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They expanded the range of geometry to many new kinds of figures, curves, surfaces, and solids ; they changed its methodology from trial-and-error to logical deduction ; they recognized that geometry studies " eternal forms ", or abstractions, of which physical objects are only approximations ; and they developed the idea of the " axiomatic method ", still in use today.
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They and expanded
They expanded under Spanish regency to encompass half of North America and half of South America.
They and other authors freely expanded or modified pre-existing models, constantly refining the moral content without interest or access to much more detail regarding the factual content.
They began as baptismal formulae and were later expanded during the Christological controversies of the 4th and 5th centuries to become statements of faith.
They have been measured in detail, and match what would be expected if small thermal variations, generated by quantum fluctuations of matter in a very tiny space, had expanded to the size of the observable universe we see today.
They also said agriculture should not be expanded, sustainable support capabilities should be incorporated into the area and pollution sources should be reduced.
They city also expanded with the incorporation of the city of Rockingham and the establishment of the Davenport Municipal Airport.
They established bases on the northern highlands of the Ethiopian Plateau and from there expanded southward.
They expanded the house from 14 to 21 rooms, and included a china closet.
They also demanded that the colour palette be expanded to 4096 colours, the same as that of the Amiga.
They expanded it to include additional language families.
They based their growth on maritime trade and expanded their colonial empire in Asia, the Americas and the South Africa.
They named Saint Kitts " Liamuiga " meaning " fertile island ", and would likely have expanded further north if not for the arrival of Europeans.
They started writing Qt in 1991, and since then Qt has steadily expanded and improved.
They predict that human beings may eventually be able to transform themselves into beings with such greatly expanded abilities as to merit the label " posthuman ".
They expanded the franchise beyond the Constitutional requirement to more nearly embrace “ the people ”.
They expanded its mission beyond education and exhibitions to include collecting.
They were expanded greatly, and began to be offered by a number of state and local governments during the early Progressive Era in the late nineteenth century.
They feature expanded cargo and passenger space however usually achieve lower mileage and cost more to manufacture.
They are notably absent from cities such as Calgary, Edmonton, and Winnipeg that lie on flat plains and have expanded outwardly on former agricultural land.
They expanded down the Orinoco River to Trinidad, and then spread rapidly up the islands of the Caribbean.
They expanded their influence to the eastern and southern coast from Bosa to Karalis, consolidating a large number of Phoenician colonies all over the western Mediterranean under one empire for the first time.
They were massively expanded during World War II, forming ten Airborne Corps plus numerous Independent Airborne Brigades, with most or all achieving Guards status.
They found that the Barrier Inlet had expanded to form a large bay, in which were hundreds of whales, which led to the immediate christening of the area as the Bay of Whales.
They had expanded the river in this area, to a width of over 150 meters.
They and range
They come in crisp basket weaves in natural honey hues, along with lacey open weaves with a lustre finish in natural, white, black and a whole range of colors.
They are written by specialists in numerous types of business enterprises, cover a wide range of subjects, and are directed to the needs and interests of the small firm.
They range from an eight-foot pram, which you can build yourself for less than $50, to auxiliary sailboats which can cost over $100,000.
They offer exceptional design freedom, making it possible to incorporate contours and details which give free range to the talents of the designer.
They usually range from 20 to 60 feet in height, but when they pour into a V-shaped inlet or harbor they may rise to mountainous proportions.
They range from the Soviet Embassy on Sixteenth Street, a gray shuttered pile suggesting a funeral-accessories display house, to what Congressman Rooney has called `` that monstrosity on Thirty-fourth Street '', the modern cement-and-glass chancery of the Belgians.
They fall within a range between approximately 7500 BC ( 9, 500 years ago ) and approximately 16, 000 BC ( 18, 000 years ago ).
They range in size from the Chinese giant salamander ( Andrias davidianus ), which can grow to a length of, to the diminutive Thorius pennatulus from Mexico which seldom exceeds.
They lived in a range of structures, including pit houses, cliff dwellings, and pueblos, designed so that they could lift entry ladders during enemy attacks, which provided security.
They were perhaps not named " Angles " at that time ; however, the territory of the Teutones probably included the Vorpommern and the region south to the Elbe ( mainly Holstein ), accounting for the implied larger range of the Angles in later sources.
They must be protected in a controlled environment where such variables are maintained within a range of damage-limiting levels.
They overlap in range with 3 other crane species but interactions with these species and other " large wader " type birds are not known.
They range from the one-day road race, criterium, and time trial to multi-stage events like the Tour de France and its sister events which make up cycling's Grand Tours.
They eat a wide range of material ; in addition to the normal prey of small rodents, reptiles, other amphibians, birds and a range of invertebrates, they also eat plants, dog food and household refuse.
They range along the Thames valley and beyond, as far as Surrey in the east and the mouth of the Severn in the west.
They postulated that extremely low frequency ( ELF ) propagation might be involved, since Faraday cage screening is less effective in the ELF range.
They cost less, they offered a vast range of new colors, and they imparted better properties to the dyed materials.
They also had the range and speed to travel effectively with a battle fleet.
They have relatively thin, fragile heads and a very different tone to a tom, but are used by some drummers to extend the tom range upwards.
They are easily produced on the euphonium as compared to other brass instruments, and the extent of the range depends on the make of the instrument in exactly the same way as just described.
They noted, however, that their data included a wide range of products, and the degree of competition in each market varied significantly, and offer that further research on this issue should be conducted to determine whether these findings remain the same when purchasing the same product for both small and high volumes.
They typically have strong, stubby beaks, which in some species can be quite large ; however, Hawaiian honeycreepers are famous for the wide range of bill shapes and sizes brought about by adaptive radiation.
They are primarily granivorous, but euphoniines include considerable amounts of arthropods and berries in their diet, and Hawaiian honeycreepers evolved to utilize a wide range of food sources, including nectar.
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