A method to trisect a series of angles having relation to each other; also another to trisect any given angle. By James Sabben. 1848 (two quarto pages).
'The consequence of years of intense thought': very likely, and very sad.
1848. The following was sent to me in manuscript. I give the whole of it:—
'Quadrature of the Circle.—A quadrant is a curvilinear angle traversing round and at an equal distance from a given point, called a centre, no two points in the curve being at the same angle, but irreptitiously graduating from 90 to 60. It is therefore a mean angle of 90 and 60, which is 75, because it is more than 60, and less than 90, approximately from 60 to 90, and from 90 to 60, with equal generation in each irreptitious approximation, therefore meeting in 75, and which is the mean angle of the quadrant.
Or, suppose a line drawn from a given point at 90, and from the same point a line at 60. Let each of these lines revolve on this point toward each other at an equal ratio. They will become one line at 75, and bisect the curve, which is one-sixth of the entire circle. The result, taking 16 as a diameter, gives an area of 201.072400, and a circumference of 50.2681.
The original conception, its natural harmony, and the result, to my own mind is a demonstrative truth, which I presume it right to make known, though perhaps at the hazard of unpleasant if not uncourteous remarks.'
I have added punctuation: the handwriting and spelling are those of an educated person; the word irreptitious is indubitable. The whole is a natural curiosity.
The quadrature and exact area of the circle demonstrated. By Wm. Peters. 8vo. n. d. (circa 1848).
Suggestions as to the necessity for a revolution in philosophy; and prospectus for the establishment of a new quarterly, to be called the Physical Philosopher and Heterodox Review. By Q. E. D. 8vo. 1848.
These works are by one author, who also published, as appears by advertisement,
'Newton rescued from the precipitancy of his followers through a century and a half,' and 'Dangers along a coast by correcting (as it is called) a ship's reckoning by bearings of the land at night fall, or in a fog, nearly out of print. Subscriptions are requested for a new edition.'
