08.03.2016

# How to find factors of a number on ti83 plus,phone number eharmony canada 2014,cell phone name @ nonono 0 - Downloads 2016

All numbers have a factor of 1 and the number itself, so you know two factors straight away. It is a good idea to work through all the numbers from 1 to 20 and identify all of the factors.
The multiples of a number are the results of multiplying the number by other numbers or put another way, all the numbers that it will divide into. Students will learn that division can be thought of in two ways, partitioning and measurement.
When you divide to find the number of groups, the division is called measuring or repeated subtraction.
Since division is the inverse, or opposite, of multiplication, you can use arrays to help students understand how multiplication and division are related.
There are other models your students can use to explore the relationship between multiplication and division. Another strategy your students may find helpful is using a related multiplication fact to divide.
When students understand the concept of division, they can proceed to explore the rules for dividing with 0 and 1.
Encourage students to think about the relationship between multiplication and division when they solve problems.
Prime Number: Prime number is a number which is greater than 1 and which can be efficiently divided by 1 and by itself not by any other number.
In number system, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. Prime factorization "is a method of finding the prime factors which is required to find the original number ".
Below are the steps that explains how to do prime factorization-Step 1:Identify the given number is prime number or not.
In the Spring semester, I will be on leave as Visiting Professor at the Toulouse School of Economics (TSE), in Toulouse, France. I also serve as faculty in the Program in Economic Policy Management (PEPM) at Columbia University's School of International and Public Affairs (SIPA). In the Spring semester (2012-2013), I will be on leave as Fulbright Senior Scholar visiting the Foreign Trade University in Hanoi, Vietnam.
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Compensates for hand movement when shooting video at the telephoto end of the zoom range, where camera shake is magnified. Some of these monographs may be thought of as an anthology of maps, which, like all anthologies, reflects the taste and predilection of the collector.
Cartography, like architecture, has attributes of both a scientific and an artistic pursuit, a dichotomy that is certainly not satisfactorily reconciled in all presentations.
The significance of maps - and much of their meaning in the past - derives from the fact that people make them to tell other people about the places or space they have experienced. It is assumed that cartography, like art, pre-dates writing; like pictures, map symbols are apt to be more universally understood than verbal or written ones. As previously mentioned, many early maps, especially those prior to the advent of mass production printing techniques, are known only through descriptions or references in the literature (having either perished or disappeared). It must be said at the outset that we have little contemporary evidence for Greco-Roman maps. Methods for accurately reproducing and eventually printing maps in sufficient quantities to enable cartographical knowledge to a€?penetrate very deepa€™ are in fact a feature only of modern times. It is nonetheless the case that many modern school atlases could not (and cannot) resist the temptation to reconstruct ancient maps by combining modern knowledge about the shape of the earth's landmass with data from ancient texts.
Many libraries and collections were not in the habit of preserving maps that they considered a€?obsoletea€? and simply discarded them.
A series of maps of one region, arranged in chronological order, can show vividly how it was discovered, explored by travelers and described in detail; this may be seen in facsimile atlases like those of America (K.
As mediators between an inner mental world and an outer physical world, maps are fundamental tools helping the human mind make sense of its universe at various scales. The history of cartography represents more than a technical and practical history of the artifacts. The only evidence we have for the mapmaking inclinations and talents of the inhabitants of Europe and adjacent parts of the Middle East and North Africa during the prehistoric period is the markings and designs on relatively indestructible materials. Although some questions will always remain unanswered, there can be no doubt that prehistoric rock and mobiliary art as a whole constitutes a major testimony of early mana€™s expression of himself and his world view.
Despite the richness of civilization in ancient Babylonia and the recovery of whole archives and libraries, a mere handful of Babylonian maps have so far been found. Although cuneiform maps may not be forerunners from which later Western maps originate, they share characteristics with other cartographic traditions in their graphic imaging of territorial, social, and cosmological space.
Where once such maps would not have been admitted within a general history of cartography, a new view of the meaning of the map can embrace them. By no means do all ancient Near Eastern maps display metrological finesse or even the use of measurement, though some characteristically do, such as the agrarian field and urban plot cadastral surveys. The maps of cities with their waterways and surrounding physical landscape combine cartography of sacred space, seen in the temple plans, with that of economic space, seen in the field surveys.
The Babylonian world map is an attempt to encompass the totality of the eartha€™s surface iconographically: land, ocean, mountain, swamp, and distant uncharted a€?regionsa€? This said, it represents more of an understanding of what the world is from the viewpoint of historical imagination than an image of its topography against a measured framework. The diversity of cultures that have sought to preserve their maps, putting them on clay, papyrus, parchment, and other writing media, points to a near universality of making maps in human culture. Egypt, which exercised so strong an influence on the ancient civilizations of southeast Europe and the Near East, has left us no more numerous cartographic documents than her neighbor Babylonia.
In so far as cartography was concerned, perhaps the greatest extant Egyptian achievement is represented by the Turin Papyrus, collected by Bernardino Drovetti before 1824 (see monograph #102) . In so far as cartography was concerned, perhaps the greatest extent that Egyptian achievement is represented is by the Turin Papyrus, collected by Bernardino Drovetti before 1824 (#102). It has often been remarked that the Greek contribution to cartography lay in the speculative and theoretical realms rather than in the practical realm, and nowhere is this truer than in the Archaic and Classical Period. To the Arab countries belongs chief credit for keeping alive an interest in astronomical studies during the so-called Christian middle ages, and we find them interested in globe construction, that is, in celestial globe construction; so far as we have knowledge, it seems doubtful that they undertook the construction of terrestrial globes.
Among the Christian peoples of Europe in this same period there was not wanting an interest in both geography and astronomy. Above the convex surface of the earth (ki-a) spread the sky (ana), itself divided into two regions - the highest heaven or firmament, which, with the fixed stars immovably attached to it, revolved, as round an axis or pivot, around an immensely high mountain, which joined it to the earth as a pillar, and was situated somewhere in the far North-East, some say North, and the lower heaven, where the planets - a sort of resplendent animals, seven in number, of beneficent nature - wandered forever on their appointed path. Now, it is remarkable that the Greeks, adopting the earlier Chaldean ideas concerning the sphericity of the earth, believed also in the circumfluent ocean; but they appear to have removed its position from latitudes encircling the Arctic regions to a latitude in close proximity to the equator.
