With the ancients, analecta signified a servant, whose business it was to gather up what fell from the tables, at meals, as the pavements of the Roman floors sometimes were too finely inlaid to admit of sweeping.

ANALOGY originally denotes a relation, similarity or agreement of things in certain respects. The knowledge which rests merely on this relation is called analogical. The conclusion deduced from the similarity of things in certain respects, that they are similar, also, in other respects, is called, in logic, an analogical conclusion, and amounts only to a probability. This reasoning is applied to the explanation of authors (analogia interpretationis), and particularly to the interpretation of the Holy Scriptures, in which consistency of doctrine is taken for granted (analogia fidei). It is also used in the application of the laws, to form a judgment, in any particular case, by a comparison of former decisions in similar cases. In practical medicine, it is used in the application of remedies.-A great part of the principles of experimental philosophy are established by inferring a further uniformity from that which has been already settled.—In grammar, by analogy is meant a conformity in the organization of words.-In mathematics, it is the similitude of certain proportions. -Newton gives analogy the second place amongst his laws of philosophizing, and may be said to have established some of the most characteristic parts of his system, as arising out of the doctrine of gravitation, on its sober and patient use. In fact, analogical reasoning is essential in inductive philosophy, though it must be used with caution. The history of philosophy shows innumerable instances of the wildest errors, as well as of the sublimest discoveries arising from its application. The modern philosophy of Germany has suffered much in point of correctness and clearness, from several bold speculators, led away by fancied analogies between the moral and physical world; though it cannot be denied, that much of the progress of that nation in philosophical investigations is due to the use of the same instrument.

ANALYSIS, in philosophy; the mode of resolving a compound idea into its simple parts, in order to consider them more distinctly, and arrive at a more precise knowledge of the whole. It is opposed to synthesis, by which we combine and class our perceptions, and contrive expressions for our thoughts, so as to repre

sent their several divisions, classes and relations. Analysis is regressive, searching into principles; synthesis is progressive, carrying forward acknowledged truths to their application.-Analysis, in mathematics, is, in the widest sense, the expression and developement of the functions of quantities by calculation. There are two ways of representing the relations between quantities, to wit, by construction, and by calculation. Pure geometry determines all magnitudes by construction, i. e., by the mental drawing of lines, whose intersections give the proposed quantities; analysis, on the contrary, makes use of symbolical formulæ, called equations, to express relations. In this widest extent of the idea of analysis, algebra, assisted by literal arithmetic, appears as the first part of the system. Analysis, in a narrower sense, is distinguished fron algebra, inasmuch as it considers quantities in a different point of view. While algebra speaks of the known and unknown, analysis treats of the unchanging or constant, and of the changing or variable. The algebraic equation, x2 + a x — b=0, for example, seeks an expression for the unknown r by means of the known a and b; but the analytical equation, y2 = =ax, expresses the law of the formation of the variable y, by means of the variable x, together with the constant a.-In its application to geometry, analysis seeks by calculation the geometrical magnitudes for an assumed or undetermined unit. The analysis of the ancients was exhibited only in geometry, and made use only of geometrical assistance, whereby it is distinguished from the analysis of the moderns, which, as before said, extends to all measurable objects, and expresses in equations the mutual dependence of magnitudes. But analysis and algebra resemble each other in this, that both, as is shown more fully in the article on algebra, reason in a language, into the expressions of which certain con ditions are translated, and then, according to the rules of the language, are treated more fully, in order to arrive at the result. Analysis, when considered in this light, appears to be the widest extent of the province of this language. Analysis, in the more limited sense, is divided into lower and higher, the bounds of which run very much into one another, because many branches of learning are accessible in both ways. While we comprise in lower analysis, besides arithmetic and algebra, the doctrines of functions, of series, combinations, logarithms and curves, we

