Page:Philosophical Transactions - Volume 003.djvu/15

 thereto, and finds the Logarithms of all Primitive Numbers under 1000 by one Multiplication, two Divisions, and the Extraction of the Square Root, but for Prime Numbers greater, much more easily.

Concerning the construction of Logarithms Mr. Nicholas Mercater hath a Treatise, intituled Logarithmotechnia, likewise at the Press, from which the Reader may receive further satisfaction. And as for Primitive Numbers, and whether any odd number proposed less than 100000 be such, the Reader will meet with a satisfactory Table at the end of a Book of Algebra, written in High Dutch by John Henry Rohn, now translated and enriched, and near ready for publick view.

The Area of an Hyperbola not being yet given by any Man, we think fit a little to explain the Author's meaning.

In Figure 1. Let the Curve  L represent an Hyperbola, whose Asymptotes O,  K, make the Right Angle  K, the Author propounds to find the Hyperbolick space  K, contained by the Hyperbolical Line  L, the Asymptote  M, and the two Right Lines  K,  M, which are parallel to the other Asymptote  O.

Whence he finds the space M

Note: If K be put for an Unit, then  M may represent 10, and  G 1000, and  E 1024: And by what is demonstrated by Gregory of St. Vincent, it holds,

As the space I, Is to the Logarithm of  M, to wit, of 10: So is the space  I, To the Logarithm of the Number represented by the Line  F, to wit, of 1024

The Author by the same method finds the Area of the space H to be 237 165 266 173 160 421 183 067, and the space LIKM abovesaid being taken for the Logarithm of 10, and tripled, is the Logarithm of 1000, the which added to the space now found, makes the sum 69314718055994529141719170, and 1024, being the 10th Power of 2, the 10th part of this number is the Hyperbolical Logarithm of the Numb. 2, to wit, 6931471805599452914171917. And it holds by proportion,

As 23025850929940456249178700, the Logarithm of 10, To 6931471805599452914171917, the correspondent Logarithm of 2: So 1 000 000 000 000 000 000 000 000 0, the Logarithm of 10 in the Tables,