The difference in form and content suggests that the Polygonal Numbers was not part of the larger work.
This may be rectangular in shape (" straight " shed), containing a series of parallel tracks on which the engines stand and which are reached by means of points and crossings diverging from a main track outside; or it may take a polygonal or circular form (round house or rotunda), the lines for the engines radiating from a turn-table which occupies the centre and can be rotated so as to serve any of the radiating lines.
They contain, however, a fragment of a separate tract on Polygonal Numbers.
An air-tube consists of an epithelium of large polygonal cells with a thin basement-membrane externally and y a chitinous layer internally, the lastnamed being continuous with the outer cuticle.
The chitinous layer is usually strengthened by thread like thickenings which, in the region close to the outer opening of the tube, form a network enclosing polygonal areas, but which, through most of the tracheal system, are arranged spirally, the strengthening thread not forming a continuous spiral, but being interrupted after a few turns around the tube.
These webs, which are typically subcircular in form, consist of a system of threads radiating from a common centre and crossed at intervals, and approximately at right angles, by a series of concentric lines, the whole being suspended in a triangular, quadrangular or polygonal framework formed of so-called foundation lines, attached to the branches or leaves of trees or other firm objects in the neighbourhood.
Remains of primitive polygonal walls which undoubtedly surrounded the entire area have been found at various points a little within the circuit of the existing parapet.
In front of the reservoir is a small open space towards which several roads converge; close by is a triangular enclosure of polygonal masonry, in which were found various relics relating to the worship of Dionysus, a very ancient wine-press (Anvos) and the remains of a small temple.
Of later date, perhaps, are the limestone polygonal retaining walls on the west front, which extended on either side of the early entrance.
The arrangements of the stage and orchestra as we now see them belong to Roman times; the cavea or auditorium dates from the administration of the orator Lycurgus (337-323 B.C.), and nothing is left of the theatre in which the plays of Sophocles were acted save a few small remnants of polygonal masonry.
(From Bosio.) polygonal, opening out of the main corridors.
In 1901-1902 excavations in the cemetery of Santa Priscilla, near the Cappella Greca, revealed a polygonal chamber.
The walls, of carefully worked polygonal blocks of stone, are still preserved in parts, and the modern town does not fill the whole area which they enclose.
In later Roman times there were added a series of polygonal bastions, of the type found at Caerwent.
In some obsidians from Teneriffe and Lipari the whole rock consists of them, so closely packed together that they assume polygonal shapes like the cells of a honeycomb.
There are also remains of the town wall in the "polygonal" style, and above the town are several massive platforms for supporting buildings, in a more archaistic form of this style; these may well belong to the Roman period, and the latter even to the empire.
The original, which consisted of a preface and thirteen books, is not lost, but we have a Latin translation of the first six books and a fragment of another on polygonal numbers by Xylander of Augsburg (1575), and Latin and Greek translations by Gaspar Bachet de Merizac (1621-1670).
A curious polygonal church of the i ith century at Rieux-Minervois, the abbey-church at St Papoul, with its graceful cloister of the 14th century, and the remains of the important abbey of St Hilaire, founded in the 6th century and rebuilt from the 12th to the 15th century, are also of antiquarian interest.
The thurible, the proper ecclesiastical term for the vessel in the Western Church, is usually spherical in form, though often square or polygonal, containing a small receptacle for the charcoal and covered by a perforated lid; it is carried and swung by three chains, a fourth being attached to the lid, thus allowing it to be raised at intervals for the volume of smoke to be increased.
The polygonal terrace wall at the back, on being cleared, proves to be covered with inscriptions, most of them concerning the manumission of slaves.
The ancient polygonal walls, which are still finely preserved, are among the best in Italy.
The only ancient remains on the mountain are those of a small building in good polygonal work (a style of construction very rare in Sicily), consisting of a passage on each side of which a chamber opens.
The cathedral has a fine polygonal apse of the r 6th century.
In the north of France and Belgium wooden tubbings, built of polygonal rings, were at one time in general use.
It is economical to have one horizontal boom and one polygonal (approximately parabolic) boom.
Above sea-level, and still retains considerable remains of the city wall, built in polygonal masonry of carefully jointed blocks of limestone, some 12 ft.
They are preserved to a considerable height on all sides, except where the ravine is precipitous and they have been carried away by a landslip; they are for the most part built of irregular blocks of great size in the so-called " Cyclopian " style; but certain portions, notably that near the chief gate, are built in almost regular courses of squared stones; there are also some later repairs in polygonal masonry.
These screes are however very flat and their lower edges generally reach all the way down to the central part of the basin, which is occupied by an expanse of yellow clay, perfectly flat and fairly hard, as well as dry and barren, often cracked into polygonal cakes and drawn out in the direction of the long axis of the valley....
It is rectangular in plan, and portions of its walls, partly in fine polygonal work and partly in opus incertum, are preserved.
