(642)

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 *DIL* represent an *Hyperbola*, whose *Asymptotes* AO, AK, make the Right Angle OAK, the Author propounds to find the Hyperbolick *space ILNK, contained by the* Hyperbolical *Line IL, the* Asymptote *KM, and the two Right Lines IK, LM, which are parallel to the other* Asymptote *AO.*

He puts the Lines IK | = | 1 000 000 000 000 | |

LM | = | 1 000 000 000 000 | 0 |

AM | = | 1 000 000 000 000 | |

Hence KM | = | 9 000 000 000 000 |

Whence he finds the space LIKM

to be | 230 258 509 299 404 562 401 78681 | too little. |

230 258 509 299 404 562 401 78704 | too great. |

*Note:* If IK be put for an *Unit*, then LM may represent 10, and HG 1000, and FE 1024: And, by what is demonstrated by *Gregory* of St. *Vincent*, it holds,

*As* the space IBLMKI, *Is* to the Logarithm of LM, to wit, of 10: *So* is the space IBEFKI, *To* the Logarithm of the Number represented by the Line EF, to wit, of 1024

The *Author* by the same method finds the *Area* of the space GEFH 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 10*th* 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,