94 NOTES.
| Proportionals. | |
| First Table. | |
| First proportional after radius, | 9999999. |
| The last proportional, | 9999900.000494998383003921217471 |
| Second Table. | |
| First proportional after radius, | 9999900. |
| The last proportional, | 9995001.224804023027881398897012 |
| Third Table. Column 1. |
|
| First proportional after radius, | 9995000. |
| The last proportional, | 9900473.578023286050198667424460 |
| Column 2. | |
| The first proportional, | 9900000. |
| Column 69. | |
| The first proportional, | 5048858.887870699519058238006143 |
| The last proportional, | 4998609.401853189325032233811730 |
| Half Radius, | 5000000. |
| One-tenth of Radius, | 1000000. |
mistake in the Second table, this was not the case with those in the Magnus Canon computed by Ursinus and published in 1624. The logarithm of 30° or half radius, for instance, is there given as 69314718 (see specimen page of his Table, given in the Catalogue), which is correct to the number 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,
