122

PROJECT FOR A NEW

TRACT 29.

l + . 2 s . S . 04 11.14..l>r.go.2 < » „

» ii ■ ■' ■ I — ~~ 1 . - ■ - ■ -• — m ■ ' " ATP •

■>3/u o. ■ . v-. ii.'. . J 4 1.6.2.12.15.18.21.2*.il 8 ’

1 + ys-irts ,V*> _ 2 . 2* . 2.5.8.11 14.2*

■H/Ll ~ 3.6 . 11 * ~6 .9 12 . 16 . 18 . 11 ° • &C »

3/1.3 -*3/?l 2 2 = 2 5 , 8.24 "I#".!.."' „

~ _ 3.6. 11* — 3 . o . 9 . 13. liro.65 )'..: 1° ° LC *

l_iv/13_ 2.2* 2.5 . 8 2 4 3.5.8.11 14 2 * „

2V 11 “ 1 + 3.6.U* 3 .6 ?9 .‘l 2 .114 + 3.6.9.13.15.18.116 “ + &c *

The last of which agrees with one found in Art. 119.

And thus we may find the sums of as many series of thesekinds as we please ; as well as the sum of any of the gene-ral series, by means of the roots of given cubic equations.And thus also may series, bv means of the roots of equa-tions of other orders, be exhibited.

TRACT XXIX.

PROJECT FOR A NEW DIVISION OF THE QUADRANT. READAT THE ROYAL SOCIETY, NOV. 21 , 1183 .

Having long since thought it would be a meritorious anduseful service, to adapt the tables of sines, tangents, andsecants, to equal parts of the radius, instead of to those ofthe quadrant; the following observations on the subject arethrown together, with a view to stimulate others, either toundertake and calculate some part of so large and painful awork, or to communicate further hints for the improvementand easier performance of it. This project then is for con-structing sines, tangents, secants, &c, to equal parts of theradius.

1. The arbitrary division of the quadrant of the circleinto equal parts, by 60ths, which has been delivered downto us from the ancients, and gradually extended by similar