(ii) Rectangle: sides a and b.
6) the inhabited earth has the shape of an oblong rectangle surrounded by an ocean which breaks in in four great gulfs - the Roman or Mediterranean, the Arabian, Persian and Caspian Sea.
Thus the C.P. of a rectangle or parallelogram with a side in the surface is at a of the depth of the lower side; of a triangle with a vertex in the surface and base horizontal is 4 of the depth of the base; but if the base is in the surface, the C.P. is at half the depth of the vertex; as on the faces of a tetrahedron, with one edge in the surface.
Among the more interesting buildings are the Schloss, a long, rectangle begun in 1255 and added to later, with a Gothic tower 277 ft.
De Sectione Determinata resolved the problem: Given two, three or four points on a straight line, to find another point on it such that its distances from the given points satisfy the condition that the square on one or the rectangle contained by two has to the square on the remaining one or the rectangle contained by the remaining two, or to the rectangle contained by the remaining one and another given straight line, a given ratio.
The state is in the form of a rectangle, except in the north-west where a triangular projection, extending to 42° 15' N.
Enfidaville is the chief settlement on the Enfida estate, a property of over 300,000 acres in the Sahel district of Tunisia, forming a rectangle between the towns of Hammamet, Susa, Kairawan and Zaghwan.
It is nearly a rectangle in shape, with a length, from N.
It is built in the form of a rectangle and surrounded by walls of 1518.
The area of a rectangle, for instance, is found by calculation from the lengths of the sides, not by construction of a square of equal area.
To say, for instance, that the area of a right-angled triangle is half the area of the rectangle contained by the two sides, is not to say what the area is, but what it is the half of.
The centroid of a rectangle is its centre, i.e.
AB, and OP is the distance of the middle point of either side of the rectangle from the axis.
De Spatii Sectione discussed the similar problem which requires the rectangle contained by the two intercepts to be equal to a given rectangle.
The columns were united into a narrow rectangle by the advanced and rear guards.
In the eastern part of the city he built for himself a large palace, which probably occupied about a sixth of the space now enclosed within the city walls, or nearly the whole of the rectangle enclosed by Strada di Porta Alberoni on the south, Strada Nuova di Porta Serrata on the west and the line of the city walls on the north and east.
For example, a pair of equal opposite vortices, moving on a line parallel to a plane boundary, will have a corresponding pair of images, forming a rectangle of vortices, and the path of a vortex will be the Cotes' spiral r sin 20 = 2a, or x-2+y-2=a-2; (io) this is therefore the path of a single vortex in a right-angled corner; and generally.
Croce outside the Roman town, which formed a rectangle of about 400 by 600 yds., with four gates, the Decumanus being represented by the Via Strozzi and Via del Corso, and the Cardo by the Via Calcinara, while the Mercato Vecchio occupied the site of the Forum.
That the surface may coincide with the edge of the orifice, which is a rectangle, whose sides are a and b, we must have pa=m7r, qb=nir, when m and n are integral numbers.
She was like a walking rectangle with a bird face, and she got outright hostile towards the beautiful women she escorted out of his home every morning.
The new city formed a rectangle, enclosed by a colossal mud rampart, the longer sides of which ran north and south.
The buildings themselves, with the usual halls, bath-rooms and magazines, together with a shrine of the Mother Goddess, occupy two sides of a rectangle, enclosing a court at a higher level approached by flights of stairs.
Within the rectangle formed by pairs of consecutive dark lines, and not far from its centre, the brightness rises to a maximum; but these subsequent maxima are in all cases much inferior to the brightness at the centre of the entire pattern (=o, n =o).
Example 3.-Analysing in this way the rotation of a rectangle filled with liquid into the two components of shear, the stream function 1//1 is to be made to satisfy the conditions v 2 /1 =0, 111+IRx 2 = IRa 2, or /11 =o when x= = a, +b1+IRx 2 = I Ra2, y ' 1 = IR(a 2 -x 2), when y = b Expanded in a Fourier series, 2 232 2 cos(2n+ I)Z?rx/a a -x 7r3 a Lim (2n+I) 3 ' (1) so that '?"
