Physical objects act upon the senses. Impressions of these objects produce perceptions of them in the understanding. The understanding deals with these perceptions in only three ways, according to its three principal faculties: memory, reason, imagination. Either the understanding simply enumerates its perceptions via memory; or it examines, compares, and directs them by Reason; or it chooses to imitate and contradict them by imagination. Whence results a general distribution of human knowledge, which seems well founded, into history which relates to memory, philosophy which emanates from reason, and poetry which originates from imagination. [...]
Philosophy, or the part of human knowledge which must be ascribed to reason, is very extensive. There is hardly any object perceived by the senses whose investigation has not formed some science. But in the multitude of these objects, there are some which stand out by their importance, "by which the infinite may be divided", and to which all the Sciences may be related. These primary ones are God, to the knowledge of whom man is elevated by considering natural and sacred history; man, who is confident of his existence by consciousness or internal sense; nature, whose history man has learnt by the use of external senses. God, man, and nature will provide us, therefore, with a general distribution of philosophy or science (since these words are synonymous); and philosophy or science will be Science of God, Science of man, and Science of nature. [...]
Science of nature. We will divide the Science of Nature into physical and mathematical. We take this division from due consideration and our tendency towards generalization. We have obtained via our senses the knowledge of real individual objects: sun, moon, Sirius, etc., Stars; air, fire, earth, water, etc., Elements; rain, snow, hail, thunder, etc., Weather; and so with the rest of natural history. We have obtained at the same time the knowledge of abstractions, color, sound, taste, smell, density, rarity, heat, cold, softness, hardness, fluidity, solidity, stiffness, elasticity, heaviness, lightness, etc., shape, distance, movement, rest, duration, extent, quantity, impenetrability.
We have found from reflection that of these abstractions, some pertain to all corporeal individual things, such as extent, movement, impenetrability, etc. We have made them the object of general physics, or metaphysics of bodies. And these same properties, considered in each individual thing in particular, with the varieties that distinguish them, such as hardness, resilience, fluidity, etc., are the object of special physics.
Another more general property of bodies, which all the others presuppose, known as quantity, forms the object of mathematics. One denotes by quantity or size anything that can be increased and diminished.
Quantity, the object of mathematics, can be considered either alone and independently of individual real things and individual abstractions of which we have knowledge; or in these real and abstract individual things; or in their effects sought from real or supposed causes; and this second view of the subject divides mathematics into pure mathematics, mixed mathematics, physico-mathematics.
Abstract quantity, object of pure mathematics, is either numerable, or extended.
Numerable abstract quantity is the object of arithmetic; and extended abstract quantity, that of geometry.
Arithmetic is divided into numerical or digital arithmetic, and algebra or universal arithmetic with letters, which is nothing but the calculation of quantities in general, and whose operations are really nothing but arithmetic operations indicated in an abridged way; since, to speak precisely, there is no calculation except with numbers.
Algebra is elementary or infinitesimal, according to the nature of the quantities to which it is applied. The infinitesimal form is either differential or integral: differential, when it concerns descending from a quantity that is (or is considered as) finite to the expression for its instantaneous increase or diminution; integral, when it concerns re-ascending from that expression to the same finite quantity.
Geometry either has as its main object the properties of the circle and the straight line, or includes in its speculations all sorts of curves; which divides it into elementary and transcendental.
Mixed mathematics has as many divisions and subdivisions as there are real entities in which quantity may be considered. Quantity, considered in such bodies as are movable or tend to move, is the object of mechanics. Mechanics has two branches, statics and dynamics. Statics has as its object quantity considered in bodies that are in equilibrium, and merely tending to move. Dynamics has as its object quantity considered in bodies that are actually moved. Statics and dynamics each have two parts. Statics is divided into statics as such, which has as its object quantity considered in solid bodies that are in equilibrium, and merely tending to move, and hydrostatics, which has as its object quantity considered in fluid bodies that are in equilibrium, and merely tending to move. Dynamics is divided into dynamics as such, which has as its object quantity considered in solid bodies that are actually moved, and hydrodynamics, which has as its object quantity considered in fluid bodies that are actually moved. But if one considers quantity in liquids that are moving, hydrodynamics takes the name hydraulics. Navigation may be related to hydrodynamics, and ballistics, or trajectories of bombs, to mechanics.
