Mzfcellanea Curio [a. 1 1 



It was firft difcovercd by Chance, and as far 

 as I can learn, firft publifh'd by Mr. Henry 

 Band, as an addition to Norwood's Epitome of 

 Navigation , about 50 Years fince, that the Me- 

 ridian Line was analogous to a Scale of Logarith- 

 mic!^ Tangents of half the Complements of tht 

 Latitudes. The difficulty to prove the truth 

 of this Proportion, feemed fuch to Mr. Mer- 

 cator, the Author of Logarithmotechnia, that he 

 propofed to wager a good fum of Moay,againft 

 wholb would fairly undertake it, that he mould 

 not demonftrate either, th#t it was true or 

 falfe: And about that time Mr. John Collins^ 

 holding a Correfpondence wi^h all the Eminent 

 Mathematicians of the Age, did excite them 

 to this enquiry 



' The firft that demonftrated the faid Analogy, 

 was the excellent Mr. James Gregory in his Ex- 

 ercitationes Geometric^ publifhed Anno 166%. 

 which he did, not without a long train of Con-, 

 fequences and Complication of Proportions, 

 whereby the evidence of the Demonftration is 

 in a great meafure loft, and the Reader wea- 

 ried before he attain it. Nor w ith lefs work 

 and apparatus hath the celebrated Dr. Barrow^ 

 in his Geometrical Lectures (Left. XI. App. i.j 

 proved, that the Sum of all the Secants of 

 any arch is analogous to the Logarithm of the 

 ratio of Radius -V Sine to Rad.—Sine, or, which 

 is all one, that the Meridional parts anfwering 

 to any degree of Latitude, are as the Logarithms 

 of the rationes of the Verfed Sines of the diftan- 

 ces from both the Voles. Since which the in- 

 comparable Dr. Wallis (on occaiion of a Para- 

 logical committed by one Mr. Norris in this 

 matter,) has more fully and clearly handled this 

 Argument, as may be feen in Num. \~j6* of 



C 3 the 



