ociation of Nations farthest remote, would attain its full lustre and
perfection.

Besides, that the same Rule would also discover a far easier way of making
_Logarithmes_, than ever was practised or known; and therefore might serve,
when ever there should be occasion, to extend the _Logarithmes_ beyond that
number of places, that is already extant.

Moreover such a rule would enable men to draw the _Meridian_ line
_geometrically_, that is, without _Tables_ or _Scales_: which indeed {217}
might also be done, by setting of the _Secants_ of every whole or half
degree, if there were not this Inconveniency in it (which is not in my
Rule:) That a Line composed of so many small parts, would be subject to
many errours, especially in a small compass.

The same Rule also will serve, to find the Course and Distance between two
Places assigned, as far, as practice shall require it; and that, without
any Table of _Meridional_ parts, and yet with as much ease and exactness.

And seeing all these things do depend on the solution of this Question,
_Whether the Artificial Tangent-line be the true Meridian-line?_ It is
therefore, that I undertake, by God's assistance, to resolve the said
Question. And to let the world know the readiness and confidence, I have to
make good this undertaking, I am willing to lay a _Wager_ against any one
or more persons that have a mind to engage, for so much as _another
Invention_ of mine (which is of less subtlety, but of far greater benefit
to the publick) may be worth to the Inventor.

For, the great advantage, that all Merchants, Mariners, and consequently
the Common-wealth, may receive from this _other Invention_, is, in my
judgment, highly valuable; seeing it will oftentimes make a ship sail,
though, according to the common way of sailing, the wind be quite contrary,
and yet as near to the place intended, as if the wind had been favourable:
Or, if you will, it will enable one to gain something in the intended way,
whether the wind be good or no (except only when you go directly South or
North) but the advantage will be most, where there is most need of it, that
is, when the Wind is contrary: So that one may very often gain a fifth,
fourth, third part, or more of the intended voyage; according as it is
longer or shorter, _viz._ always more in a longer Voyage, where the gain is
more considerable, and more welcome; not only by saving Time, but also
Victuals, Water, Fuel, Mens health, and so much Roo