Notwithstanding this encroachment of the external ocean - encroachment which may have obliterated indications of a certain northern portion of Australia, and which certainly filled those regions with the great earth - surrounding river Okeanos - the traditions relating to the existence of an island, of immense extent, beyond the known world, were kept up, for they pervade the writings of many of the authors of antiquity.
In a fragment of the works of Theopompus, preserved by Aelian, is the account of a conversation between Silenus and Midas, King of Phrygia, in which the former says that Europe, Asia, and Africa were lands surrounded by the sea; but that beyond this known world was another island, of immense extent, of which he gives a description. Theopompus declareth that Midas, the Phrygian, and Selenus were knit in familiaritie and acquaintance. The side of the boat curves inwards, so that when reversed the figure of it would be like an orange with a slice taken off the top, and then set on its flat side. Comparing these early notions, as to the shape and extent of the habitable world, with the later ideas which limited the habitable portion of the globe to the equatorial regions, we may surmise how it came to pass that islands--to say nothing of continents which could not be represented for want of space - belonging to the southern hemisphere were set down as belonging to the northern hemisphere. We have no positive proof of this having been done at a very early period, as the earlier globes and maps have all disappeared; but we may safely conjecture as much, judging from copies that have been handed down.
Early maps of the world, as distinguished from globes, take us back to a somewhat more remote period; they all bear most of the disproportions of the Ptolemaic geography, for none belonging to the pre-Ptolemaic period are known to exist.
We have seen that, according to the earliest geographical notions, the habitable world was represented as having the shape of an inverted round boat, with a broad river or ocean flowing all round its rim, beyond which opened out the Abyss or bottomless pit, which was beneath the habitable crust. The description is sufficiently clear, and there is no mistaking its general sense, the only point that needs elucidation being that which refers to the position of the earth or globe as viewed by the spectator.
Our modern notions and our way of looking at a terrestrial globe or map with the north at the top, would lead us to conclude that the abyss or bottomless pit of the inverted Chaldean boat, the Hades and Tartaros of the Greek conception, should be situated to the south, somewhere in the Antarctic regions. The internal evidence of the Poems points to a northern as well as a southern location for the entrance to the infernal regions.
Another probable source of information: The Phoinikes of Homer are the same Phoenicians who as pilots of King Solomona€™s fleets brought gold and silver, ivory, apes and peacocks from Asia beyond the Ganges and the East Indian islands. European mariners and geographers of the Homeric period considered the bearing of land and sea only in connection with the rising and setting of the sun and with the four winds Boreas, Euros, Notos, and Sephuros. These mariners and geographers adopted the plan - an arbitrary one - of considering the earth as having the north above and the south below, and, after globes or maps had been constructed with the north at the top, and this method had been handed down to us, we took for granted that it had obtained universally and in all times.
Such has not been the case, for the earliest navigators, the Phoenicians, the Arabs, the Chinese, and perhaps all Asiatic nations, considered the south to be above and the north below. It is strange that some historians, in pointing out so cleverly that the Chaldean conception was more in accordance with the true doctrine concerning the form of the globe than had been suspected, fails, at the same time, to notice that Homer in his brain-map reversed the Chaldean terrestrial globe and placed the north at the top. During the middle ages, we shall see a reversion take place, and the terrestrial paradise and heavenly paradise placed according to the earlier Chaldean notions; and on maps of this epoch, encircling the known world from the North Pole to the equator, flows the antic Ocean, which in days of yore encircled the infernal regions. At a later period, during which planispheric maps, showing one hemisphere of the world, may have been constructed, the circumfluent ocean must have encircled the world as represented by the geographical exponents of the time being; albeit in a totally different way than expressed in the Shumiro-Accadian records.
It follows from all this that, as mariners did actually traverse those regions and penetrate south of the equator, the islands they visited most, such as Java, its eastern prolongation of islands, Sumbawa, etc., were believed to be in the northern hemisphere, and were consequently placed there by geographers, as the earliest maps of the various editions of Ptolemya€™s Geography bear witness. These mistakes were the result doubtless of an erroneous interpretation of information received; and the most likely period during which cognizance of these islands was obtained was when Alexandria was the center of the Eastern and Western commerce of the world.
But to return to the earlier Pre-Ptolemaic period and to form an idea of the chances of information which the traffic carried on in the Indian Ocean may have offered to the Greeks and Romans, here is what Antonio Galvano, Governor of Ternate says in 1555, quoting Strabo and Pliny (Strabo, lib.
