i6 JMifcellanea Curkja. 



42. And thefe Arches (in parts infinitely 

 fmaH) are to be reputed equivalent to the por- 

 tions of their refpedive Tangents intercepted 

 fefetween the fame ordinates. As in Fig. 7. 9. 



43. That is, equivalent to the portions of 

 the Tangents of Latitude. 



44. And thefe portions of Tangents are, to 

 the Equai intervals in the bafe, as the Tan- 

 gent (of Latitude) to its Sine. 



45. To find therefore the true Magnitude of 

 the Parallelograms for fegments of the Figure;^ 

 we mull either protrad the equal fegments of* 

 the bafe, Fig. 7. (in fuch proportion as is the 

 refpedive Tangent to the Sine) to make them 

 equal to thofe of Fig. 8. 



4.6. Or elfe (which is equivalent) retaining 

 the equal intervals of Fig. 7. protrad the Se- 

 cants in the fame proportion. ( For, either way 

 the Intercepted Redangle.s or Parallelograms 

 will be equally encreafed) As L M Fig. 9. 



47. Namely *, As the Sine (of Latiude) to 

 its Tangent ; fo is the Secant to a Fourth ; 

 which is to ftand (on the Radius equally divi- 

 ded) inftead of that Secant. 



SR R*, R3 



S. T( - : S • R ) : : T W?ZTS2^L M, Fig. 9 . 



48. Which therefore are as the Ordinate^ 

 in (what I call Arith. Infin. Prof, 104) Recifro^ 

 ca Secundinorurn : fuppofing ^ 2 to be fquares 

 ia the order of Secundajies. 



