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GENERAL DEMONSTRATIONS of the THEOREMS for the 

 SINES and COSINES of MULTIPLE CIRCULAR ARCS, 

 and alfo of the THEOREMS for exprejfmg the POWERS of 

 SINES and COSINES by the SINES and COSINES of MUL- 

 TIPLE ARCS ; to which is added a THEOREM hy help whereof 

 the fame METHOD may be applied to demonjlrate the PRO- 

 PERTIES of MULTIPLE HYPERBOLIC AREAS. By the 

 Rev. J. BRINKLEY, J.M. ANDREWS' Profeffor of AJlronomy^ 

 and M. R. I. A. 



1 HEOREMS by help of which the chords of multiple cir- 

 cular arcs may be found in terms of the chord of the fimple 1797. 

 arc were firft given by Vieta, and afterwards in a different 

 manner by Mr. Briggs, which are very fully explained in the 

 Trigonometria Britannica, and their ufes in conflru<5ling trigo- 

 nometrical tables fhewn. From thefe may readily be deduced 

 theorems for the cofines of multiple arcs in terms of the cofine 

 of the fimple arc, and for the fines in terms of the fine of 

 the fimple arc when the multiplier is an odd number, and 

 confequently the fcries firft given by Sir Ifaac Newton for the 

 fine of a multiple arc when the multiplier is an odd number, the 

 only -cafe in which that feries terniinates — Afterwards fimilar 



D 2 theorems 