Now as the above articles of commerce, mentioned by Strabo and Pliny, after leaving their original ports in Asia and Austral-Asia, were conveyed from one island to another, any information, when sought for, concerning the location of the islands from which the spices came, must necessarily have been of a very unreliable character, for the different islands at which any stay was made were invariably confounded with those from which the spices originally came. From these facts, and many others, such as the positions given to the Mountain of the East or North-East of the Shumiro-Accads, the Mountain of the South, or Southwest, of Homer, and the Infernal Regions, we may conclude that the North Pole of the Ancients was situated somewhere in the neighborhood of the Sea of Okhotsk. It is in the Classical Period of Greek cartography that we can start to trace a continuous tradition of theoretical concepts about the size and shape of the earth. Likewise, it should be emphasized that the vast majority of our knowledge about Greek cartography in this early period is known primarily only from second- or third-hand accounts. There is no complete break between the development of cartography in Classical and in Hellenistic Greece. In spite of these speculations, however, Greek cartography might have remained largely the province of philosophy had it not been for a vigorous and parallel growth of empirical knowledge. That such a change should occur is due both to political and military factors and to cultural developments within Greek society as a whole. The librarians not only brought together existing texts, they corrected them for publication, listed them in descriptive catalogs, and tried to keep them up to date. The other great factor underlying the increasing realism of maps of the inhabited world in the Hellenistic Period was the expansion of the Greek world through conquest and discovery, with a consequent acquisition of new geographical knowledge. Among the contemporaries of Alexander was Pytheas, a navigator and astronomer from Massalia [Marseilles], who as a private citizen embarked upon an exploration of the oceanic coasts of Western Europe. As exemplified by the journeys of Alexander and Pytheas, the combination of theoretical knowledge with direct observation and the fruits of extensive travel gradually provided new data for the compilation of world maps. The importance of the Hellenistic Period in the history of ancient world cartography, however, has been clearly established. In the history of geographical (or terrestrial) mapping, the great practical step forward during this period was to locate the inhabited world exactly on the terrestrial globe. Thus it was at various scales of mapping, from the purely local to the representation of the cosmos, that the Greeks of the Hellenistic Period enhanced and then disseminated a knowledge of maps. The Roman Republic offers a good case for continuing to treat the Greek contribution to mapping as a separate strand in the history of classical cartography. The remarkable influence of Ptolemy on the development of European, Arabic, and ultimately world cartography can hardly be denied. Notwithstanding his immense importance in the study of the history of cartography, Ptolemy remains in many respects a complicated figure to assess.
Still the culmination of Greek cartographic thought is seen in the work of Claudius Ptolemy, who worked within the framework of the early Roman Empire. When we turn to Roman cartography, it has been shown that by the end of the Augustan era many of its essential characteristics were already in existence. In the course of the early empire large-scale maps were harnessed to a number of clearly defined aspects of everyday life. Maps in the period of the decline of the empire and its sequel in the Byzantine civilization were of course greatly influenced by Christianity. Continuity between the classical period and succeeding ages was interrupted, and there was disruption of the old way of life with its technological achievements, which also involved mapmaking.
Although at this level students may not use these names, you can convey the meaning of both kinds of division so that they can have a better understanding of the division process. If in multiplication we find the product of two factors, in division we find the missing factor if the other factor and the product are known. In multiplication the numbers you multiply are called factors; the answer is called the product.
Expose your students to the different models and let each student choose which model is most helpful to him or her. Lead students to discover the rules themselves by having them use counters to model the division. For example, they can use a related multiplication fact to find the unit cost of an item—for example the cost of one baseball cap priced at 3 for \$18.
It is also a whole number.An Integer P > 1 is called a prime number when its only divisors are ± 1 and ± P. The process of finding these numbers is called integer factorization, or prime factorization.The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicity.
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Some maps are successful in their display of material but are scientifically barren, while in others an important message may be obscured because of the poverty of presentation.
Maps constitute a specialized graphic language, an instrument of communication that has influenced behavioral characteristics and the social life of humanity throughout history. Maps produced by contemporary primitive peoples have been likened to so-called prehistoric maps. But the trans-local culture did not penetrate very deep The high culture owed this peculiar combination of wide expanse and superficiality to the nature of communications in the preindustrial world, in combination with scarcity and political factors.

Ancient a€?educated mena€? covered huge distances in both place and time to debate scientific questions about geography.
In the modern world, the nature of communications allows original texts and graphics to be preserved, transmitted and accessed for extended periods of time.
In earlier times these maps were considered to be ephemeral material, like newspapers and pamphlets, and large wall-maps received particularly careless treatment because they were difficult to store. When, in 1918, a mosaic floor was discovered in the ancient TransJordanian church of Madaba showing a map of Palestine, Syria and part of Egypt, a whole series of reproductions and treatises was published on the geography of Palestine at that time.
Kretschner, 1892), Japan (P.Teleki, 1909), Madagascar (Gravier, 1896), Albania (Nopcsa, 1916), Spitzbergen (Wieder, 1919), the northwest of America (Wagner, 1937), and others. Indeed, much of its universal appeal is that the simpler types of map can be read and interpreted with only a little training. Crone remarked that a€?a map can be considered from several aspects, as a scientific report, a historical document, a research tool, and an object of art.
It may also be viewed as an aspect of the history of human thought, so that while the study of the techniques that influence the medium of that thought is important, it also considers the social significance of cartographic innovation and the way maps have impinged on the many other facets of human history they touch. It is reasonable to expect some evidence in this art of the societya€™s spatial consciousness. There is, for example, clear evidence in the prehistoric art of Europe that maps - permanent graphic images epitomizing the spatial distribution of objects and events - were being made as early as the Upper Paleolithic. In Mesopotamia the invention by the Sumerians of cuneiform writing in the fourth millennium B.C. In the former field, among other things, they attained a remarkably close approximation for a?s2, namely 1.414213. The courses of the Tigris and Euphrates rivers offered major routes to and from the north, and the northwest, and the Persian Gulf allowed contact by sea along the coasts of Arabia and east to India. Cuneiform texts provide several varieties of evidence for the ancient Mesopotamian efforts to express order by describing, delimiting, and measuring the heaven and earth of their experience, producing house, temple, plot, and field plans, city maps, and, with respect to the celestial landscape, diagrammatic depictions of stars. The historiography of maps and cartography has emerged from criticisms similar in nature to those made against the modernist or presentist historiography of science, namely, that in reifying science or sciences such as cartography, false evolutionary histories are liable to be constructed. Concern for orientation is attested in a number of maps, but not always in the same way, although with a tendency toward an oblique orientation northwest to southeast. The cities of Nippur and Babylon had a religious and cosmological function as well as a political and economic one. It offers a selective account of the relationship of Babylon to other places, including those that were at the furthest reach of knowledge.
Cognitive psychologists claim that we come into our physical world mentally equipped to perceive and describe space and spatial relationships.
