This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1889 edition. Excerpt: ...of places given. But in a table of the logarithms of ratios (corresponding to the table in sect. 53 of the Constructio), which is given by Ursinus on page 223 of the ' Trigonometria, ' the value is stated as 69314718.28, which exceeds the true value by.22. This example will explain how some of the logarithms ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1889 edition. Excerpt: ...of places given. But in a table of the logarithms of ratios (corresponding to the table in sect. 53 of the Constructio), which is given by Ursinus on page 223 of the ' Trigonometria, ' the value is stated as 69314718.28, which exceeds the true value by.22. This example will explain how some of the logarithms at the end of the Magnus Canon are too great by 1 in the units place. Notwithstanding this, the Magnus Canon may safely be used to correct the figures in the text and in the Canon of 1614, as the latter is to one place less. I find no reference by Ursinus to the discrepancies between the logarithms of the two Canons. The mistake in the Second table may possibly not have been observed by him, as the preparatory tables for the Canons were different. The mistake was observed by Mr Edward Sang in 1865, when recomputing in full the preparatory tables of Napier's Canon to 15 places. It had been previously pointed out by M. Biot, in his articles on Napier in the'Journal de Savants'for 1835, p. 255. The following M 4 translation translation of the passage is given in the ' Edinburgh New Philosophical Journal' for April 1836, p. 285: --It has been said, and Delambre repeats the remark, that the last figures of his Napier's numbers are inaccurate: this is a truth, but it would have been a truth of more value to have ascertained whether the inaccuracy resulted from the method, or from some error of calculation in its applications. This I have done, and thereby have detected that there is in fact a slight error of this kind, a very slight error, in the last term of the second progression which he forms preparatory 'o the calculation of his table. Now all the subsequent steps are deduced from 'hat, which infuses those slight errors that have been remarked....
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