Mtfcellanea Curio fa. 35 

 which remains to make this Doctrine compleat, 

 and that is this. 



A Ship fails from a given Latitude, and ha- 

 ving run a certain number of Leagues, has al- 

 tered her Longitude by a given angle, it is re- 

 quired to find the Courfe fteared. The folu- 

 tion hereof would be very acceptable, if not 

 to the Publick, at leaft to the Author of this 

 Tract, being likely to open fome further Light 

 into the Myfteries of Geometry. 



To conclude, I lhall only add, That Uni- 

 ty being Radius*, the Co-fine of the Arch A, 

 according to the fame Rules of Mr. Newt on ^ 

 will be 



from which and the former Series exhibiting 

 the Sine by the Arch^ by divifion, it is eafie 

 to conclude, that the Natural Tangent of the 

 Arch A^ is 



and the Natural Secant to the fame Arch 



and from the Arithmetick of Infinites, the 

 Number of thefe Secants being the Arch A, 

 it follows, that the fum Total of all the la- 

 finite Secants on that Arch, is 



A'Yi A*+j\ ^ L +?ik AH^ilU A\ &c. 

 D 2 



the 