232

comprehend in the higher the differential and integral calculus, which are also included in the name infinitesimal calculus; the first of which the French consider as belonging, in a wider sense, to the théorie des fonctions analytiques.-A good account of the ancient analysis is given by Pappus of Alexandria, a mathematician of the 4th century, in his Collection of Geometrical Problems,* in which there is also a list of the analytical writings of the ancients. What progress was made after the destruction of the Roman empire, particularly by the Arabians, in algebraical, and, as interwoven with them, in analytical inquiries, has been related in the article on algebra. Newton and Leibnitz (q. v.) invented the above-mentioned infinitesimal calculus. After them, Euler and the brothers Bernoulli (q. v.) labored with splendid success for the further improvement of mathematical analysis; and, in later times, d'Alembert, Laplace, Lagrange, &c. have raised it still higher. Hindenburg (q. v.) is the inventor of the analysis of combinations. We have not room here to go into detail with respect to the other analytical doctrines.-Euler's Introductio in Analysin Infinitorum,† Lausanne, 1748, 2 vols. (new ed., Leyden, 1797) still continues one of the most important works, in regard to the analysis of finite quantities. In close connexion with this stands the same author's Institutiones Calculi differentialis, Petersburg, 1755, 4to. Lagrange's Théorie des Fonctions Analytiques (new ed., Paris, 1813, 4to.) is, on account of the depth of its views and its many valuable applications to geometry and mechanics, a valuable work for the study of the connexion between the analysis of finite quantities, and the so named (though, indeed, here considered in a very different light) calculation of infinities. As this work cannot be understood without a good acquaintance with general and very abstract calculations, we would connect with it the same author's Leçons sur le Calcul des Fonctions (new ed., Paris, 1806). Arbogast's Calcul des Derivations, Strasburg, 1800, 4to., is new in its views of the analysis of finite quantities. The most excellent of the old works on the integral calculus is Euler's Institutiones Calculi Integralis, Petersburg, 1768-1770, 3

There is a Latin translation of it by Commandinus-Mathemat, Collationes, Commentariis illustrate, Bonn, 1659, folio. The Greek text is not published.

It has this title on account of the application which is here made of the idea of the infinite, and its connexion with the higher analysis

vols., 4to. The present state of the inte gral calculus, after the improvements of the French analysts, may be learned from Lacroix's Traité du Calcul différentiel et dr. Calcul intégrai, Paris, 1797 and seq., 3 vols., 4to. (There has since appeared & new edition.)-For beginners, we recom mend Pasquich's Mathematical Analysis, Leipsic, 1791, and, for more advanced students, the same author's Elementa Analyseos sublimioris, Leipsic, 1799, 4to. Nürnberger's Exposition of the Formation of all derived Functions, Hamburg, 1821, treats this subject in a new point of view. For A. in chemistry, see Chemistry.

ANAMORPHOSIS; a perspective projection of any thing, so that it shall appear at one point of view deformed; at another, an exact representation.

ANAPEST. (See Rhythm.)

ANANAS, in botany; a species of bromelia, commonly called pine-apple (q. v.), from the similarity of its shape to the cones of firs and pines.

ANAPHORA (Greek, aragoga, repetition); a rhetorical figure, which consists in the repetition of the same word or phrase at the beginning of several successive sentences. A similar repetition at the end of sentences is called epiphora, or homoioteleuton. Anaphora is sometimes used as the general name for both figures; the former is then called epanaphora. The anaphora aims to increase the energy of the phrase, but is often rendered ineffectual by too frequent repetition.

ANASTASIUS I, emperor of the East, succeeded Zeno, A. D. 491. He distinguished himself by his moderation towards different Christian sects, whose quarrels at that time disturbed the peace and safety of the Byzantine empire. Moreover, he repealed a very heavy tax, called chrysargyrum, and prohibited the fighting with wild beasts. He died A. D. 518, after a reign of 27 years.-A. II was another emperor of the East, dethroned by Theodosius, in 719, and afterwards put to death.-A., surnamed Bibliothecarius, a Roman abbot, keeper of the Vatican library, and one of the most learned men in the 9th century, assisted, in 829, at the 4th general council, the acts and canons of which he translated from the Greek into Latin. He also composed the lives of several popes, and other works, the best edition of which is that of the Vatican, 4 vols. fol., 1718.

