Moreover such a rule would enable men to draw the Meridian line geometrically, that is, without Tables or Scales: which indeed
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 Room in the ship.
All this, which is here pretended, the Proposer is to make good by the Verdict of some able Men, who also may give a guess, what this latter Invention may be worth to the owner: And for so much, and no more, he will stand engaged against
any one or more Persons, that he will and shall resolve the Question above-mention'd, viz. Whether the Artificial Tangent-line be the true Meridian-line, yea or no? And if he do not, that then he will loose, and transport to the other Party the whole benefit of the last mentioned invention. But if, on the contrary, he do prove or disprove the Identity of the said two lines, to the Judgment of some able Mathematicians, That then so much money be paid him by the other Party, as the said Invention was valued.
And, whereas there are often Wagers laid about things that concern the Engagers little or nothing; 'tis thought, that it would concern all Merchants, Mariners, and all Lovers of the common good, rather to lay wagers against one another about Things of this nature, where the Gainer doth gain as well, as if he had laid his wager about something else, and the Looser hath so far the benefit as well as the Gaine, That he seeth thereby promoted the thing, that concerns them both alike.
Now therefore, to the end, that the Looser may have his benefit by it, as well as the Gainer, it would not be amiss, that the condition were made thus, that the latter should grant the moity of his gain to the Proposer; that thereby he might be enabled to bring to light both those, and some other useful inventions, for the Service of Mankind. And to manifest, that it is not for his own interest only, that the Proposer mentions this; he is willing to impart from that moity, so received, the full moity again to any other person within his Majesty's Dominions, who shall first of all give notice of his Undertaking to prove or disprove the said Identity, and perform it accordingly within the space of two Months, to be computed from the present Date. Those that have a mind to engage, may repair to the Printers of these Tracts, where they may know further.