Within this span of some three thousand years, the main achievements in Greek cartography took place from about the sixth century B.C. Stevenson, it is not easy to fix, with anything like a satisfactory measure of certainty, the beginning of globe construction; very naturally it was not until a spherical theory concerning the heavens and the earth had been accepted, and for this we are led back quite to Aristotle and beyond, back indeed to the Pythagoreans if not yet farther. We are now learning that those centuries were not entirely barren of a certain interest in sciences other than theological. It has now been ascertained and demonstrated beyond doubt that the earliest ideas concerning the laws of the universe and the shape of the earth were, in many respects, more correct and clearer than those of a subsequent period.
Ragozin, says the Shumiro-Accads had formed a very elaborate and clever idea of what they supposed the world to be like; they imagined it to have the shape of an inverted round boat or bowl, the thickness of which would represent the mixture of land and water (ki-a) which we call the crust of the earth, while the hollow beneath this inhabitable crust was fancied as a bottomless pit or abyss (ge), in which dwelt many powers. The account of this conversation, which is too lengthy here to give in full, was written three centuries and a half before the Christian era. Of the familiaritie of Midas, the Phrigian, and Selenus, and of certaine circumstances which he incredibly reported. This Selenus was the sonne of a nymphe inferiour to the gods in condition and degree, but superiour to men concerning mortalytie and death. The Chaldean conception, thus rudely described, shows a yet nearer approximation to the true doctrine concerning the form of the globe, when we bear in mind that this actually is in shape a flattened sphere, with the vertical diameter the shorter one.
A curious example of the difficulties that early cartographers of the circumfluent ocean period had to contend with, and of the sans faA§on method of dealing with them, occurs in the celebrated Fra Mauro mappamundi (Book III, #249), which is one of the last in which the external ocean is still retained. The influence of the Ptolemaic astronomical and geographical system was very great, and lasted for over thirteen hundred years.
There are reasons to believe however, apart from the evidence we gather in the Poems, that these abyssal regions were supposed or believed to be situated around the North Pole.
Homer, The Outward Geography Eastwards: a€?The outer geography eastwards, or wonderland, has for its exterior boundary the great river Okeanos, a noble conception, in everlasting flux and reflux, roundabout the territory given to living man. The Phoenician reports referred to came most likely therefore, not so much from the north, as from these regions which, tradition tells us (Fra Mauroa€™s mappamundi #249), were situated propinqua ale tenebre. These winds covered the arcs intervening between our four cardinal points of the compass, which points were not located exactly as with us; but the north leaning to the east, the east to the south, the south to the west and the west to the north (see Beatusa€™ Turin map, Book II, #207). The reason for this is plausible, for whereas the northern seaman regulated his navigation by the North Star, the Asiatic sailor turned to southern constellations for his guidance. This is all the more strange when we take into consideration that, in the light of his context, the fact is apparent and of great importance as coinciding with other European views concerning the location of the north on terrestrial globes and maps. The Chaldeans placed their heaven in the east or northeast; Homer placed his heaven in the south or southwest. In this ocean we find also EA the Exalted Fish, but, deprived of his ancient grandeur and divinity, he is no doubt considered nothing more than a merman at the period when acquaintance is renewed with him on the SchA¶ner-Frankfort gores of Asiatic origin bearing the date 1515 (Book IV, #328). The divergence was probably owing in a great measure to the inability of representing graphically the perspective appearance of the globe on a plane; but may be also traceable to an erroneous interpretation of the original idea, caused by the reversion of the cardinal points of the compass. According to this division other continents south of the equator were supposed to exist and habited, some said, but not to be approached by those inhabiting the northern hemisphere on account of the presumed impossibility of traversing the equatorial regions, the heat of which was believed to be too intense.
We shall see, when dealing with Ptolemy's map of the world, some of the results of this confusion. Thomas, after the dispersion of the Apostles, preached the Gospel to the Parthians and Persians; then went to India, where he gave up his life for Jesus Christ.
That he corroborates Homera€™s views as to the sphericity of the earth by describing Cratesa€™ terrestrial globe (Geographica; Book ii. That he accentuates Homera€™s views concerning the black races that lived some in the west (the African race) others in the east (the Australian race).
That he shows the four cardinal points of the compass to have been situated somewhat differently than with us, for he says (Book 1, c. That he appears to be perpetuating an ancient tradition when he supposes the existence of a vast continent or antichthonos in the southern hemisphere to counterbalance the weight of the northern continents.
The relativeness of these positions appears to have been maintained on some mediaeval maps. To appreciate how this period laid the foundations for the developments of the ensuing Hellenistic Period, it is necessary to draw on a wide range of Greek writings containing references to maps.
We have no original texts of Anaximander, Pythagoras, or Eratosthenes - all pillars of the development of Greek cartographic thought. In contrast to many periods in the ancient and medieval world and despite the fragmentary artifacts, we are able to reconstruct throughout the Greek period, and indeed into the Roman, a continuum in cartographic thought and practice.
Indeed, one of the salient trends in the history of the Hellenistic Period of cartography was the growing tendency to relate theories and mathematical models to newly acquired facts about the world - especially those gathered in the course of Greek exploration or embodied in direct observations such as those recorded by Eratosthenes in his scientific measurement of the circumference of the earth. With respect to the latter, we can see how Greek cartography started to be influenced by a new infrastructure for learning that had a profound effect on the growth of formalized knowledge in general.
Thus Alexandria became a clearing-house for cartographic and geographical knowledge; it was a center where this could be codified and evaluated and where, we may assume, new maps as well as texts could be produced in parallel with the growth of empirical knowledge. In his treatise On the Ocean, Pytheas relates his journey and provides geographical and astronomical information about the countries that he observed. While we can assume a priori that such a linkage was crucial to the development of Hellenistic cartography, again there is no hard evidence, as in so many other aspects of its history, that allows us to reconstruct the technical processes and physical qualities of the maps themselves. Its outstanding characteristic was the fruitful marriage of theoretical and empirical knowledge. Eratosthenes was apparently the first to accomplish this, and his map was the earliest scientific attempt to give the different parts of the world represented on a plane surface approximately their true proportions. By so improving the mimesis or imitation of the world, founded on sound theoretical premises, they made other intellectual advances possible and helped to extend the Greek vision far beyond the Aegean.