ANATHEMA (cursed by God) is the form of excommunication from the church. Hence, to pronounce the anathema, or to anathematize, means, in the Roman Cath

olic church, to excommunicate the living from the church, and the dead from salvation. How important an instrument of spiritual power the anathema was, in the hands of the popes, in the middle ages, how much disorder they gave rise to, and how little they have been regarded in modern times, is matter of history. Napoleon died in excommunication, and yet a priest attended him, and the circumstance is hardly mentioned.-Originally, the word was applied to various persons and things separated from ordinary life or uses to the will of a real or supposed deity, a gift hung up in a temple, and dedicated to some god, a votive offering; but, as the word is derived from rati9qui (to separate), it has been, in later ages, used for expulsion, curse. The Greek and Ro

man Catholic churches both make use of the anathema. In the latter, it can be pronounced only by a pope, council, or some of the superior clergy. The subject of the anathema is declared an outcast from the Catholic church, all Catholics are forbidden to associate with him, and utter destruction is denounced against him, both body and soul. The curse is terrible. Mere excommunication is less severe. The heretic has also to anathematize his errors. Once in every year, the pope publicly repeats the anathcma against all heretics, amongst whom the Protestants, Luther, &c., are mentioned. When councils declare any belief heretical, the declaration is couched in the following form: Si quis dixerit, &c., anathema sit, which often occurs in the decisions of the councils. (See Excommunication.) ANATOMICAL PREPARATIONS. Dead bodies and parts of bodies, notwithstanding their tendency to decomposition, can be preserved by art. It is important to the physician, for the determination of the medical treatment proper in similar cases, to preserve the organs, which have been attacked by diseases, in their diseased state, and, as a counterpart, the same organ in its sound condition. The anatomical preparations of healthy parts may serve for instruction in anatomy. Preparations of this sort can be preserved either by drying them, as is done with skeletons, or by putting them into liquids, e. g., alcohol, spirits of turpentine, &c., as is done with the intestines and the other soft parts of the body, or by injection. The injection is used with vessels, the course and distribution of which are to be made sensible, and the shape of which is to be retained. The beginning of the vessel, e. g., the aorta among the arteries,

is filled, by means of a syringe, with a soft, colored mass, which penetrates into all, even the smallest branches of the vessels, dries them, and makes them visible. The finest capillary vessels may be thus made perfectly distinguishable. The infusion usually consists of a mixture of soap, pitch, oil and turpentine, to which is added a coloring substance; for instance, red for the arteries, green or blue for the veins, white for the lymphatic vessels. For very fine vessels, e. g., for the absorbing lymphatic vessels, quicksilver is preferred, on account of its extreme divisibility. Dried preparations are the bones, cleared of all the soft parts by boiling, and bleached, or any of the soft parts, covered with a protecting but transparent varnish; e. g., muscles, intestines, &c. The quicker the drying of the organs destined for preparation can be effected, the better they will be preserved. For the purpose of preserving them, alcohol is used; the more colorless, the better. Spirits of wine, distilled with pepper, or very strong pimento, are also used, together with some muriatic acid. Washing with acids (lately, pyro-ligneous acid has been used) gives to the preparation sometimes firmness, and sometimes whiteness. Washing is particularly necessary with bones which are in a state of putrefaction. Muscles are usually tanned; and all that is in danger of being eaten by worms, or injured by a damp atmosphere, is covered with a suitable varnish. tions treated thus are fixed upon a solid body, or in a frame. Preparations preserved in liquids are usually kept in transparent glasses, hermetically sealed, to secure them from the destroying influences of dust, air, humidity, heat, cold, the sun, insects, &c. Damaged preparations can seldomn be perfectly restored.

