Nicole Oresme

"Every measurable thing except numbers is imagined in the manner of a continuous quantity. Therefore, for the mensuration of such a thing, it is necessary that points, lines, and surfaces, or their properties, be imagined. For in them... measure or ratio is initially found... Therefore, every intensity which can be acquired successively ought to be imagined by a straight line perpendicularly erected on some point of the space or subject of the intensible thing, e.g., a quality... And since the quantity or ratio of lines is better known and is more readily conceived by us—nay the line is in the first species of continua, therefore such intensity ought to be imagined by lines... Therefore, equal intensities are designated by equal lines, a double intensity by a double line, and always in the same way if one proceeds proportionally."

"Since money belongs to the community … it would seem that the community may control it as it wills, and therefore may make as much profit from alteration as it likes, and treat money as its own property."

"I am of the opinion that the main and final cause why the prince pretends to the power of altering the coinage is the profit or gain which he can get from it."

"Whenever kingship approaches tyranny it is near its end, for by this it becomes ripe for division, change of dynasty, or total destruction, especially in a temperate climate … where men are habitually, morally and naturally free."

"People marvel at … things only because they rarely happen; but the causes for these are as apparent as for others … For example, at night a fearful man who sees a wolf in the fields, or a cat in his room, will immediately assert and judge that it is an enemy or a devil … because he fixes his imagination on these and fears them. And a person devout and rapt [in ecstasy] will judge that it is an angel … A vigorous imagining of a retained species, then, together with a small external appearance or with an imbalance of some internal disposition … produces marvelous appearances in healthy as well as in sick people."

"God in His infinite grandeur without any quantity and absolutely indivisible, which we call immensity, is necessarily all in every extension or space or place which exists or can be imagined."

"The heavenly bodies move with such regularity, orderliness, and symmetry that it is truly a marvel; and they continue always to act in this manner ceaselessly, following the established system, without increasing or reducing speed and continuing without respite, as the Scripture says: Summer and winter, night and day they never rest."

"It appears that here and there some of our modern ideas were anticipated by writers of the Middle Ages. Thus, Nicole Oresme... first conceived the notion of fractional powers, afterwards, rediscovered by Stevin, and suggested a notation [other than our modern notation]. Since 4^3 = 64 and 64^\frac{1}{2} = 8, Oresme concluded that 4^\frac{3}{2} = 8. Some of the mathematicians of the Middle Ages possessed some idea of a function. Oresme even attempted a graphic representation. But of a numeric dependence of one quantity upon another, as found in Descartes, there is no trace among them."

"Nicole Oresme introduced the important concept of graphical representations, or geometrical "configurations", of intensities of qualities. ...He proposes to measure the intensity of the quality at each point of the reference interval by a perpendicular line segment at that point, thereby constructing a graph with the reference interval as its base. ...He refers to the reference interval as its longitude, and its intensity at a point as its latitude or altitude there (perhaps adapting these terms from their geographical use). ...Oresme... provided the Merton Rule with a geometrical verification."

"Coordinates had been used in astronomy and geography since ... Oresme called his coordinates "longitude" and "latitude," but he seems to have been the first to use them to represent functions such as velocity as a function of time. Setting up the coordinates before determining the curve was Oresme's step beyond the Greeks, but he too lacked the algebra to go further."

"Perhaps the first to approach the fourth dimension from the side of physics, was the Frenchman, Nicole Oresme, of the fourteenth century. In a manuscript treatise, he sought a graphic representation of the Aristotelian forms, such as heat, velocity, sweetness, by laying down a line as a basis designated longitudo, and taking one of the forms to be represented by lines (straight or circular) perpendicular to this either as a latitudo or an altitudo. The form was thus represented graphically by a surface. Oresme extended this process by taking a surface as the basis which, together with the latitudo, formed a solid. Proceeding still further, he took a solid as a basis and upon each point of this solid he entered the increment. He saw that this process demanded a fourth dimension which he rejected; he overcame the difficulty by dividing the solid into numberless planes and treating each plane in the same manner as the plane above, thereby obtaining an infinite number of solids which reached over each other. He uses the phrase "fourth dimension" (4am dimensionem)."