ifcellanea Curlofa. 



a I yra \ $r*a I J'^a , 



which is coincident with Dr- WMish fblution 

 ill £siimb. 176". of the Philofophicai TranfaUions* 

 And this fame Series being half the Logarithm 

 of the ratio of to R~s, that is, of the far- 

 fed- fines of the diftances from both Poles, does 

 agree with what Dr. Barrow had fhewn in his 

 Xlth. Letture. 



The fame ratio of r to * may be expreffed alfo 

 by that of the Sum of the Co-fines of the two Lati- 

 tudes, to the fine of their difference : As likewife 

 by that of the Sine of the Sum of the two Lati- 

 tudes, to the difference of their Co- fines : Or by 

 that of the Ver fed-fine of the Sum of the Co-lati- 

 tudes, to the difference of the fines of the Latitudes: 

 Or as the fame difference of the fines of the Lati* 

 tudes, to the Verfed^fine of the difference of the La- 

 titudes ; all which are in the fame ratio of the 

 Co-fine of the middle Latitude, to the Sine of 

 half the difference of the Latitudes. As it 

 were ealle to demonfirate, if the Reader were 

 not fuppofed capable to do it himfelf, upon a 

 bare infpe&ion of a Scheme duly reprefenting 

 thefe Lines. 



This variety of Expreffion of the fame ra- 

 tio I thought not fit to be omitted, becaufe by 

 help of the rationality of the Sine of iogr* 

 in all cafes where the Sum or difference of die 

 Latitudes is sogr. 6ogr. $cgr. nogr. or 150 

 degrees, fome one of them will exhibit a limple 

 feries, wherein great part of the Labour will be 

 faved : And befides I am willing to give the 

 Reader his choice which of thefe equippoleat 

 methods to make ufe of - 7 but for his exercife 



fcall 



