Pentagon

“ When is a polygon said to be inscribed in a circle ? 15.
When a tangent is drawn from a given point, how many points of a circle can it touch ?
16.
What is the proportion between the radius of a Circle and one side of a hexagon inscribed in it ?
17.
What is meant by unequal circles ? (p. 20.)
18.
What is meant by a regular Polygon ? (p. 21.)
19.
What is a regular hexagon ?
20.
What is a regular pentagon ?
21.
What is a regular octagon?
22.
How will you circumscribe a triangle with a circle ?
23.
How will you find the Centre of a circle to be in- scribed in a triangle ? ”

“ Furious at his perversity, and especially indignant that he professed to be ignorant of my sex, I retorted in no measured terms, "Besotted Being! You think yourself the perfection of existence, while you are in reality the most imperfect and imbecile. You profess to see, whereas you can see nothing but a Point! You plume yourself on inferring the existence of a Straight Line; but I CAN SEE Straight Lines, and infer the existence of Angles, Triangles, Squares, Pentagons, Hexagons, and even Circles. ”

“ Over those assembled giant cities we raced, the great mass of them below us almost hiding the ground beneath. As we shot above them, I saw now that they had been ranged in a tremendous circle, the great capital of New York hanging in the center. Across the great ring of the air-cities we rushed; were racing at last above New York, toward its own giant power-tower. Then we had reached it, and were sinking vertically downward, until our hundred cruisers came to rest upon the central plaza. ”

“ I’ve been seeing a dream picture in the sky; it’s the dream city all our artists have been painting ever since the Wrights flew their first plane off Kill Devil Hill. In this pictured city-to-be, airplane terminals are built right upon the roofs of high down-town buildings; every little home has its private landing field upon its own rooftop; big planes, little planes swoop straight up without ever a wasted acre of runway. Until this minute, we have never been an inch nearer that marvelous goal than we were twenty-seven years ago. Suddenly you open up a new world in aviation. ”

“ A few seconds later the two great propellers (or rather tractors) began to [3] flash around. With a snap and a roar the battle-plane started slowly forward, gained in speed till we were running along the big field like a racing automobile, then suddenly the people standing around dropped away from us as if on a gigantic express elevator leaving one standing on the upper floor of a skyscraper, and in a moment more the earth had become a strange and placid panorama with which we had no connection or concern. ”

“ Now they saw through their field glasses that the great plane was lumbering slowly across the field, gaining momentum as it headed westward into the breeze. Then it seemed to be barely clearing the great skyscrapers that towered twenty-four hundred feet into the air, arching over four or five city blocks. From this height they were toys made of colored paper, soft colors glistening in the hot noon sunlight, and around and about them wove lines of flashing, moving helicopters, the individual lost in the mass of the million or so swiftly moving machines. ”

“ Night lay over the world now, and from our window we saw the cities illumined by their lights stretching out to the horizon. On the landing plazas of the air-city beneath us rested the great European Federation battle-fleet. In the plaza directly beneath us, that which surrounded the base of our great electrostatic tower, there rested but a few score of cruisers, those of the commanders who were now at the headquarters inside the great tower's base. ”

“ The fleet that we must meet has twice the number of cruisers of our own, and there have been rumors of some new method being prepared by them with which to attack us, now or later. We have to aid us only the air-forts about this city, which have been equipped with a new device. I have ordered them to move east of the city to lie between it and the enemy. This great air-city itself, when we go out from it, will move inland at its highest speed away from the battle, just as Boston and Charleston and Miami and San Francisco and Los Angeles and all our great air-cities, north and south. ”

“ And as the cables are slipped from the mooring tower, the light gangway is drawn back, the crowd down below cheer, and the giant airship backs out, carried by the force of the wind alone till she is well clear of the station. Then her engines open up gradually. She turns until her nose points almost due west, then slips away on her four thousand miles' journey over many a classic land, desert, forest and sea towards the centre of the world's greatest empire. ”

