On the principles and methodology of the measurement of the Earth and the Heavens

by Bartolomeo Gagliardi

In writing this work it is my most earnest hope that it will prove of some utility to mathematicians, navigators and those who seek to further our knowledge of this world and its many distant places. All herein is dedicated to the greater glory of God, from whom all knowledge does come and to which all in turn shall return.

That the world is a sphere is well known, and recorded in the Geographia of Ptolemy so recently translated to the elucidation of all by Martin Waldseemuller, whose essays on perspective have helped inspire this work. Magister Waldseemuller writes eloquently of the difficulties in establishing perspective and in measuring it accurately in the absence of full observatory and globe. It is to that problem I now turn myself.

Where it is desired that an accurate map be prepared many things are required. Of these, among the more important is the calculation of longitude and one's position upon the globe. That longitude is measurable with recourse to but the simpler instruments I shall now seek to demonstrate.

The Moon circumnavigates the Earth according to a fixed procedure, at any time its declination being a matter of calculation and observation. Further, the Moon in its passages retains a fixed distance from the Earth. Behind its motion it may be observed that the stars themselves appear fixed, although this be not so, for the Moon's transit across the sky is far greater in rapidity than their own. Indeed, in but one hour the Moon moves through the entirety of its diameter.

If therefore, one can but measure the distance from the Moon to certain already selected stars one can calculate the absolute time in the Heavens, which when compared to the time at the place of measurement on Earth will itself reveal the longitude of the observer.

To this end I have developed a device I name Jacob's Ladder, a staff with moveable tablets crafted after the manner of the Jacob staff of Levi ben Gerson which that most learned of men used for the measurement of the altitude of the Sun, Moon and stars.

Given a stable platform on which to rest and an accurate guidance to the time where one stands, the tool may be used to determine the Moon's altitude and the altitude of those stars selected by the observer. In turn, this allows the comparison of earthly with celestial time and thus reveals the precise longitude at which the astronomer is to be found.

That this instrument may also be utilised in the measurement of longitude by virtue of the observation of the eclipses of the Moon, as proposed by the learned Hipparchus of Rhodes, should I trust be readily apparent.

Accordingly, it is my proposal that my Jacob's Ladder be developed and applied in the assistance of navigation and exploration, that the glories of our Lord God's creation be laid bare for all to marvel and wonder at his work.