The axes will not be parallel, nor will they intersect each other.
These plateaus, with an average elevation of Boo to 1000 ft., are mostly covered with forests of oak, beech and lime, and are deeply cut by river valleys, some being narrow and craggy, and others broad, with gentle slopes and marshy bottoms. Narrow ravines intersect them in all directions, and they often assume, especially in the east, the character of wild, impassable, woody and marshy tracts.
They intersect regularly at right angles, dividing the town into square blocks, like modern Mannheim or Turin, according to a Roman system usual in both Italy and the provinces: plainly they were laid out all at once, possibly by Agricola (Tac. Agr.
In obtaining the minor Aik in the form of a determinant we erased certain rows and columns, and we would have erased in an exactly similar manner had we been forming the determinant associated with A2:8, since the deleting lines intersect rk in two pairs of points.
In these thoroughfares and in several of the streets which intersect them are the offices of the mining companies, the banks, clubs, newspaper offices, hotels and shops, the majority being handsome stone or brick buildings, while the survival of some wooden shanties and corrugated iron buildings recalls the early character of the town.
In 1754 Prome was besieged by the king of Pegu, who was again defeated by Alompra, and the war was transferred from the upper provinces to the mouths of the navigable rivers, and the numerous creeks and canals which intersect the lower country.
With variation of temperature, the surfaces of equal pressure and density need not coincide; but, taking the pressure, density and temperature as connected by some relation,such as the gas-equation, the surfaces of equal density and temperature must intersect in lines lying on a surface of equal pressure.
The central zone includes Hejaz (or Hijaz), Nejd and El Hasa; much of it is a dry, stony or sandy steppe, with few wells or watering-places, and only occupied by nomad tribes; but the great wadis which intersect it contain many fertile stretches of alluvial soil, where cultivation is possible and which support a considerable settled population, with several large towns and numerous villages.
Taking this ideal limit as a theoretical or absolute zero, the value of H may be represented on the diagram by the whole area included between the two adiabatics BAZ, CDZ' down to the points where they intersect the isothermal of absolute zero, or the zero isopiestic OV asymptotically at infinity.
The soft shales or clays of the hills bounding the valley render these hills especially subject to the action of denudation, and the result, in rounded slopes and easily accessible crests, determines the nature of the easy tracks and passes which intersect them.
The best soils when abundantly irrigated yield from 50to 60-fold, and the water for this purpose is supplied by the innumerable streams which intersect the province.
If r, r i be the radii of two spheres, d the distance between the centres, and 0 the angle at which they intersect, then d2=r2+ r12 2rr l cos ¢ hence 2rr 1 cos =d2r2 - r22.
Two spheres intersect in a plane, and the equation to a system of spheres which intersect in a common circle is x 2 + y 2 + z 2 +2Ax -fD = o, in which A varies from sphere to sphere, and D is constant for all the spheres, the plane yz being the plane of intersection, and the axis of x the line of centres.
Obviously these equations show that the curves intersect in four points, two of which lie on the intersection of the line, 2 (g - g')x +2 (f - f')y+c - c'=o, the radical axis, with the circles, and the other two where the lines x2+y2= (x+iy) (x - iy) =o (where i = - - I) intersect the circles.
The equation x 2 +y 2 =o denotes a pair of perpendicular imaginary lines; it follows, therefore, that circles always intersect in two imaginary points at infinity along these lines, and since the terms x 2 +y 2 occur in the equation of every circle, it is seen that all circles pass through two fixed points at infinity.
Consider the case of two circles, and in the first place suppose them to intersect in two real points A and B.
The circles intersect in real or imaginary points according to the lower or upper sign of k 2, and the limiting points are real for the upper sign and imaginary for the lower sign.
When the solution ceases to be dilute in the thermodynamic sense of the word, that is, when the spheres of influence of the solute particles intersect each other, this reasoning ceases to apply, and the resulting modification of the gas laws as applied to solutions becomes a matter for further investigation, theoretical or experimental.
Such a rule of the two diameters not only guides us toward the sun in the system and the heart in man, but draws lines through the length and breadth of the aggregate of a man's particular daily behaviors and waves of life into his coves and inlets, and where they intersect will be the height or depth of his character.
Numerous canals intersect the district, affording ample means of irrigation.
Paris is served by the Vandalia, and the Cleveland, Cincinnati, Chicago & St Louis (New York Central system) railways; the main line and the Cairo division of the latter intersect here, and the city is the transfer point for traffic from the E.
We may observe that the asymptotes intersect this circle in the same points as the directrices.
Two canals, the Oude and the Nieuwe Gracht, intersect the town from end to end.
These coils are placed with their axes at right angles to one another, and at the point where the axes intersect a small pivoted needle of soft iron is placed, carrying a longer index needle moving over a scale.
Slates properly so-called do not, except on rare occasions, split along the bedding, but along planes of cleavage, which intersect the bedding usually at high angles.
Deep gorges, through which tributaries of the Chorokh force their passage to the main river, intersect these highlands, forming most picturesque gorges.
The state constitution adopted in 1802 followed the enabling act in accepting this line, but made the proviso that if it should not intersect Lake Erie east of the mouth of the Miami river, then the northern boundary should be a line from the southern end of Lake Michigan to the most northern cape of Maumee Bay and thence to the Territorial line, and to the Pennsylvania line.
Electric tramways intersect the town, and are continued for 3 m.
At its northern edge, where the waterless forest tract of the Bhabar ends, a series of springs burst from the surface, and these, increasing and uniting in their progress, form the numerous streams that intersect the Tarai.
Two of the principal thoroughfares, Federal and Ohio streets, intersect at a central square, in which are the city hall, public library, post office and the marketplace; and surrounding the main business section on the E., N.
These equations show that the circles touch where they intersect the lines x 2 +y 2 = o, i.e.