geometrician (jeometrishan)

[ worm. section Geometrina, or its larva; a measuring Geometridæ (je-ō-metri-dē), n. pl. [NL., Ennomina, Enochromina, A mph i das inæ, Boarminæ, Boletobiinæ, Geometrinæ, Microcerina, Palyadinæ, Ephy rinæ, Acidalinæ, Mecocerina, Caber inæ, Macarinæ, Fido In divided hamiland, Bosna, niince, Hazine, Zerenince, Ligince, Hyberninæ, Larentiince, Eubolinæ , Sionine, Hedyline, Era tein in a, Emplocinæ , In as and Hypochrosince in some systems, Guences, these and the superfamily thus constituted, called Phalœnites, is the Geometrina of English authors. The names Geo me tride and Phalænidæ are exactly synonymous; and the various names resulting from the changes in termination of the two words are applied to what is practically an identical group of moths, rated higher or lower in the taxonomic scale, to cla ificatory IMG:content-2226.png:[blocks in formation] 2. A text-book of geometry.-Abstract geometry, the general theory of the connections of more than two variables. Geometry, in its analytical treatment, appears as identical with the algebra of two or three variables. A similar study of the connections of a number of variables in general is called m-dimensional geometry, and abstract geometry as not descending to particulars. Algebraic, algorithmic, analytical, Cartes i an, coördinate, etc., geometry. See the adjectives. Common or elementary geometry, that treatment of geometry which a umes no previous knowledge of the subject, and is supposed to be well known in all other mathematical writings. This discipline remains in nearly the condition in which Euclid left it. See Euclidean geometry.- Descriptive geometry (invented by Gaspard Monge, 1794), the theory of making projections of any accurately defined figure such that from them can be deduced, not only its projective, but also its metrical properties. It is highly useful in engineering. The name is by means of projections. - Elliptic geometry, a system also applied to the theory of geometry in general treated which a umes that space returns into itself, so that there are no points whose distance exceeds a certain finite distance.-Enumerative or denumerative geometry, the theory of the number of solutions of geometrical prob lems, and of the number of incidences and coincidences in a diagram drawn under given conditions. - Euclidean geometry, a system of geometry which adopts the a umptions of Euclid with regard to space, namely, that space bodies are capable of translation and rotation in all direcis an infinite continuum of three dimensions, that rigid tions in every position, and that the sum of the three angles of a plane triangle is equal to two right angles. - Geometry of forces, the theory of congruencies and com plexes of forces. - Geometry of position. (a) A branch of geometry created by the French revolutionary statesman Carnot, which traces the connection between the changes of an equation and the changes of position of a locus. (b) Modern projective geometry, commonly written in German Geometrie der Lage, to distinguish it from ( a ). — Geometry of space, geometry of three dimensions, geometry of figures not restricted to a plane or other surface. Geometry of the compa es, a system of geometry in which the postulate that a right line be describable is not admitted, but instead links turn about pivots and are connected together. The first important discovery in this branch of geometry was the Peaucellier cell. See cell. - Graphical geometry. Same as projective ge and Haplodes. The Geometridæ or Phalænidæ form a family of great size, being exceeded in numbers among the Lepidoptera only by the noctuids and tineids, and probably equalled only by the pyralids and tortricids. They are widely distributed over the globe, and the caterpillars of many species have proved very destructive to some of our most important vegetable productions. The moths have rather long, slender bodies, the thorax without tufts or crests. Ocelli are present in some species, and absent in others. The antennæ are either simple, ciliated, or pectinated. The fore wings are large and triangular; the outer margin is nearly as long as the hinder margin. The hind are wings are ample. In some [species), the females are wingle , or have only rudimentary wings, which are usele for flight.. The caterpillars are slender and naked, usually with two pairs of abdominal legs, though rarely they have three or four pairs. This deficiency causes them to move along with a looping gait, and hence they are often called "measuring-worms," from which fact the family name [ Geometridæ ] was given. Stand . Nat . Hist ., II. 445.