The approach is, as we have seen, often guarded by additional constructions; the fact that the door and window face south is another argument in favour of this theory, and the access from one part of the interior to another is sometimes purposely rendered difficult by a sudden vertical rise of 5 or 6 ft.
And the algebraists or arithmeticians of the 16th century, such as Luca Pacioli (Lucas de Borgo), Geronimo or Girolamo Cardano (1501-1576), and Niccola Tartaglia (1506-1559), had used geometrical constructions to throw light on the solution of particular equations.
These figures include not only the categories of income and expenditure proper, but also those known as movement of capital, railway constructions and part ite di giro, which do not constitute real income and expenditure.i Considering only income and expenditure proper, the approximate totals are:
His style is clear, direct and remarkably free from cumbrous Latin constructions; he employed, whenever he could, the pithy and homely sayings of the peasants, and is not reluctant to point his moral with a rough humour.
(3) Apologists maintain that Jesus " claimed " Messiahship. There are speculative constructions of gospel history which eliminate that claim; and no doubt apologetics could - with more or less difficulty - restate its position in a changed form if the paradox of to-day became accepted as historical fact to-morrow.
In the course of constructions for surfaces to reflect to one and the same point (1) all rays in whatever direction passing through another point, (2) a set of parallel rays, Anthemius assumes a property of an ellipse not found in Apollonius (the equality of the angles subtended at a.
(a) Hebrew constructions and expressions are to be found in every page.
They teach further the solution of problems leading to equations of the first and second degree, to determinate and indeterminate equations, not by single and double position only, but by real algebra, proved by means of geometric constructions, and including the use of letters as symbols for known numbers, the unknown quantity being called res and its square census.
Spiders form at least two kinds of constructions - snares for the capture of prey and nests for the preservation of the young.
LORENZO MASCHERONI (1750-1800), Italian geometer, was professor of mathematics at the university of Pavia, and published a variety of mathematical works, the best known of which is his Geometria del compasso (Pavia, 1797), a collection of geometrical constructions in which the use of the circle alone is postulated.
Many of the solutions are most ingenious, and some of the constructions of considerable practical importance.
If ABCD is a tetrahedron of reference, any point P in space is determined by an equation of the form (a+13+ - y+5) P = aA+sB +yC +SD: a, a, y, b are, in fact, equivalent to a set of homogeneous coordinates of P. For constructions in a fixed plane three points of reference are sufficient.
He improved the methods for solving equations, and devised geometrical constructions with the aid of the conic sections.
So far the development of algebra and geometry had been mutually independent, except for a few isolated applications of geometrical constructions to the solution of algebraical problems. Certain minds had long suspected the advantages which would accrue from the unrestricted application of algebra to geometry, but it was not until the advent of the philosopher Rene Descartes that the co-ordination was effected.
After it had been supplanted by Arabic in the ordinary intercourse of life its literary use was more and more affected by Arabic words and constructions, and its freedom as a vehicle of thought was much impaired.
2 Manicheans, Bogomils, Cathars and Paulicians for like reasons denied the name of church to material constructions of wood and stone.
Thick, must represent a period of about 3000 years, more especially as older constructions had to be levelled before the pavement was laid.
- In laboratory practice use is made of a fairly constant type of apparatus, only trifling modifications being generally necessary to adapt the apparatus for any distillation or fractionation; in technology, on the other hand, many questions have to be considered which generally demand the adoption of special constructions for the economic distillation of different substances.
The nymphaea of the Roman period were borrowed from the constructions of the Hellenistic east.
Contrivances of the most diverse constructions have been employed.
This class of burner forms a basis on which all the later constructions of burner have been founded, but had the drawback that if the flame was turned low, insufficient air to prevent carbonization of the burner tips was drawn in, owing to the reduced flow of gas.
All the great prose writers of France could not fail to be influenced by the racy phrase, the quaint and picturesque vocabulary, and the unconstrained constructions of Montaigne.
Similar constructions have been described by travellers, among the Dyaks of Borneo, in Celebes, in the Caroline Islands, on the Gold Coast of Africa, and in other places.
The archaeological researches of the past fifty years have shown that such artificial constructions in lakes were used as defensive dwellings by the Celtic people from an early period to medieval times (see Crannog).
They are most abundant in the plains of northern Italy traversed by the Po and its tributaries, though similar constructions have been found in Hungary in the valley of the Theiss.
Some of the Italian terremare show quadrangular constructions made like the modern log houses, of undressed tree trunks superposed longitudinally and overlapping at the ends, as at Castione in the province of Parma.
