In the case of two non-intersecting circles it may be shown that the radical axis has the same metrical relations to the line of centres.
Intersecting rainbows are sometimes observed.
The coastal plain varies in width and character: in some places low and sandy, or swampy, filled with lagoons and intersecting canals; in others more elevated, rolling and very fertile.
The outside of the church is plain, except the aisle walls and three eastern apses, which are decorated with intersecting pointed arches and other ornaments inlaid in marble.
A comparison of the relation of created beings to a number of intersecting circles is as old as the days of Nieremberg, who in 1635 wrote (Historia naturae, lib.
Draw a vertical at D, intersecting fh, kg, in s and q.
This obviously represents a conic intersecting the circle a(3y+bya ca(3=o in points on the common chords la+m(3+ny=o, as+b(3 +cy =o.
Two intersecting central streets also divide the city into four sections, in each of which the streets are methodically named and numbered, as North 3rd, 5th, 7th, &c., or West 2nd, 4th, 6th, &c., according to direction and location.
In general it rather resembles a closed crown, consisting of a circlet from which rise two arches intersecting each other at right angles.
Other notable examples of this style are the Palazzo Ariani at San Raffaelle, with its handsome window in a design of intersecting circles; the beautiful window with the symbols of the four Evangelists in the spandrils, in the facade of a house at San Stae; the row of three Giustinian palaces at S.
Meanwhile the Spanish governor-general, Manuel Macias y Casado, had ordered the forces under his command in the southern part of the island to fall back towards the ridge of mountains intersecting it from east to west, just north of the town of Coamo.
Parallels and meridians were represented by straight lines intersecting each other at right angles, the relative proportions between degrees of longitude and latitude being retained only along the parallel of Rhodes.
Marco Polo mentions such charts; Vasco da Gama (1498) found them in the hands of his Indian pilot, and their nature is fully explained in the Mohit or encyclopaedia of the sea compiled from ancient sources by the Turkish admiral Sidi Ali Ben Hosein in 1554.1 These charts are covered with a close network of lines intersecting each other at right angles.
(From Marchi.) and two on the other, connected by a passage intersecting the gallery at right angles.
The method of electrical images will enable the stream function, )' to be inferred from a distribution of doublets, finite in number when the surface is composed of two spheres intersecting at an angle 7r/m, where m is an integer (R.
Two equal spheres, intersecting at 120°, will require - I U j x _ a 3 a4(a 7 2 x) a3 a4(a+2x)] (II) 2 - _ 2 y a 271 3 271 +2Y2 3 2720 ' with a similar expression for cylinders; so that the plane x=o may be introduced as a boundary, cutting the surface at 60°.
According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was utilized by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.
Among the principal buildings are the ancient castle, formerly the residence of the counts of Hanau; the church of St John, dating from the 17th century, with a handsome tower; the old church of St Mary, containing the burial vault of the counts of Hanau; the church in the new town, built by the Walloons in the beginning of the 17th century in the form of two intersecting circles; the Roman Catholic church, the synagogue, the theatre, the barracks, the arsenal and the hospital.
A cissoid angle is the angle included between the concave sides of two intersecting curves; the convex sides include the sistroid angle.
Portion of the Russian railway system was further completed by the opening in 1906 of a line from St Petersburg via Vologda to Vyatka, intersecting the MoscowArchangel line at Vologda.
Intersecting the mountains are numerous ravines and passes.
With regular streets intersecting at right angles; the form is preserved, and in a picturesque open space in the centre stands the church of St Thomas a Becket.
It was obtained by punching the dots in intersecting lines, so arranged that the dots fell uniformly into diamond-shaped groups of five each.
(iii) Take any straight line intersecting or not intersecting the figure, and draw perpendiculars Aa, Bb, Cc, Dd,.
- The solid or surface generated by the revolution of a plane closed figure or a plane continuous line about a straight line in its plane, not intersecting it, is a solid of revolution or surface of revolution, the straight line being its axis.
The physical geography of New Zealand is closely connected with its geological structure, and is dominated by two intersecting lines of mountains and earth movements.
Circular nodal lines unaccompanied by intersecting lines cannot be produced in the manner described; but may be got either by drilling a small hole through the centre, and drawing a horse-hair along its edge to bring out the note, or by attaching a long thin elastic rod to the centre of the plate, at right angles to it, holding the rod by the.
Every point is equidistant from a fixed point within the surface; this point is the "centre," the constant distance the "radius," and any line through the centre and intersecting the sphere is a "diameter."
In the case of non-intersecting circles, it is seen that the minimum circles of the coaxal system are a pair of points I and I', where the orthogonal circle to the system intersects the line of centres; these points are named the " limiti,ng points."
Its western slopes, where it abuts on the mountain masses which dominate the Kabul plain, are forest-covered and picturesque, with deep glens intersecting them, and bold craggy ridges; the same may be said of the northern spurs which reach downward through the Shinwari country towards Gandamak and Jalalabad.
A solid angle is definable as the space contained by three or more planes intersecting in a common point; it is familiarly represented by a corner.
A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs on a sphere, and is measured by the angle between the planes containing the arcs and the centre of the sphere.
