCOVERY OF THE MINIMUM.
6, A physical excursion for contemplating the nature of the soul (p. 73)	1, That true doctrine concludes all things from a few very clear principles (p. 97)
7, Plato calls the circle a polygon, a total angle composed of the straight and the curved (p. 75)	2, Every magnitude grows from the minimum and is thinned down into the minimum (p. 98)
8, That a polygon does not grow by a minimum, nor does a circle (p. 77)	3, That even for Euclid an angle is not divided into more than two parts Bruno is likely challenging Euclidean geometry's assumptions about the infinite divisibility of angles. (p. 104)
9, A body touches another body or a plane neither with itself nor with a part of itself This refers to the paradoxes of contact at an atomic level. (p. 84)	4, That the center is not the endpoint of all lines from the circumference (p. 106)
10, That contact occurs at the minimum; and the difference between that which touches and that by which it touches (p. 85)	5, How a positive progression may be made toward any minimum whatsoever without error (p. 108)
11, How a sphere original: "globus" touches a sphere and a plane at a point—the common people do not understand this (p. 86)	6, That the mother of the doctrine of irrational original: "alogis," from the Greek for "without reason" or "incommensurable." and asymmetric numbers is ignorance of the minimum (p. 110)
12, Why, while contact remains at a point, a larger circle moves faster over the same plane than a smaller one (p. 88)	7, However large a part may be, how much it is of the whole is examined, and the sine tables are cast aside Bruno argues his method makes traditional trigonometric tables unnecessary. (p. 111)
13, A slanted line falling onto a plane does not touch it at a point (p. 89)	8, The second method (p. 115)
14, How a straight line equal to a circle is marked out from contact at a point, and the successive transition of infinite points in a finite time (p. 91)	9, The minima in a circle are found, and the canons Rules or mathematical tables. of spherical triangles are cast aside (p. 119)
15, From the force of habit in believing false things, even the sense itself is disturbed (p. 94)	10, Any polygon is outlined; an arc or circle is divided in a given ratio (p. 122)
	11, Given an arc, it is determined what part of the circle it is (p. 124)
	12, A common measure is found (p. 127)