The Dutch Tiphys

Most Illustrious States, [you have shown] also your care. For how often have those who attempted to make the use of rhumb lines loxodromia: paths of constant bearing on a chart, which appear as straight lines on a Mercator projection but as spirals on a globe easier and more successful experienced your generosity? This remains true whether they explained the concept on flat charts or on the curved segments of spheres. Indeed, no one is thought to have aided maritime affairs in this regard who has not actually experienced that YOU strive with all solicitude and care so that this branch of science might be as perfect as its nature allows. You consider this work so worthy of your Majesty original: Majeſtate; here referring to the sovereign authority of the Dutch States General that you even voluntarily encourage the studies of everyone.

And not without cause: since the fortunes of so many men are daily committed to the rigging and float in that vast Ocean. For just as we yield to no nation in the industry of sailing, so in the multitude and agility of our vessels we are easily the equals of the rest. And since many men, out of a praiseworthy zeal for serving their country well, frequently weary your ears and desire to present to you methods for determining longitude original: longitudinis rationes; the "longitude problem"—finding one's East-West position at sea—was the most critical scientific challenge for 17th-century navigation explained for use at sea: I did not think that I too should be wanting to my country, or to those eager for these matters.

Therefore, I have resolved to derive all these things from the very foundation with solid reasoning, so that from there it might be definitely established how much the matter itself yields at sea, or how close it approaches the truth. I have therefore made an effort so that, with the difficulties noted with the greatest diligence—which can be avoided, or [interposed]...