The prepara

ANATOMY (Greek, avatturer, to dissect); the art of dissection; that of brutes is frequently called zootomy. Anatomy is a part of natural history, and is one of the most important branches of the science of medicine. The dissection of the human body was but little practised by the ancients. The old Egyptians held it in great abhorrence, and even pursued with stones those men, who, in embalming the dead, were obliged to cut open their bodies. The Greeks were prevented by the principles of their religion from studying anatomy, since these required them to bury the bodies of the deceased as soon as possible. Even in the time of Hippocrates, anatomical knowledge was imperfect, and was probably derived from the

dissection of animals; the skeleton, however, was better known. When, in later times, under the Ptolemies, Alexandria in Egypt became the seat of the arts and sciences, anatomy was also brought to a high degree of perfection, by Herophilus of Chalcedon, 300 B. C., and by Erasistratus of Chios. According to the testimony of Celsus, the former obtained permission to open living criminals. He enriched anatomy with many important discoveries; e. g., respecting the brain, the functions of the nerves, the blood-vessels of the mesentery, which go to the liver, &c. Erasistratus determined many facts in the construction of the brain with greater distinctness, and, among other improvements, gave to the valves in the vena cava the names which are yet used. In later times, the study of anatomy was again neglected, particularly by the empirics. Galen, educated in Alexandria (born A. D. 131), collected all the anatomical knowledge of his contemporaries, and of earlier physicians, but seems not to have much enriched human anatomy himself, as he was principally occupied with the dissection of animals, and only applied his observations on them to the structure of the human body. Among the Arabians, anatomy was not practised; it was forbidden by their religion. Their physicians, therefore, took their anatomical information merely from the writings of the Greeks, particularly from those of Galen. Thus anatomy was checked in its progress for several centuries. Finally, in the fourteenth century, individuals arose, who, not satisfied with the anatomical instruction of the age, ventured to make investigations of their own. The superstitious fear of the dissection of human corpses, which had hitherto prevailed, appeared to subside by degrees, when a philosophical spirit gave birth to more liberty of thought. Mondini di Luzzi, professor at Bologna, first publicly dissected two corpses, in 1315, and soon afterwards published a description of the human body, which for a long time was the common compendium of anatomy, though many errors were contained in it. From this time it became customary, in all universities, to make public dissections once or twice a year. Anatomy, however, made but slow progress, since the dissections were intended only as illustrations of the writings of Galen and the compendium of Mondini. Montagnana alone, professor at Padua in the 15th century, could boast of having performed 14 dissections, which was then a great

number. In the 16th century, there were many celebrated anatomists, by whose influence the study of anatomy became more general. Fallopia, Eustachi, Vesal, Varol and many others enriched anatomy with new discoveries. In the 17th century, there were likewise many famous anatomists, and many discoveries were made; thus Harvey discovered the circulation of the blood, Wirsung the pancreatic duct, Schneider the mucus membrane, &c. In the 18th century, Pacchioni, Valsalva, Keil, Lancisi, Ruish, Haller, Boerhaave, Vicq-d'Azir and others distinguished themselves by their skill in anatomy. Meckel, Soemmering, Loder, Reil, Bichat, Rosenmüller, are worthy to be mentioned as renowned anatomists of later times. According to the parts of the body described, the different divisions of anatomy receive different names; as, osteology, the description of the bones; myology, of the muscles; desmology, of the ligaments and sinews, &c.; splanchnology, of the viscera or bowels, in which are reckoned the lungs, stomach and intestines, the liver, spleen, kidneys, bladder, pancreas, &c. Angiology describes the vessels through which the liquids in the human body are conducted, including the blood-vessels, which are divided into arteries and veins, and the lymphatic vessels, part of which absorb the chyle from the bowels, while others are distributed through the whole body, absorbing the secreted humors, and carrying them back into the blood. Neurology describes the system of the nerves and of the brain; dermology, of the skin. Comparative anatomy is the science which compares the anatomy of different classes or species of animals; e. g., that of man with quadrupeds, or that of fish with quadrupeds. It is a science which has greatly increased our knowledge of nature, and affords one of the most interesting subjects of study. Among anatomical labors are particularly to be mentioned the making and preserving of anatomical preparations. (q. v.) By preparing, we mean the separating of any organ, or of an entire system, or of single parts, from all the other parts of the body. Thus, for instance, the whole system of bones, cleared from all the adherent muscles, tendons and other parts, is prepared, and called the skeleton; so, too, the muscles, nerves, intestines, their vessels and distrioutions are laid open in order to examine their peculiar construction. These labors require considerable anatomical knowledge. ANATOMY OF PLANTS. (See Plants, anat omy of.)