While there was a considerable blending and interdependence of Greek and Roman concepts and skills, the fundamental distinction between the often theoretical nature of the Greek contribution and the increasingly practical uses for maps devised by the Romans forms a familiar but satisfactory division for their respective cartographic influences. The profound difference between the Roman and the Greek mind is illustrated with peculiar clarity in their maps. Through both the Mathematical Syntaxis (a treatise on mathematics and astronomy in thirteen books, also called the Almagest and the Geography (in eight books), it can be said that Ptolemy tended to dominate both astronomy and geography, and hence their cartographic manifestations, for over fourteen centuries. A modern analysis of Ptolemaic scholarship offers nothing to revise the long-held consensus that he is a key figure in the long term development of scientific mapping. In its most obvious aspect, the exaggerated size of Jerusalem on the Madaba mosaic map (# 121) was no doubt an attempt to make the Holy City not only dominant but also more accurately depicted in this difficult medium.
When you divide to find the number of objects in each group, the division is called fair sharing or partitioning. In division the number being divided is the dividend, the number that divides it is the divisor, and the answer is the quotient.
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The camera then makes optimal settings to ensure the best possible image capture, whether you're shooting stills or video.
When shooting video, the system automatically selects among Dynamic, Powered, Macro and Tripod modes. They have often served as memory banks for spatial data and as mnemonics in societies without the printed word and can speak across the barriers of ordinary language, constituting a common language used by men of different races and tongues to express the relationship of their society to a geographic environment.
Certain carvings on bone and petroglyphs have been identified as prehistoric route maps, although according to a strict definition, they might not qualify as a€?mapsa€?. In the present work, reconstruction of maps no longer extant are used in place of originals or assumed originals. They communicated in the same a€?learned languagea€?a€” Greek a€” and discussed a€?the same body of ideasa€?. The pre-modern world, on the other hand, had only a series of copies to work with, made over the centuries on organic material. Only Senefeldera€™s invention of lithography in 1796, and the innovative use of it for the mass printing of graphics, including in color, In the century that followed, allowed maps to be printed and distributed in quantity. Since the maps were missing, he drew them himself from indications in the ancient text, and when the work was finished, he commemorated this too in verse. The map answered many hitherto insoluble or disputed questions, for example the question as to where the Virgin Mary met the mother of John Baptist. A series of maps of a coastal region (for example, that of Holland or Friesland) or of river estuaries (the Po, Mississippi, Volga, or lower Yellow River) gives information on the rate of changes in outline and their causes. Maps represent an excellent mirror of culture and civilizationa€?, but they are also more than a mere reflection: maps in their own right enter the historical process by means of reciprocally structured relationships.
But when it comes to drawing up the balance sheet of evidence for prehistoric maps, we must admit that the evidence is tenuous and certainly inconclusive.
The same evidence shows, too, that the quintessentially cartographic concept of representation in plan was already in use in that period.
Our divisions into 60 and 360 for minutes, seconds and degrees are a direct inheritance from the Babylonians, who thought in these terms. Various orders of power are implicit in the expression of these aspects of order in the environment.
Some originating point is identified, such as the origins of science in Greece, or of mapmaking in Babylonia, from which a continuous history may be written from a presentist perspective, a tale of a discipline's inexorable progress from its originating moment to the present. Ancient Near Eastern maps may not have invariably been meant as exact or direct replications of territory, but there can be little doubt that they distinctively reflect the conceptual terrain of their social community and culture at large. In the periods of their supremacy each was viewed as the center of the universe, as the meeting ground between heaven and the netherworld. The linguistic act of spatial description is perhaps a proto-mapmaking function of our very desire and attempt to place ourselves in relation to the physical world.
The Pharaohs organized military campaigns, trade missions, and even purely geographical expeditions to explore various countries. From earliest times much of the area covered by the annual Nile floods had, upon their retreat, to be re-surveyed in order to establish the exact boundaries of properties. We find allusions to celestial globes in the days of Eudoxus and Archimedes, to terrestrial globes in the days of Crates and Hipparchus. In Justiniana€™s day, or near it, one Leontius Mechanicus busied himself in Constantinople with globe construction, and we have left to us his brief descriptive reference to his work. But above all these, higher in rank and greater in power, is the Spirit (Zi) of heaven (ana), ZI-ANA, or, as often, simply ANA--Heaven.
On this map of the world the islands of the Malay Archipelago follow the shores of Asia from Malacca to Japan.
Even the Arabs, who, after the fall of the Roman Empire, developed the geographical knowledge of the world during the first period of the middle ages, adopted many of its errors. Volcanoes were supposed to be the entrances to the infernal regions, and towards the southeast the whole region beyond the river Okeanos of Homer, from Java to Sumbawa and the Sea of Banda, was sufficiently studded with mighty peaks to warrant the idea they may have originated.
Many cartographers of the renascence, whose charts indeed we cannot read unless we reverse them, must have followed Asiatic cartographical methods, and this perhaps through copying local charts obtained in the countries visited by them.
Taprobana was the Greek corruption of the Tamravarna of Arabian, or even perhaps Phoenician, nomenclature; our modern Sumatra.
Geographical science was on the eve of reaching its apogee with the Greeks, were it was doomed to retrograde with the decline of the Roman Empire. John III, King of Portugal, ordered his remains to be sought for in a little ruined chapel that was over his tomb, outside Meliapur or Maliapor. In some cases the authors of these texts are not normally thought of in the context of geographic or cartographic science, but nevertheless they reflect a widespread and often critical interest in such questions. In particular, there are relatively few surviving artifacts in the form of graphic representations that may be considered maps. Despite a continuing lack of surviving maps and original texts throughout the period - which continues to limit our understanding of the changing form and content of cartography - it can be shown that, by the perioda€™s end, a markedly different cartographic image of the inhabited world had emerged. Of particular importance for the history of the map was the growth of Alexandria as a major center of learning, far surpassing in this respect the Macedonian court at Pella. Later geographers used the accounts of Alexandera€™s journeys extensively to make maps of Asia and to fill in the outline of the inhabited world.