He has applied the theory with especial ingenuity to the interpretation of the circular bony plates in the carapace of the aberrant leather-back sea-turtles (Sphargidae) by prefacing an initial land phase, in which the typical armature of land tortoises was acquired, a first marine or pelagic phase, in which this armature was lost, a third littoral or seashore phase, in which a new polygonal armature was acquired, and a fourth resumed or secondary marine phase, in which this polygonal armature began to degenerate.
From these intralobular capillaries run toward the centre of the lobule, forming a network among the polygonal hepatic cells.
Within these, and forming by far the largest part of the seed, are large polygonal cells filled with very numerous and very minute angular starch grains.
The east end was usually square, but the Friars Church at Winchelsea had a polygonal apse.
The polygonal walls of the acropolis may still be seen in a fair state of preservation on a circular hill standing about 500 ft.
Remains of Cyclopean and polygonal walls exist at Kaligoni (south of Amaxikhi), probably the site of the ancient acropolis of Neritus (or Nericus), and of the later and lower Corinthian settlement of Leucas.
Considerable portions of the southern wall of the ancient citadel, built in very massive Cyclopean masonry of blocks of limestone, are still to be seen; and the two walls, also polygonal, which formerly united the citadel with the town, can still be traced.
(It is to be remembered, however, that the standard width of a Roman highroad in the neighbourhood of Rome itself is about 14 ft.) They are uniformly paved with large polygonal blocks of hard basaltic lava, fitted very closely together, though now in many cases marked with deep ruts from the passage of vehicles in ancient times.
Some scanty remains of its ancient polygonal walls may still be seen.
On the hill above are still to be seen the massive remains of the citadel, built partly in polygonal style.
It is chiefly remarkable for its finely preserved fortifications constructed of tetrahedral and polygonal blocks of local limestone well jointed, with maximum dimensions of about 3 by i z ft.; the outer circuit of the city wall measures about 22 m.
In the first two periods the construction is rough, while in the third the blocks are very well and finely jointed, and the faces smoothed; they are mostly polygonal in form and are much larger (the maximum about io by 6 ft.) than those of the city wall.
The shapes of all polygonal and all cylindrical and conical forms are obtained by simple development - that is, the envelopments of these bodies are marked out on a flat plane, and when cut, are bent or folded to give the required envelopes.
On the uppermost terrace, defined by the great Cyclopean supporting wall, exactly as described by Pausanias, the excavations revealed a layer of ashes and charred wood, below which were found numerous objects of earliest date, together with some remains of the walls resting on a polygonal platform - all forming part of the earliest temple.
The external walls, which have a circuit of about 2 m., are constructed of polygonal masonry; the blocks are carefully jointed, and the faces smoothed.
A triple line of defences of later date (possibly added by the Roman colonists), inasmuch as both the city wall proper and the double wall thrown out in front of it are partly constructed of concrete, and faced with finer polygonal masonry (in which horizontal joints seem to be purposely avoided).
Of ancient remains hardly anything is left - some traces of an amphitheatre and fragments of polygonal walls only.
The outermost layer of endosperm, the aleuron-layer, consists of regular cells filled with small proteid granules; the rest is made up of large polygonal cells containing numerous starch-grains in a matrix of proteid which may be continuous (horny endosperm) or granular (mealy endosperm).
Within the city are four similar canals (grachten) with their ends resting on the Y, extending in the form of polygonal crescents nearly parallel to each other and to the outer canal.
It is in the nature of the secondary xylem that the Coniferales are most readily distinguished from the Dicotyledons and Cycadaceae; the wood is homogeneous in structure, consisting almost entirely of tracheids with circular or polygonal bordered pits on the radial walls, more particularly in the late summer wood.
In the Araucarian type of wood (Araucaria and Agathis) the bordered pits, which occur in two or three rows on the radial walls of the tracheids, are in mutual contact and polygonal in shape, the pits of the different rows are alternate and not on the same level; in this type of wood the annual rings are often much less distinct than in Cupressus, Pinus and other genera.
Traditional still, but supported by greater probability, a story states that Sebert, eastern cloister walk), and choir of polygonal apsidal form, with six chapels (four polygonal) opening north and south of it, and an eastern Lady Chapel, known as Henry VII.'s chapel.
Larger star-shaped cavities, called calices, in which the zooids are lodged, and very numerous smaller round or polygonal apertures, which in life contain as many short unbranched A FIG.
Polygonal of a of or onal bates, 7.
But these were exceptional, the usual material of an altar was marble, and its form, both among the Greeks and Romans, was either square or round; polygonal altars, of which examples still exist, being exceptions.
The polygonal terrace walls, which exist in considerable numbers in the district, are shortly described in Romische Mitteilungen (1903), 147 seq., but require further study.
Remains of the city walls, in the polygonal style, still exist, to which Roman gates were added.
There are considerable remains of perhaps pre-Roman polygonal walls - in one place a piece of this walling has masonry of rectangular blocks superposed, with an inscription of two of the Roman municipal magistrates (quattuorviri).
The rock above the town was included within the polygonal walls: but Totila fortified, not this rock, but the amphitheatre, which remained the citadel until 1364, when Cardinal Albornoz destroyed it and erected the present Rocca, which was enlarged by Pope Nicholas V.; it is now a prison.