ANATRON; the scum which swims upon the molten glass in the furnace, sometimes called sal vitri, which, when taken off, melts in the air, and coagulates into common salt. It is also that salt which gathers upon the walls of vaults; likewise the same with natron. (q. v.) Anatron is also a compound salt, made of quick-lime, alum, vitriol, common salt and nitre, used as a flux to promote the fusion and purification of metals. It is also used for the terra saracenica.

ANAXAGORAS, one of the principal Ionic philosophers, born at Clazomene, in Ionia, in the first year of the 70th Olympiad (500 B. C.), of rich and respectable parents, devoted himself to the study of philosophy, under Anaximenes of Miletus, or, according to some, under Hermotimus, his countryman. At the age of 20 years, he set out on his travels, visited Egypt, and all the countries where the sciences flourished, and finally settled at Athens. There he formed an intimacy with Pericles, and numbered among his disciples the most respectable citizens; e. g., Archelaus (the natural son of Perdiccas, king of Macedonia, who himself reigned 9 years) and Euripides. A profound study of the natural sciences enabled him to explain the eclipses of the sun and moon, earthquakes, and similar phenomena; but, by the intrigues of his enemies, he became suspected of blasphemy, and, in consequence of this accusation, was obliged to leave Athens, in 431. He went to Lampsacus, where he died after three years, 72 years old. The principle of A. was," from nothing comes nothing." He adopted, therefore, the idea of a chaos, and, as the primary element of all bodies, a kind of atoms, of the same nature as the bodies which they formed. These atoms, in themselves motionless, were, in the beginning, put in motion by another equally eternal, immaterial, spiritual, elementary being, which he called Nous (Intelligence). By this motion, and by the separation of the dissimilar particles, and the combination of those of the same nature, the world was formed; the earthy bodies sunk down, whilst the æther or fire rose and spread in the upper regions. The stars, however, were, according to him, of earthy materials, and the sun a glowing mass of stone, about as large as the Peloponnesus. The milky way he thought to be, like the rainbow, the reflection of light. The earth was, according to him, flat; the moon, a dark, inhabitable body, receiving its light from the sun; the comets, wandering stars. He contended that the

real existence of things, perceived by our senses, could not be demonstrably proved and considered reason as the source of truth. On account of this principle, many have regarded him as the first theis among the philosophers. Archelaus of Athens was his disciple.

ANAXIMANDER, Son of Praxiades, a dis ciple of Thales, and an original thinker was born at Miletus in the 42d Olympiad (610 B. C.) His chief study was mathematics. He discovered, or taught, at least, the inclination of the ecliptic, and determined the solstices and equinoxes, by means of a dial (gnomon). He first used figures, to illustrate the propositions of geometry. He was also the first who attempted to sketch the outlines of lands and seas on a globe, and made a celestial globe, for the explanation of his system of the universe. Yet his statements are not to be entirely relied upon. His ideas concerning the first principle of things are so obscurely stated, that they cannot well be ascertained. His system seems to have been that infinity, ro unapov, is the origin of all existence, from which all emanates, and to which every thing returns. He has not, however, defined the nature of this eternal, incorruptible, original matter, the parts of which are variable, the whole unchangeable. The number of worlds is, according to him, infinite. The firmament is composed of heat and cold, the stars of air and fire. The sun occupies the highest place in the heavens, has a circumference 28 times larger than the earth, and resembles a cylinder, from which streams of fire issue. When its opening is obstructed, it appears eclipsed. The moon is, according to him, likewise a cylinder, 19 times larger than the earth; its inclination produces the phases, its entire revolution the eclipses. Thunder and lightning are productions of the wind, compressed within the clouds. The earth has the shape of a cylinder, and is placed in the midst of the universe, where it remains suspended.-He died in the 58th Olympiad (546 B. C.), 64 years of age.

ANAXIMENES of Miletus flourished about the 56th Olympiad (556 B. C.) He was a disciple of Anaximander, from whose doctrines he, however, deviated. According to him, the air (a) is the infinite, divine, perpetually active, first principle of all things. He taught that the exterior circumference of the heavens consisted of earth; that the stats were solid bodies, surrounded by fire; that the sun, by whose course alone the seasons