Of temperature (o' - o") is small, the figure ABCD may be regarded as a parallelogram, and its area W as equal to the rectangle BE XEC. This is accurately true in the limit when (0' - 0") is infinitesimal, but in practice it is necessary to measure specific heats, &c., over finite ranges of temperature, and the error involved is generally negligible if the range does not exceed a few degrees.
R is represented by the rectangle MDdO, bounded by the isopiestic and the isometric through D.
The second rectangle contains a small hypostyle hall with six columns, and the sanctuary, with their subsidiary chambers.
The statement that, if the adjacent sides of a rectangle are represented numerically by 3 and 4, the diagonal is represented by 5, is as much a matter of mensuration as the statement that the area is represented by 12.
That the area of a parallelogram is equal to the area of a rectangle on the same base and between the same parallels, or that the volume of a cone is one-third that of a cylinder on the same base and of the same height, may be established by a proof which is admitted to be rigorous, or be accepted in good faith without proof, and yet fail to be a matter of conviction, even though there may be a clear conception of the relative lengths of the diagonal and the side of a square or of the relative contents of two vessels of different shapes.
The measure of the area of a rectangle is thus presented as the product of the measures of the sides, and arithmetic and mensuration are developed concurrently.
This is the process adopted, for instance, for comparison of the area of a parallelogram with that of a rectangle on the same base and of the same height.
The rectangle, for instance, has so far been regarded as a plane figure bounded by one pair of parallel straight lines and another pair at right angles to them, so that the conception of " rectangularity " has had reference to boundary rather than to content; analytically, the rectangle must be regarded as the figure generated by an ordinate of constant length moving parallel to itself with one extremity on a straight line perpendicular to it.
In E'; the case of a parallelogram, the equivalent right,, trapezium is a rectangle; in the case of a triangle, Al it is a right-angled triangle.
The corresponding element of the revolving figure is approximately a rectangle of area h.
3 by the height AH, such that the rectangle Ahkb is equal to the area Apdb; and the M.E.P. multiplied by 41rd 2, the cross-section of the bore in square inches, gives in tons the mean effective thrust of the powder on the base of the shot; and multiplied again by 1, the length in inches of the travel AB of the shot up the bore, gives the work realized in inch-tons; which work is thus equal to the M.E.P. multiplied by 41+-d 2 l = B -C, the volume in cubic inches of the rifled part AB of the bore, the difference between B the total volume of the bore and C the volume of the powder-chamber.
Will be equal to 4AB CD; by the same process find a point C2 such that the rectangle B 1 C 2 will be equal to 1B C I; and so on ad infinitum.
A striking point about the inner town is that it forms a large rectangle, enclosed by four wide boulevards or "walls."
The ancient town walls, enclosing a rectangle 793 by 62 4 yds., are still preserved almost in their entire extent.
When it is taken out the B rectangle Aacc if filled up by a liquid film.
The grave of Confucius is in a large rectangle separated from the rest of the Kung cemetery, outside the city of K`iuh-fow.
Of the dam, and g its centre of gravity, the centre of pressure upon the base will be vertically under g, that is, at the centre of the base, and the load will be properly represented by the rectangle bfgc, of which the area represents the total load and the uniform depth of its uniform intensity.
The square on the semi-major axis equals the rectangle contained by the distances of the focus and directrix from the centre; and 2a = SP+S'P, where P is any point on the curve, i.e.
Then the square of the ordinate intercepted between the diameter and the curve is equal to the rectangle contained by the portion of the diameter between the first vertex and the foot of the ordinate, and the segment of the ordinate intercepted between the diameter and the line joining the extremity of the latus rectum to the second vertex.
Their barracks at Rome covering a rectangle of 39 acres (1210 by 1410 ft.), were included by Aurelian in the walls of Rome, and three sides of the enceinte can still be seen near the Porta Pia, with brickwork as old as Tiberius: the interior (now barracks for the Italian army) is archaeologically less interesting.
If, in the rectangle Aacc, Aa= a, and AC = b, its area is S = ab, and its energy Tab.
The Roman town formed a rectangle 2 526 ft.
It forms a rectangle, the south front being 830 ft.