Not even the improved maps that resulted from these processes have survived, and the literary references to their existence (enabling a partial reconstruction of their content) can even in their entirety refer only to a tiny fraction of the number of maps once made and once in circulation. It has been demonstrated beyond doubt that the geometric study of the sphere, as expressed in theorems and physical models, had important practical applications and that its principles underlay the development both of mathematical geography and of scientific cartography as applied to celestial and terrestrial phenomena. On his map, moreover, one could have distinguished the geometric shapes of the countries, and one could have used the map as a tool to estimate the distances between places. To Rome, Hellenistic Greece left a seminal cartographic heritage - one that, in the first instance at least, was barely challenged in the intellectual centers of Roman society.
Certainly the political expansion of Rome, whose domination was rapidly extending over the Mediterranean, did not lead to an eclipse of Greek influence.
Such knowledge, relating to both terrestrial and celestial mapping, had been transmitted through a succession of well-defined master-pupil relationships, and the preservation of texts and three-dimensional models had been aided by the growth of libraries. The Romans were indifferent to mathematical geography, with its system of latitudes and longitudes, its astronomical measurements, and its problem of projections. Yet Ptolemy, as much through the accidental survival and transmission of his texts when so many others perished as through his comprehensive approach to mapping, does nevertheless stride like a colossus over the cartographic knowledge of the later Greco-Roman world and the Renaissance. Pilgrims from distant lands obviously needed itineraries like that starting at Bordeaux, giving fairly simple instructions. In this chapter your students will learn how to use arrays to show the relationship between multiplication and division.
Discuss the relationship of these numbers as you explain how multiplication and division are related. The camera is shockproof to 6.5 feet, and temperature resistant all the way from 14 Degree to 104 Degree. As a signal is received from GPS satellites, take sufficient measures when using in locations where the use of electronics is regulated. And with the Movie Digest mode, you can record more of your dive without interrupting your enjoyment of it. The Canon HS SYSTEM takes the frustration out of low-light shooting, delivering clear, blur-free images. In addition to being able to shoot Full HD 1080p video at 24* frames per second, the PowerShot D30 can also shoot 720p HD video at 30** frames per second. You can maximize the usefulness of the GPS feature by using the special bundled Map Utility software that makes it fun to share the memories of your world adventures. Smart AUTO also includes Advanced Subject Detection, which allows the camera to detect and track non-human moving subjects like animals and vehicles. With Intelligent IS, you can concentrate on image capture, letting the camera make the most effective IS settings to help capture the steadiest possible image. This implies that throughout history maps have been more than just the sum of technical processes or the craftsmanship in their production and more than just a static image of their content frozen in time.
The reconstructions of such maps appear in the correct chronology of the originals, irrespective of the date of the reconstruction.
Their debate a€?did not penetrate very deepa€? within the culture, which is why one should draw a sharp distinction between descriptive geography, with its wide application, and mathematical or scientific geography, for which no such application was envisaged or achieved.

The process was almost manageable for texts, multiple copies of which could be created by copyist teams working fro dictation.
After the fall of Byzantium in 1453, its conqueror, the Turkish Sultan Mohammed II, found in the library that he inherited from the Byzantine rulers a manuscript of Ptolemya€™s Geographia, which lacked the world-map, and he commissioned Georgios Aminutzes, a philosopher in his entourage, to draw up a world map based on Ptolemya€™s text. Comparison of travelersa€™ maps from various periods show the development and change of routes or road-building and allows us to draw conclusions of every kind about the development or decay of farms, villages and towns. They were artistic treasure-houses, being often decorated with fine miniatures portraying life and customs in distant lands, various types of ships, coats-of-arms, portraits of rulers, and so on.
The development of the map, whether it occurred in one place or at a number of independent hearths, was clearly a conceptual advance - an important increment to the technology of the intellect - that in some respects may be compared to the emergence of literacy or numeracy. The historian of cartography, looking for maps in the art of prehistoric Europe and its adjacent regions, is in exactly the same position as any other scholar seeking to interpret the content, functions, and meanings of that art.
Moreover, there is sufficient evidence for the use of cartographic signs from at least the post-Paleolithic period. They are impressed on small clay tablets like those generally used by the Babylonians for cuneiform inscriptions of documents, a medium which must have limited the cartographera€™s scope. Administrative and economic powers support, or even require, the making of maps, as well as determining overtly the topographies that maps depict. Critical cartographic history, however, has laid aside such ideas, and we no longer look to (in the words of Denis Wood), a€?a hero saga involving such men as Eratosthenes, Ptolemy, Mercator, and the Cassinis, that tracked cartographic progress from humble origins in Mesopotamia to the putative accomplishments of the Greeks and Romansa€?. The maps of buildings and fields focus on the urban and agricultural environment, matters of critical importance to whatever political and economic powers prevailed. The map of the principal temple in Babylon, E-sagil, which was the earthly abode of the national deity Marduk, represents the terrestrial counterpart to the celestial residence of the great god Enlil, designed, figuratively speaking, on the blueprint of the cosmic subterranean sweet watery region of the Apsu.
By extension, we should not doubt that mapmaking too, in all its historical subjectivity, is a universal feature of human culture. The survey was carried out, mostly in squares, by professional surveyors with knotted ropes.
