An Eajie Demonjiration of the Analogy of the 
Logarithmic\ Tangents to the Meridian Line or 
fum of the Secants : with various Methods 
for computing the fame to the ntmoji ExaSl 
nefsy by E. Halley. 
IT is now near loo Years fince our Worthy Countryman 
Mr. Edward Wright publilhed his Corre^^on of Errors in 
Navigations SL Book well deferving the perufal of all (uch as 
defign to ufe the Sea Therein he confide; s the Courfe of a 
Ship on the Globe, ftearing obliquely to the Meridian ; and 
having fliewn, that the Departure fVom the Meridian, is in all 
cafes lefi than the Difference of Longitude, in the ratio of Ra- 
dius to the fecant of the Latitude, he concludes, That the fuin 
of the Secants of each point in the Quadrant being added fuc- 
ceffively, would exhibit a Line divided into Spaces, fuch as 
the intervals of the parallels of Latitude ought to be in a true 
Sea Chart, whereon the Meridians are made parallel Lines, 
atid the Rhombs or Oblique Courfes reprelenccd by right 
Lines. This is commonly known by the name of che Meri- 
dian Line, which though it generally be called Mercators, was 
yet undoubtedly Mr. Wrights Invention, ( as he has made it 
appear in his Preface. ) And the Table thereof is to be 
met with in moft Books treating of Navigation, computed 
wich fufficient exadnefi for the purpole. 
It was firft difcovered by chance, and as far as I can learn, 
firft publilht by Mr. Henry Bond, as an addition to Norwoods 
Epitome of Navigation about fO Years fince, that the Aderi- 
dian Line was Analogous to a Scale of Logarithmick Tangents of 
half the Complements of the Latitudes. The difficulty to prove 
the truth or this Pfopofition, leemed fiich to Mr» Mercatcr, 
the Author of Logarithmotechnia, that he propofed to wager 
a good fum of Money, againft whofo would fairly under- 
take it, that hefhould not demonftrate either, that it was 
trueor falle : And about that time Mr. John Collins, holding i 
a Correfpondence with all the Eminent Mathematicians of j 
the Age, did excite them to this Enquiry. ' i 
The I 
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