Desor, Les Palafittes ou constructions lacustres du lac de Neuchatel (Paris, 1865); E.
Perrin, Etude prehistorique sur la Savoie specialement a l'époque lacustre (Les Palafittes du lac de Bourget, Paris, 1870); Ernest Chantre, Les Palafittes ou constructions lacustres du lac de Paladru (Chambery, 1871); Bartolomeo Gastaldi, Lake Habitations and prehistoric Remains in the Turbaries and Marl-beds of Northern and Central Italy, translated by C. H.
Overhead railways are virtually continuous bridge constructions, and much attention has been given to a study of the special conditions appertaining to that case.
The queen sadly needed such of Wel a counsellor, for Prince Albert's position was one full of difficulty, and party malignity was continually putting wrong constructions upon the advice which he gave, and imputing to him advice which he did not give.
Confirmatory evidence of this is to be found, not only in the character of their constructions, but in the circumstance that a tribe closely akin to the Mayas (the Huastecos) still occupies a retired mountain valley of Vera Cruz, entirely separated from their kinsmen of the south, and that a dialect of the Maya language is still spoken in northern Vera Cruz.
But the fantastic relations imagined by him of planetary movements and distances to musical intervals and geometrical constructions seemed to himself discoveries no less admirable than the achievements which have secured his lasting fame.
Other words, by a non-Euclidean construction he trisected the angle AOC, for it is readily seen that, since FD' = FO = OC, the angle FOB = 2 AOC. 6 This couplet of constructions is as important from the calculator's point of view as it is interesting geometrically.
The tower resembles similar constructions found beside Irish churches of the 7th and 8th centuries and has walls 3 ft.
Amongst the legitimate reasons for suspecting the correctness of a text are patent contradictions in a passage or its immediate neighbourhood, proved and inexplicable deviations from the standards for forms, constructions and usages (mere rarity or singularity is not enough), weak and purposeless repetitions of a word (if there is no reason for attributing these to the writer), violations of the laws of metre and rhythm as observed by the author, obvious breaks in the thought (incoherence) or disorderly sequence in the same (double or multiple incoherence).
So popular has it become that besides being used for massive constructions like breakwaters, dock walls, culverts, and for foundations of buildings, lighthouses and bridges, it is also proving its usefulness to the architect and engineer in many other ways.
Similar constructions are to be found on the seaward side of the islands of Walcheren, Schouwen and Voorne, and between 's Gravenzande and Scheveningen, and Katwijk and Noordwijk.
The meaning of many words may be still unknown, and many constructions are still obscure; but at least he can distinguish fairly between a correct text and a corrupt text.
- Geometrical constructions of the parabola are to be found in T.
Descartes used the curve to solve sextic equations by determining its intersections with a circle; mechanical constructions were given by Descartes (Geometry, lib.
The following is a list of the best timbers for different situations: for general construction, spruce and pine of the different varieties; for heavy constructions, pitch pine, oak (preferably of English growth), teak, jarrah; for constructions immersed in water, Baltic pine, elm, oak, teak, jarrah; for very dry situations, spruce, pines, mahogany, teak, birch, sycamore.
This aqueduct still exists, and is one of the most remarkable constructions in Greece (see AQUEDUCT: Greek).
Even these had been preceded by earlier Pythagorean constructions envisaging the divine life in divine triangles.
At Haibak there is a very perfect excavation called the Takht-iRustam (a general name for all incomprehensible constructions amongst the modern inhabitants of Afghan Turkestan), which consists of an annular ditch enclosing a platform, with a small house about 21 ft.
To this Akkadian occupation succeeded an occupation by the first Semitic dynasty of Ur, and the constructions of Ur-Gur or Ur-Engur, the great builder of Babylonian temples, are superimposed immediately upon the constructions of Naram-Sin.
Partly razing the constructions of his predecessors, he erected a terrace of unbaked bricks, some 40 ft.
This device was never remote from the constructions of writers for whom the teaching of Spinoza and Leibnitz was an integral part of their intellectual equipment, Other modes of correlation, however, find favour also, and in some variety.
His constructions are based on the idea that the imaginaries d - 1 represent a unit line, and its reverse, perpendicular to the line on which the real units 1 are measured.
(A.McA.) 2 Essai sur une maniere de representer les Quantites Imaginaires dans les Constructions Geometriques.
Swedenborg is usually reckoned among the theosophists, and some parts of his theory justify this inclusion; but his system as a whole has little in common with those speculative constructions of the Divine nature which form the essence of theosophy, as strictly understood.