We find that the Greek geographer Strabo gives us quite a definite word concerning their value and their construction, and that Ptolemy is so definite in his references to them as to lead to a belief that globes were by no means uncommon instruments in his day, and that they were regarded of much value in the study of geography and astronomy, particularly of the latter science. With stress laid, during the many centuries succeeding, upon matters pertaining to the religious life, there naturally was less concern than there had been in the humanistic days of classical antiquity as to whether the earth is spherical in form, or flat like a circular disc, nor was it thought to matter much as to the form of the heavens. Hyde Clarke has more than once pointed out in The Legend of the Atlantis of Plato, Royal Historical Society 1886, etc., that Australia must have been known in the most remote antiquity of the early history of civilization, at a time when the intercourse with America was still maintained. Between the lower heaven and the surface of the earth is the atmospheric region, the realm of IM or MERMER, the Wind, where he drives the clouds, rouses the storms, and whence he pours down the rain, which is stored in the great reservoir of Ana, in the heavenly ocean. Then in a northeasterly direction Homera€™s great river Okeanos would flow along the shores of the Sandwich group, where the volcanic peak of Mt. Aristotlea€™s writings, for example, provide a summary of the theoretical knowledge that underlay the construction of world maps by the end of the Greek Classical Period. Our cartographic knowledge must, therefore, be gleaned largely from literary descriptions, often couched in poetic language and difficult to interpret.
The ambition of Eratosthenes to draw a general map of the oikumene based on new discoveries was also partly inspired by Alexandera€™s exploration.
In this case too, the generalizations drawn herein by various authorities (ancient and modern scholars, historians, geographers, and cartographers) are founded upon the chance survival of references made to maps by individual authors. Yet this evidence should not be interpreted to suggest that the Greek contribution to cartography in the early Roman world was merely a passive recital of the substance of earlier advances. If land survey did play such an important part, then these plans, being based on centuriation requirements and therefore square or rectangular, may have influenced the shape of smaller-scale maps.
This is perhaps more remarkable in that his work was primarily instructional and theoretical, and it remains debatable if he bequeathed a set of images that could be automatically copied by an uninterrupted succession of manuscript illuminators. The built-in GPS tracker records the location and time of all the images and videos you capture, and the new Sunlight LCD mode makes it easy to see the monitor even on bright, sunny days.
The mode captures a still image plus up to 4 seconds of video prior to pressing the shutter, all without using the REC button. In addition to displaying all your photos' locations on a world map, the camera's GPS system can also track your route from photo to photo – a great way to visualize each trip! Indeed, any history of maps is compounded by a complex series of interactions, involving their intent, their use and their purpose, as well as the process of their making. All reconstructions are, to a greater or lesser degree, the product of the compiler and the technology of his times. The reasons for this divide include the limited quantity of scientific geographic scholarship, the nature of communications and scarcity, and political factors.
But it was not feasible for graphics, the copying of which inevitably led to increasing distortion. Any assumption that maps were widely available in the preindustrial world thus derives from anachronistic thinking based on later developments.
There is no evidence for the use of such forms of representation in ancient maps, and this book deliberately presents no such reconstructions. He knew it would be out of date, but that is precisely what he wanted - an ancient map; to perpetuate it, he also had a carpet woven from the drawing.
Inferences have to be made about states of mind separated from the present not only by millennia but also - where ethnography is called into service to help illuminate the prehistoric evidence - by the geographical distance and different cultural contexts of other continents. Two of the basic map styles of the historical period, the picture map (perspective view) and the plan (ichnographic view), also have their prehistoric counterparts. The interest of the cuneiform maps lies in their rich articulation of such a feature, uniquely shaped by the particular social norms and forces that emerged and changed within ancient Mesopotamian history.
However, the measurement of circular and triangular plots was envisaged: advice on this, and plans, are given in the Rhind Mathematical Papyrus of ca. From Ptolemaic Egypt there is a rough rectangular plan of surveyed land accompanying the text of the Lille Papyrus I, now in Paris; also two from the estate of Apollonius, minister of Ptolemy II. There is, however, but one example known, which has come down to us from that ancient day, this a celestial globe, briefly described as the Farnese globe.
Yet there was no century, not even in those ages we happily are learning to call no longer a€?darka€?, that geography and astronomy were not studied and taught, and globes celestial as well as armillary spheres, if not terrestrial globes, were constructed. Here however he makes his hero confess that he is wholly out of his bearings, and cannot well say where the sun is to set or to rise (Od.
Although these views were continued and developed to a certain extent by their successors, Strabo and Ptolemy, through the Roman period, and more or less entertained during the Middle Ages, they became obscured as time rolled on. The bones of the holy apostle were found, with some relics that were placed in a rich vase. Again, if we consider the Atlantic and North Pacific Oceans as devoid of the American Continent, and the Atlantic Ocean as stretching to the shores of Asia, as Strabo did, the parallel of Iberia (Spain) would have taken Columbusa€™ ships to the north of Japan--i.e. At the time when Alexander the Great set off to conquer and explore Asia and when Pytheas of Massalia was exploring northern Europe, therefore, the sum of geographic and cartographic knowledge in the Greek world was already considerable and was demonstrated in a variety of graphic and three-dimensional representations of the heavens and the earth.
In addition, many other ancient texts alluding to maps are further distorted by being written centuries after the period they record; they too must be viewed with caution because they are similarly interpretative as well as descriptive. Eudoxus had already formulated the geocentric hypothesis in mathematical models; and he had also translated his concepts into celestial globes that may be regarded as anticipating the sphairopoiia [mechanical spheres]. And it was at Alexandria that this Ptolemy, son of Ptolemy I Soter, a companion of Alexander, had founded the library, soon to become famous through the Mediterranean world. It seems, though, that having left Massalia, Pytheas put into Gades [Cadiz], then followed the coasts of Iberia [Spain] and France to Brittany, crossing to Cornwall and sailing north along the west coast of England and Scotland to the Orkney Islands.
On the contrary, a principal characteristic of the new age was the extent to which it was openly critical of earlier attempts at mapping. Disregarding the elaborate projections of the Greeks, they reverted to the old disk map of the Ionian geographers as being better adapted to their purposes. This shape was also one which suited the Roman habit of placing a large map on a wall of a temple or colonnade. 90-168), Greek and Roman influences in cartography had been fused to a considerable extent into one tradition.
The Almagest, although translated into Latin by Gerard of Cremona in the 12th century, appears to have had little direct influence on the development of cartography. Ptolemya€™s principal legacy was thus to cartographic method, and both the Almagest and the Geography may be regarded as among the most influential works in cartographic history. Whether you're underwater or on dry land, images are beautifully clear, steady and loaded with detail and natural color thanks to the Canon HS system and Intelligent IS. You can also create and share custom maps and personal mini-travel guides with friends and family members.