“ Turning in a great, slow arc, the plane descended until it was skimming only a few feet above the waters of a broad bay. Peggy wondered if they had flown in on a seaplane, and if they were to land in the water and have to take a boat to shore, but even as the thought occurred to her, the rocky shoreline suddenly appeared beneath her, and the plane swiftly settled down on the long, concrete runway of New York’s LaGuardia Airport. ”

“ The TIDE PROJECTILE TRANSPORTATION Co.
By Will H. Gray
Author of "The Star of Dead Love"
Even in this age of wonders, people still turned aside, or came out of their houses to witness the start of Number Two, just as two hundred years before, people had looked up whenever an airplane buzzed overhead. . . . With a tremendous jar and shriek of parted air, the huge projectile was hurled nearly on the vertical into the blue sky. . .
HOW would you like to fly from San Francisco to New York in about 17 minutes? Impossible! ”

“ The air was filled with planes, droves of them, flying in formation, casting their shadows over the Marine Aviation Base at Pensacola, Florida, like a great body of locusts.
Suddenly, a lone pursuit plane flew over the field like a majestic eagle.
The pilot pushed the stick forward and the plane slowly glided down toward earth, an almost human thing, beautiful to gaze upon, graceful as a large bird and perfectly handled at the controls by an expert airman. ”

“ The great mammoth now rode easily with the wind, moored by three stout cables to the great tower which rose above the roof gardens of the air-station. An electric lift conveyed the passengers and mails to the summit of this lofty tower, from whence a covered-in gangway led to the long corridors which lined the interior of the rigid airship.
"Have all the engines been tested?" the captain asks of the chief engineer, as he comes aboard with his navigating officer. ”

“ The gallant white towers had fallen now, and shorn of all but a little reefed square of topsail, two tiny mutton-legs of storm-jib and spanker, the Provincetown bowled along through the murk, holding well to her course, when the real gale struck her. ”

“ It must have been an impressive sight for friend or foe to witness the departure of each aerial vessel on its venturesome mission. The bold plunge into space above the roofs of the imprisoned city; the rapid climb into the sky and, later, the pearl drop high in air floating away to its uncertain and hazardous haven, running the gauntlet of the enemy's fire by day or braving what at first appeared to be equal danger, attending the darkness of night. ”

“ In truth, a man-of-war is a city afloat, with long avenues set out with guns instead of trees, and numerous shady lanes, courts, and by-ways. The quarter-deck is a grand square, park, or parade ground, with a great Pittsfield elm, in the shape of the main-mast, at one end, and fronted at the other by the palace of the Commodore's cabin. ”

“ And now my own flagship and the designated few agreed on were dipping swiftly toward the great tower-platform, where stood the ray-projector which we had fought our way from universe to universe to reach. We were dropping lower, gradually decreasing our speed as we neared the platform, lower, lower....
A cry of fierce rage rang through the hull beneath me, and at the same moment I was aware of a long, dark shape that suddenly flashed down past us from above, a last cruiser of the globe-men which must have hovered high above us until that moment. ”

“ Here high over the city, though, the shells of all the heat-guns that now were booming toward us could not reach us, and through battling ships and whirling beams and gloom of night we rushed westward over the giant air-city until in a moment more we were pausing over the western arsenals, and the western plaza where rested other massed cruisers of the great European battle-fleet. ”

“ As we drew nearer, the aerial structures which we had first seen began to tower up to an amazing height, just perceptibly swaying and undulating with the gentle currents of air that flowed through their traceried lattices, while behind them began to loom an immense number of floating towers, rising stage above stage, like the steel monsters of New York before they have received their outer coverings, but incomparably lighter in appearance, and more delicate and graceful ”

