ANAGNI ANALYTICAL GEOMETRY 455 of ether is of almost any quantity, as much as two quarts having been employed in some long- continued and severe operations. ANAGNI (anc. Anagnia), a town of Italy, about 40 m. S. E. of Rome; pop. about 7,500. Anagnia was one of the most ancient cities of Latium, the capital of the Hernici, and an early antagonist of Rome. It is the residence of some of the most powerful families of Italy, and it has given birth to several Roman pon- tiffs, among others to Gregory IX., Alexander IV., and Boniface VIII. ANAGRAM (Gr. dvd, backward, and yp&^fia, letter), the transposition of the letters form- ing a word or sentence into a new word or sentence having some bearing upon the sub- ject of the former one ; as, Honor est a Nilo, formed from the letters in the name of Horatio Nelson. To make a true anagram, every letter of the original words must be retained in the transposition, and no new one must be added. In ancient times anagrams were regarded as prophetic, or as embodying a direction to the man on whose name they were made; it is said that Pierre de St. Louis became a Carmel- ite monk on finding that his name, Ludovicus Bartelemi, could be transposed into Carmelo se devolvet. Satirical anagrams were very common in the 16th and 17th centuries; Cam- den, the English historian, devoted a treatise to them, and many of the most learned men spent their leisure in making them upon the names of their contemporaries. Perhaps the best anagram ever made is the one which trans- poses Pontius Pilate's question to Christ Quid est veritas? (What is the truth?) into the answer, Est vir qui adest (It is the man who is before you). The following are a few excel- lent anagrams: Arthur Wellesley, duke of Wellington " Let well-foiled Gaul secure thy renown." Napoleon Bonaparte "No, appear not at Elba." Louis Napoleon Bonaparte "Arouse, Albion; an open plot." For some curious anagrams, and their history, see the introduction to "Macaronic Poetry," by James Appleton Morgan (New York, 1872). ANAHUAC, an aboriginal name, signifying, in the Nahuatl or ancient Mexican language, by or near the water ; from att, water, and nahuac, near. The name has come to be applied spe- cifically to the valley, or rather the plateau of the city of Mexico, although in the early writers we find references to several Anahuacs; as, for instance, Anahuac-Ayotlan and Anahuac- Xicalanco, the latter applied to the district around the lake or lagoon of Xicalanco in Tabasco. From the circumstance of their having established themselves originally around the lakes of Chalco and Tezcuco, the tradi- tional tribes of Mexico have been called Ana- hualtecas, people living by the water. It is alleged that these tribes came from some northern region, supposed by some to have been from Asia by way of Behring strait, and that the ruins of ancient edifices, known as casas grandes, in New Mexico and Chihuahua, mark the path of their migration. It is, how- ever, known to critical students that their original seats, figuratively represented as seven caves, were somewhere in the vicinity, proba- bly on some of the islands, of Lake Michoacan ; and that when they reached the region of Anahuac, they were simple barbarians, clothed in skins and living by the chase. Around the lakes of Mexico, however, they found the feeble remnants of a people far advanced in civilization, agriculturists and architects the Tulhuatecas, a name corrupted by uncritical writers into Toltecs. These Tulhuatecas were unable to resist the irruption of the seven war- like tribes, but gradually taught them agricul- ture and the arts, and thus laid the foundation of the Tezcucan and Mexican empires, in which civilization and barbarism, lofty religious pre- cepts and the most cruel rites, were incon- gruously mingled. The Anahualtecas were precisely the people better known as Aztecs (see AZTECS); and the name of Anahuac is now only understood as applying to the plateau of the city of Mexico. This great table land comprises three fifths of the territory belong- ing to the Mexican republic, and has an eleva- tion of 4,000 to 8,000 feet above the level of the sea. E. and W. it is bounded by the two great chains of mountains into which the Cor- dillera of Central America is subdivided in its northward progress. Out of this plateau rise many lofty mountains, including the stu- pendous volcanoes of Jorullo and Popocatepetl, but it is generally level. ANAITIS, or Anahid, an oriental goddess, anciently worshipped by the Lydians, Arme- nians, Cappadocians, and Assyrians. The clas- sical writers identify her sometimes with Di- ana, sometimes with Venus, and she appears to have combined the attributes of both these goddesses. Her temple was magnificent, her statute golden, her worship most lascivious. ANALYTICAL GEOMETRY, a branch of mathe- matical science which consists in the applica- tion of algebra to geometry. It may be divided into three parts, according to the branch of geometry to which the algebra .is applied. 1. Applying algebra to elementary geometry, it furnishes means for the easy solution of the most intricate problems, the simplification of demonstrations, the finding of constructions, the discovery of new propositions, &c. 2. The application of algebra to the conic sections and other curves has simplified this study and great- ly expanded the knowledge of the higher geom- etry, which treats of other curves than the circle. 3. Its application to the system of coordinates in space, invented by Descartes, gave birth to a new view of the geometry of space, simplifying and expanding largely that branch called stereometry. 1st. In the solution of geometrical problems by algebra the figures are drawn as if the problem was solved, and if. necessary, such additional lines as may establish known relations between the different quan- tities ; then the known and unknown quantities
