Abstract
II.
MR. H. HARBORD, who hails from Hull, has put forth three letters, with which we have been favoured. “The Circle Squared” (in November 1867) has, we guess, been noticed by Prof. De Morgan. There is a nicely drawn diagram, two concentric circles, two squares, said to be their respective equivalents, all in black; an equilateral triangle and its circumscribing circle in red ink; the former is described on a side of the smaller square, and the red circle passes through the extremities of the same side. A statement is made, which appears to be a statement and nothing more, for it proves nothing. From “Squaring the Circle” (April 15, 1874) we learn that the writer has leisure (fons et origo mali!), and so has ventured to amuse himself by considering the relation of the equilateral triangle, the square, and the circle. He obtains the positive altitude of an equilateral triangle on a side of the square to be 7.754485597711125,and requires the exact side of the square and the proportion of the triangle to the square and the equivalent circle. He winds up, like many of his race, with the following reflections:—“I think if the learned in geometry, mathematics, and trigonometry, abandoned approximating theories, and would take the trouble to elucidate the above-stated propositions, they would undoubtedly be able to subvert all anomalous and vague theorems, free the study of geometry, &c., from ambiguity, enable tutors to explain correctly, remove burthens imposed on the mind of the pupil, and establish a system of teaching which shall be correct and intelligible, for it is evident the result of minute calculations proves there is no mystery in geometry, mathematics, or trigonometry; they are uniform, and may be more easily taught and comprehended with perfect truthfulness without approximation.” To prevent trouble, this man of leisure appends the rule; it is: Add one-seventh to the altitude, and we get the base; and so on,. Not satisfied with the above remarks, we have a note to the “learned” (see above); and it is the following curious sentence:—“It is worthy of remark, and more especially to those who are interested in the forthcoming ‘Transit of Venus’ when the true distance of the earth from the sun is to be determined, and a difference of about three millions of miles accounted for, to be in a position to prove the fact. Now all this can be accomplished by anxious, minute observation and correct calculation !” He then appends (we don't see the connection): “Length of an arc of one degree, .017... to twenty-seven places final.” We got the last communication a few days ago; it is, “Construction of the Perfect Ellipse” (Dec. 22, 1874). This is a fine large figure on a sheet of paper gome eighteen inches by fourteen. He finds that the true ellipse is only to be described on the perpendicular of the equilateral triangle. Mr. Harbord has evidently an idea, and that is, that the equilateral triangle is the key to unlock many geometrical mysteries.
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Among the Cyclometers and some other Paradoxers * . Nature 13, 28–30 (1875). https://doi.org/10.1038/013028a0
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DOI: https://doi.org/10.1038/013028a0