“ So I hurried down with the Aviation Captain to his tent to put on a warm aviation suit, while the Caudron was prepared for our flight. [83] As we approached his tent, a single-motored aeroplane took aboard its pilot and observer, its propellers whirred and roared, and it rolled casually away up the gradual slope, through a field of standing grain, till near the hilltop it took to the air as easily as a bird and spiralled up toward the low-lying dark clouds. ”

“ Beneath us we could make out in swift flashes of vision masses of the air-traffic between those cities, great passenger-liners and bulky freight-carriers and slender private craft, but in our own military-craft level there moved only a few cruisers like our own racing eastward toward New York in answer to the alarm. ”

“ On a raised platform, amidst his fireworks, stood Pettingill.
He felt that the great hour of his life had come, and, in a firm, clear voice, he said:
"The fust fireworks, feller-citizens, will be a rocket, which will go up in the air, bust, and assume the shape of a serpint."
He applied a match to the rocket, but instead of going up in the air, it flew wildly down into the grass, running some distance with a hissing kind of sound, and causing the masses to jump round in a very insane manner. ”

“ To rush forth to battle, to the annihilation of our own cities, in their great air-cities! To send those gigantic cities of the air, Berlin and Peking and Tokio and all the scores of others of the two great Federations, thundering through the air to battle, each with its masses of towers on it. They have made provision for all people who are not entirely engaged in battle, to descend to the earth and remain there in specially constructed buildings. ”

“ So Jack and all the others of the fleet went sightseeing. They went to Petropolis, the summer capital, with its temperate climate, in the tropics, and only twenty-two miles away, up back of the Organ Mountains. You climb the heights on a cog railroad, just as you climb Pike's Peak, and you see the magnificent views of valleys, the bay, the ravines and gulches that would do credit to the Rocky Mountains. ”

“ The long chain and the ropes had been taken off, but the handcuffs remained. I did not like to go down that ladder into the gloom below, but there was no alternative. The darkness hid every object from view, but I clambered down step by step to a depth of fully thirteen [173] feet,—for the place, as I afterwards learned when I had more leisure for observation, was of cubic form, just thirteen feet in length, breadth, and height. I stepped off the ladder, treading on human beings I could not discern, and crowded in as best I could. ”

“ Two hours of sleep, a stack of pancakes, three cups of black coffee, and he was ready to lead his fighters out over the island that lay like a dark, gray shadow rising out of the sea in the first flush of dawn.
One by one the planes left the carrier. Fighters, scout planes, dive bombers, torpedo planes—all thundered away toward their target.
Leading them all, Kentucky felt important and very happy.
“Hot diggity!” he exclaimed to the morning air. “This is what I call life! And here’s where we pay the Japs a little on account for Pearl Harbor.” ”

“ And passing constantly along these routes will be a volume of air-borne traffic—neat, privately owned planes; large and speedy passenger machines; multi-winged craft for the transport of goods; and here and there, flying swiftly and high, some slim-built war machine. Upon the land in the day-time, to indicate the direction of the airways, will be signs which may be read from high aloft; while at night, from signal towers, will flash forth lights, differing in the frequency and the colour of the beams they throw skyward, to guide the airman on his path. ”

“ Advantage of Pontoon-Ship as Aeroplane Base. The pontoon-ship as an aeroplane base possesses certain and obvious disadvantages; an area for alighting such as is presented by the deck of a ship, although it may be, say, 90 ft. beam by 400 ft. or more in length, is none too large under really bad conditions of weather for even a skilled pilot, especially if the vessel be rolling in a heavy seaway. ”

“ Now the plane climbed steadily in a long bank; up, up, up she went, and gradually the terrific roar of the engine died to a low throbbing hum as the low pressure of the air silenced the noise.
Below them the giant city contracted as the great ship [Pg. 25] rode higher. The tiny private helicops were darting about below them like streams of nigh invisible individuals, creeping black lines among the buildings of the city. The towering buildings shone in the noon sun in riotous hues as the colored tile facing reflected the brilliant sunlight with glowing warmth of color. ”