Towards its mouth its waters find their way into all the channels intersecting the South Holland archipelago.
Mecklenburg lies wholly within the great North-European plain, and its flat surface is interrupted only by one raiIge of low hills, intersecting the country from south-east to north-west, and forming the watershed between the Baltic Sea and the Elba.
At Inverell in New South Wales a diamond (1906) has been found embedded in a hornblende diabase which is described as a dyke intersecting the granite.
On the left bank of the Aude, between it and the Canal du Midi, lies the new town, clean, well-built and flourishing, with streets intersecting each other at right angles.
Alexandria and Antioch were both traversed from end to end by one long straight street, crossed by shorter ones at right angles; Nicaea was a square from the centre of which all the four gates could be seen at the ends of the intersecting thoroughfares (Strabo xii.
In the third-order complex the centre locus becomes a finite closed quartic surface, with three (one always real) intersecting nodal axes, every plane section of which is a trinodal quartic. The chief defect of the geometrical properties of these bi-quaternions is that the ordinary algebraic scalar finds no place among them, and in consequence Q:1 is meaningless.
Waycross is served by the Atlanta, Birmingham & Atlantic, and the Atlantic Coast Line railways, several branches of the latter intersecting here.
(ii) Two forces in intersecting lines may be replaced by a force which is their geometric sum, acting through the intersection.
Successive halfturns about intersecting axes a, b are equivalent to a rotation about the common perpendicular to a, b at their intersection, Of amount equal to twice the acute angle between them, in the direction from a to b.
If AB, AC represent infinitesimal rotations about intersecting axes, the consequent displacement of any point 0 in the plane BAC will be at right angles to this plane, and will be represented by twice the sum of the areas OAB, OAC, taken with proper signs.
We will briefly notice the case of two degrees, which involves an interesting generalization of the method (already explained) of compounding rotations about intersecting axes.
That for a pair of turning pieces with intersecting axes the line of contact is also straight, and traverses the~ point of intersection of the axes; and hence that the rolling surfaces are conical, with a common apex (the term conical including all surfaces generated by the motion of a straight line which traverses a fixed point).
Coupling of Intersecting AxesHookes Universal Joint.
The Improvement Commissioners constituted by this act included the mayor, bailiffs and four aldermen of Liverpool, under whose care the main streets were laid out on a regular plan, intersecting one another at right angles; and the first iron tramway in England was laid down.
North-east of Lake Titicaca there is a confused mass or knot (the Nudo de Apolobamba) of lofty intersecting ridges which include some of the highest peaks in South America.
Between these and the Cordillera Oriental is an apparently confused mass of broken, intersecting ranges, which on closer examination are found to conform more or less closely to the two outside ranges.
14) be two catenaries having the same directrix and intersecting in A and B.
From the south side of the Kiinigs-platz crossing the Tiergarten and intersecting the avenue from the Brandenburg Gate to Charlottenburg runs the broad Sieges-allee adorned by thirty-two groups of marble statuary representing famous rulers of the house of Hohenzollern, the gift of the emperor William II.
This twisting is in a great measure owing to the manner in which the bones of the wing are twisted upon themselves, and the spiral nature of their articular surfaces - the long axes of the joints always intersecting each other b FIG.
The maximum principal stresses are represented by the directions and thicknesses of the two systems of intersecting lines mutually at right angles.
Mount Vernon Place and Washington Place, intersecting near the centre of the city, Eutaw Place farther N.W., and Broadway running N.
Reverting to the purely plane theory, infinity is a line, related like any other right line to the curve, and thus intersecting it in m points, real or imaginary, distinct or coincident.
It is a leading point in the theory that a curve in space cannot in general be represented by means of two equations U= o, V = o; the two equations represent surfaces, intersecting in a curve; but there are curves which are not the complete intersection of any two surfaces; thus we have the cubic in space, or skew cubic, which is the residual intersection of two quadric surfaces which have a line in common; the equations U= o, V= o of the two quadric surfaces represent the cubic curve, not by itself, but together with the line.
The town fronts Sullivan's Cove, a picturesque bay opening into the estuary of the river Derwent, and is nearly square in form, laid out with wide streets intersecting at right angles, the chief of which are served by electric tramways.
Conceiving the line NN' to be that of the nodes at any time, and the earth and lunar orbit to be moving in the direction of the straight arrows, the earth will be on one side of the ecliptic from M2 to M5, and on the other side from M6 to M 1, intersecting it at the nodes.
In the troubled waters of conflicting and intersecting intrigues that eddied about the Emperor's headquarters, it was possible to succeed in many ways unthinkable at other times.
The town was laid out at great expense in straight, broad streets, intersecting each other at right angles, by the architect Hippodamus of Miletus in the time of Pericles.
Of the fortress built by William the Conqueror in 1068 some portions were probably incorporated in Clifford's tower, the shell of which, showing an unusual ground plan of four intersecting circles, rises from an artificial mound.
The resultant horizontal thrust in any direction is obtained by drawing parallel horizontal lines round the boundary, and intersecting a plane perpendicular to their direction in a plane curve; and then investigating the thrust on this plane area, which will be the same as on the curved surface.