1 Def. A line is said to increase uniformly, when the point by which it is described passes through equal intervals, in equal times. 2 Def. A line is said to diminish to a shorter one proportionally, when the point passing along it cuts off in equal times segments proportional to the remainder. 6 Def. The logarithm of any sine is the number most nearly denoting the line, which has increased uniformly, whilst the radius has diminished to that sine proportionally, the initial velocity being the same in both motions. (Mirifici logarithmorum canonis descriptio, Edinburgi 1614.) This last definition contains what we should now call the differential equation between a number and the logarithm of its reciprocal. [201] Histoire del'Astronomie Moderne, Paris, 1821. Transcriber's Notes. Corrections. The first line indicates the original, the second the correction. Life of Galileo Galilei p. 20: success very inadeqnate to the zeal success very inadequate to the zeal p. 20: "New method of Guaging, "New method of Gauging, p. 23: the knowlege, if it existed the knowledge, if it existed p. 30, note: to represent terrestial objects correctly. to represent terrestrial objects correctly. p. 64: the palace of the Archishop Piccolomini the palace of the Archbishop Piccolomini p. 68: that ladies ringlets that ladies' ringlets p. 69: For hitherto I have never happened to see the terrestial earth For hitherto I have never happened to see the terrestrial earth p. 106: 80 1 50, _for_ any _read_ an indefinitely small. 80 2 44, _for_ any _read_ an indefinitely small. Life of Kepler p. 6: Now, inscribe in the Earth an icosaedron, the circle inscribed in it will be Venus. Now, inscribe in the Earth an icosahedron, the circle inscribed in it will be Venus. Inscribe an octaedron in Venus, the circle inscribed in it will be Mercury. Inscribe an octahedron in Venus, the circle inscribed in it will be Mercury. p. 32: Butthere are no such means But there are no such means p. 48: the compound ratio of the rectangle of the axes directly, and subduplicatly the compound ratio of the rectangle of the axes directly, and subduplicately p. 52: and was in-intended to illustrate the appearances and was intended to illustrate the appearances End of the Project Gutenberg EBook of The Life of Galileo Galilei, with Illustrations of the Advancement , by John Elliot Drinkwater Bethune