In short, I don't know.
One problem in the 17th century was that astronomers didn't know the scale of the Sun-Earth-Moon system. The approximate sizes of the Earth and the Moon and their approximate average distance had been known since antiquity, but I doubt whether the exact distance between the Moon and a point on the Earth's surface at any specific time could be precdicted very accurately. And more important, it was known that the Sun was many times farther than the Moon, but there was not yet any reasonably accurate measurement of the Astronomical Unit, the distance between the Sun and the Earth. This meant that astronomers couldn't use geometry to predict the width of the Moon's shadow on Earth.
They could use reports of the width of the Moon's shadow in previous eclipses, but that varied according to the exact distances between the Earth, hte Moon, and the Sun in each eclipse, and those distances vary due to the ellipical orbits of the Earth and the Moon.
Some information about the history of eclipse predicitons.
One of the first accounts of an eclipse—though one should note that this might be an old wives tale—dates back to 2136 B.C. Legend has it that the Emperor Chung K’ang executed his royal astronomers, Hi and Ho, for failing to predict an eclipse.
The eclipse of Thales was a solar eclipse that was, according to The Histories of Herodotus, accurately predicted by the Greek philosopher Thales of Miletus. If Herodotus's account is accurate, this eclipse is the earliest recorded as being known in advance of its occurrence. Many historians believe that the predicted eclipse was the solar eclipse of 28 May 585 BC.1 How exactly Thales predicted the eclipse remains uncertain; some scholars assert the eclipse was never predicted at all.35 Others have argued for different dates, but only the eclipse of 28 May 585 BC matches the conditions of visibility necessary to explain the historical event.
Answers to this question discuss the history of eclipse predictions:
The Antikythera mechanism (/ˌæntɪkɪˈθɪərə/ AN-tih-kih-THEER-ə) is an ancient Greek hand-powered orrery, described as the first analogue computer,1 the oldest known example of such a device24[excessive citations] used to predict astronomical positions and eclipses for calendar and astrological purposes decades in advance. It could also be used to track the four-year cycle of athletic games which was similar to an Olympiad, the cycle of the ancient Olympic Games.
A total lunar eclipse occurred on 1 March 1504, visible at sunset for the Americas, and later over night over Europe and Africa, and near sunrise over Asia.
Christopher Columbus, in an effort to induce the natives of Jamaica to continue provisioning him and his hungry men, successfully intimidated the natives by correctly predicting a total lunar eclipse for 1 March 1504 (visible on the evening of 29 February in the Americas). Some have claimed that Columbus used the Ephemeris of the German astronomer Regiomontanus,1 but Columbus himself attributed the prediction to the Almanach by Abraham Zacuto.2
On 30 June 1503, Christopher Columbus beached his two last caravels and was stranded in Jamaica. The indigenous people of the island welcomed Columbus and his crew and fed them, but after six months, the natives halted the food supply.4 Columbus had on board an almanac authored by Abraham Zacuto of astronomical tables covering the years 1475–1506.4 Upon consulting the book, he noticed the date and the time of an upcoming lunar eclipse. He was able to use this information to his advantage. He requested a meeting for that day with the Cacique, the leader, and told him that God was angry with the local people's treatment of Columbus and his men. Columbus said God would provide a clear sign of displeasure by making the rising full Moon appear "inflamed with wrath".
Of course this famous story is about a lunar eclipse visible from an entire hemisphere at any one moment, and not a solar eclipse visible only over a long, narrow path. Predicting where a solar eclipse will be visible is much more difficult.