Quantity considered in the movements of the celestial bodies is geometrical astronomy; from which arise cosmography or description of the universe, which is divided into uranography or description of the heavens, hydrography or description of waters, and geography; whence also arise chronology and gnomonics, or the art of constructing sundials.
Quantity considered in light is optics, and quantity considered in the movement of light gives the different branches of optics: light moved in a direct line, optics as such; light reflected in one and the same medium, catoptrics; light broken in passing from one medium to another, dioptrics. It is to optics that we must relate perspective.
Quantity considered in sound, in its strength, movement, degrees, reflections, speed, etc., is acoustics.
Quantity considered in air, its weight, movement, condensation, rarefaction, etc., is pneumatics.
Quantity considered in the possibility of events is the art of conjecturing, whence arises the analysis of games of chance.
The object of mathematical sciences being purely intellectual, nobody should be surprised at the exactness of its divisions.
Special physics must follow the same division as natural history. From the study, taken by the senses, of the stars, of their movements, perceptible appearances, etc., consideration has passed to the study of their origins, of the causes of their phenomena, etc., and produced the science that is called physical astronomy, to which must be related the science of their influences, which is called astrology; whence physical astrology, and the illusion of judicial astrology. From the study, taken by the senses, of wind, rain, hail, thunder, etc., consideration has passed to the study of their origins, causes, effects, etc., and produced the science called meteorology.
From the study, taken by the senses, of the ocean, the earth, rivers, mountains, ebb and flow, etc., consideration has passed to the study of their causes, origins, etc., and has given birth to cosmology or the science of the universe, which is divided into uranology or science of the heavens, aerology or science of air, geology or science of the continents, and hydrology or science of waters. From the study of mines, taken by the senses, consideration has passed to the study of their formation, working, etc., and has given birth to the Science called mineralogy. From the study of Plants, taken by the senses, consideration has passed to the study of their husbandry, propagation, culture, vegetation, etc., and engendered botany, of which two branches are agriculture and horticulture.
From the study of animals, taken by the senses, consideration has passed to the study of their husbandry, propagation, usage, constitution, etc., and produced the Science called zoology; whence have arisen medicine, veterinary science, and horsemanship; hunting, fishing, and falconry; simple and comparative anatomy. Medicine (following the classification of Boerhaave) either concerns itself with the organization of the human body and rationally studies its anatomy, whence arises physiology; or concerns the manner of preventing diseases, and is called hygiene; or considers the diseased body, and deals with the causes, the differences, and the symptoms of diseases, and is called pathology; or has as its object the indicators of life, of health, and of diseases, their diagnosis and prognosis, and takes the name semiotics; or teaches the art of cures, and is subdivided into nutrition, pharmacy and surgery, the three branches of therapy.
Hygiene can be considered relative to the health of the body, to its beauty, and its strength, and may be subdivided into hygiene as such, cosmetics, and athletics. Cosmetics produces orthopedics or the art of giving a fitting shape to the limbs; and athletics produces gymnastics, the art of exercising them.
From experimental knowledge or study taken by the senses of perceptible, apparent, etc., external qualities of natural bodies, consideration has led us to artful research into their internal and hidden properties, and that art is called chemistry. Chemistry is the imitator and rival of nature; its object is almost as extensive as that of nature herself. It either decomposes beings or restores them, or transforms them, etc.
Chemistry has given rise to alchemy and natural magic. Metallurgy or the art of treating metal on a large scale is an important branch of chemistry. With that art, moreover, may be associated dyeing.
Nature has its blunders, and reason its abuses. We have related monsters to the blunders of nature; and it is to the abuse of reason that we must refer all sciences and arts which reveal nothing but the greed, wickedness and superstition of man, and which dishonor him.
This is the philosophical part of human knowledge, which must be referred to reason.