Page:Philosophical Transactions - Volume 014.djvu/186

Rh From a number propos'd fubllraél: an Unit, let that be Numerator, and to it add an Unit, let that be Denominator and call that fraction N.

s as 1 9 H is

Thgn N1-i+1r+N+N+N+N, ée. 15

I 2 f 7 i II .13

Equal to half the Hyperbolick Logarithm fought. EXAMPLE in the Number

TheFra<9cionis§ I, 3333333===33;33g3 3, 370370:-=-' 123456

5, 41 1 >'1== 8230

The Rank 1§ 7 is easily 7, 4-)'7z==:= 5.5-3 made by dividing ev'ry 9, SO 8=== 5 6 precedingnumberby 9.11, 562: 5-13, 6==:= o

3465733

6931466 which is

Thg Hypcrbolick Logarithm of 2 fought. I want time to consider the prrmifes, but hope you will, (in re ard you seem to think it strange that any diflicnlrieg houlg remain about Cubielgs that are not presently resolved) your considerations wherein will be very acceptable and worthy Publick view-Other

Other Series in Print of M€Yfdl07f,4 dc- dispatch not as this doth neither thereby can the Logarithm of 1 be ealil y made, but by making the Logarithms of such mixt nnmbersor fractions that multiplied together make the result 2 just as zxr;:=3; whence having and finding that of 15, you presently have the Logarithm of 3.»2

2 A Cardanuk Equation that is a Cnbick one wanting the second term, may be multiplied or divided by a rank of continual proportionals, so as to render the coefficient of the roots canonick, that is, to make it the same with the }Equations of the Table, that find the Sine, Tangent, or Secant oi' the third part of that arch to which any Sine, Tangent, or Seeant is pro ounded, and so finding the roots in the tables, those fought are thence obtained by Multiplication or Division- Yea, and the coefficient of the roots may in like manner be rendred an Unit, and then the Resolvends fought in a table of the sums or differences of the Cubes of numbers and their roots, shall help you to Inch roots, as multiplied or divided as aforesaid shall be the true ones fought.

23 It is an enquiry worth consideration, whether two of the roots of a biquadratick may not be kept constant, and the