An elaborate woodcut border frames the entire text area, featuring architectural elements, floral motifs, and grotesque figures. At the bottom, a horizontal panel depicts a series of animal heads within circular wreaths.

A decorative initial 'O' contains a small figure or face.

to omit that the history of travel is what provides knowledge for such an institution, as it brings much knowledge from the tradition of those who, through the aforementioned speculative science, have traveled through particular regions. And because this consideration and tradition is partly geometrical, and partly consists of the observation of the higher things, it clearly looks to Geometry, which through subtle dimensions of distances makes the positions of places among themselves manifest, but it looks to the observation of the higher things, which is done through appearances from instruments by which stars and shadows are observed, which is both more perfect and more certain, while the other is more difficult and needs the help of the former. For first, since it is necessary that it be supposed, according to either mode, toward what position of the world the distance of two searched-out places tends (for it is not sufficient to know simply or only how much one place is distant from another, but toward where, that is, so that we may know how to say whether it tends toward the north or the east, or toward their more partial inclinations), it is impossible to consider this exactly without observation, which is done through the aforementioned instruments, by which in every place and time the position of the meridian line is easily shown, and through it the unknown distances of places. Hence it is also necessary to concede that the dimension which is made through the number of stadia units of distance by no means provides us with a discovery according to the truth, since it happens rarely that one encounters straight paths, because of the various circuits which are accustomed to occur both to those going by land and those sailing. And because it is necessary, in order to find the straightness, to subtract from the whole stadia by conjecturing only what results in paths both from qualities and quantities. In voyages, however, the blowing of the winds, which for the most part do not maintain the same strengths, lacks any norm for judging. Furthermore, even if some distance between two places measured exactly were known, the ratio of it to the circumference of the whole earth, nor the position, whether it tends toward the equinoctial or the poles, will not therefore be revealed. But the dimension which is made through the appearances of the sky brings certain knowledge of each of these things, and shows what kind of circumferences the circles, parallels, and meridians intercept among themselves through the places below, that is, the circumferences of the parallels which fall between them, and of the equinoctial and the meridians, but those are the ones which are contained by them, and of the equinoctial and the parallels, and also what kind of circumference two places intercept of that circle which is the greatest on the earth.

Finally, it needs no counting of stadia, whether in relation to the ratio of those parts which are from the earth, or to the universal circuit of the description; for it is sufficient to suppose the circumference of the earth in as many parts as we wish, and through the same number of parts to show the distances in the greatest circles described upon the surface of the earth. But perhaps for dividing our dimensions of the whole circumference, or parts of it, into the subject and known intervals, these are less sufficient. Therefore, for the sake of this thing only, it was necessary to adapt a certain straight path to the circumference, which would be similar to the greatest circle according to the containment, and to take the ratio of this to the circle which is made from the appearances, and the number of stadia which is contained under it from the dimension which is made from the given part, and thus to demonstrate the multitude of stadia of the whole circumference. For since it is presupposed from mathematical things that the continuous surface of both earth and sea is round through all its parts, and has the same center with the sphere of the celestial bodies, it follows also that its individual common incisions, which are emitted from the center into the plane as well as from the said surfaces, make circles that are the greatest in themselves, and intercept the angles concluded in the plane itself to the center, similar to the portions of the arcs, and for that reason the quantity of stadia which are on the earth can be taken from the dimensions when they are straight, but the ratio which is to the whole circumference cannot be taken from them in any way, due to the defect of the reaching parabola. But from the similar circumference of the celestial circle, they are rightly taken, since the ratio of it to its own circumference can be detected, and the same also becomes from the similar part around the earth, to the circle that is greatest in it.

HOW THE CIRCUMFERENCE OF THE NUMBER OF STADIA OF ANY STRAIGHT DISTANCE, ALTHOUGH IT IS NOT UNDER THE SAME MERIDIAN, IS TAKEN, AND CONVERSELY

CHAPTER IV.

A circular emblem within a square frame depicts a stylized vessel or font with flames or plants emerging from it, flanked by two stars.

THose who were before us searched not only for the straight distance on the earth, where it makes the circumference of the greatest circle, but also that which had a position in the plane of one meridian,