Therefore, reconstructions are used here only to illustrate the general geographic concepts of the period in which the lost original map was made.
All this is also evident in the history of cartography (a modern term created via a combination of Greek chartes, a€?charta€™, and graphein, a€?writea€™ or a€?drawa€™), that is, the study of maps as a special form of communicating geographic knowledge. Copies of copies of copies must generally have been very different from the vanished original, hence the scarcity of scholarly, illustrations transmitted from the ancient world. There is even a temptation to go beyond reconstructions and invent a€” that is, falsify a€” maps from the ancient world. It was said that as the Archangel Gabriel appeared to Zacharias in the holy of holies, Zacharias must have been High Priest and have lived in Jerusalem; John the Baptist would then have been born in Jerusalem.
I have not been able to find any such evidence or artifacts of map making that originated in the South America or Australia.
This is described in an inscription in the Temple of Der-el-Bahri where the ship used for this journey is delineated, but there is no map. It is of marble, and is thought by some to date from the time of Eudoxus, that is, three hundred years before the Christian era. The Venerable Bede, Pope Sylvester I, the Emperor Frederick II, and King Alfonso of Castile, not to name many others of perhaps lesser significance, displayed an interest in globes and making. See the sketch below of an inverted Chaldean boat transformed into a terrestrial globe, which will give an idea of the possible appearance of early globes. Indeed, wherever we look round the margin of the circumfluent ocean for an appropriate entrance to Hades and Tartaros, we find it, whether in Japan, Iceland, the Azores, or Cape Verde Islands. Terrestrial maps and celestial globes were widely used as instruments of teaching and research. Despite what may appear to be reasonable continuity of some aspects of cartographic thought and practice, in this particular era scholars must extrapolate over large gaps to arrive at their conclusions. By the beginning of the Hellenistic Period there had been developed not only the various celestial globes, but also systems of concentric spheres, together with maps of the inhabited world that fostered a scientific curiosity about fundamental cartographic questions. The library not only accumulated the greatest collection of books available anywhere in the Hellenistic Period but, together with the museum, likewise founded by Ptolemy II, also constituted a meeting place for the scholars of three continents. From there, some authors believe, he made an Arctic voyage to Thule [probably Iceland] after which he penetrated the Baltic. Intellectual life moved to more energetic centers such as Pergamum, Rhodes, and above all Rome, but this promoted the diffusion and development of Greek knowledge about maps rather than its extinction. The main texts, whether surviving or whether lost and known only through later writers, were strongly revisionist in their line of argument, so that the historian of cartography has to isolate the substantial challenge to earlier theories and frequently their reformulation of new maps.
There is a case, accordingly, for treating them as a history of one already unified stream of thought and practice.
With translation of the text of the Geography into Latin in the early 15th century, however, the influence of Ptolemy was to structure European cartography directly for over a century. It would be wrong to over emphasize, as so much of the topographical literature has tended to do, a catalog of Ptolemya€™s a€?errorsa€?: what is vital for the cartographic historian is that his texts were the carriers of the idea of celestial and terrestrial mapping long after the factual content of the coordinates had been made obsolete through new discoveries and exploration. Similarly, in the towns, although only the Forma Urbis Romae is known to us in detail, large-scale maps were recognized as practical tools recording the lines of public utilities such as aqueducts, displaying the size and shape of imperial and religious buildings, and indicating the layout of streets and private property. No one person or area of study is capable of embracing the whole field; and cartographers, like workers in other activities, have become more and more specialized with the advantages and disadvantages which this inevitably brings. Nevertheless, reconstructions of maps which are known to have existed, and which have been made a long time after the missing originals, can be of great interest and utility to scholars. Maps are generally two-dimensional representations, often to scale, of portions of the earth's surface.
Every generation or so, a new a€?discoverya€™ of such a map is announced, only to be exposed as either a hoax designed to embarrass an individual scholar or scholars in general, or an attempt to make money from an unsuspecting public. The fact that King Sargon of Akkad was making military expeditions westwards from about 2,330 B.C. It has been shown how these could have appealed to the imagination not only of an educated minority, for whom they sometimes became the subject of careful scholarly commentary, but also of a wider Greek public that was already learning to think about the world in a physical and social sense through the medium of maps.
The relative smallness of the inhabited world, for example, later to be proved by Eratosthenes, had already been dimly envisaged. The confirmation of the sources of tin (in the ancient Cassiterides or Tin Islands) and amber (in the Baltic) was of primary interest to him, together with new trade routes for these commodities.
Indeed, we can see how the conditions of Roman expansion positively favored the growth and applications of cartography in both a theoretical and a practical sense.
The context shows that he must be talking about a map, since he makes the philosopher among his group start with Eratosthenesa€™ division of the world into North and South. Here, however, though such a unity existed, the discussion is focused primarily on the cartographic contributions of Ptolemy, writing in Greek within the institutions of Roman society. In the history of the transmission of cartographic ideas it is indeed his work, straddling the European Middle Ages, that provides the strongest link in the chain between the knowledge of mapping in the ancient and early modem worlds.
Finally, the interpretation of modem scholars has progressively come down on the side of the opinion that Ptolemy or a contemporary probably did make at least some of the maps so clearly specified in his texts.
Some types of Roman maps had come to possess standard formats as well as regular scales and established conventions for depicting ground detail. The possibilities include those for which specific information is available to the compiler and those that are described or merely referred to in the literature. Some saw in the a€?hill countrya€™ Hebron, a place that had for a long time been a leading Levitical city, while others held that Juda was the Levitical city concerned. The whole northern region, of sea as he supposed it, from west to east, was known to him only by Phoenician reports.
If a literal interpretation was followed, the cartographic image of the inhabited world, like that of the universe as a whole, was often misleading; it could create confusion or it could help establish and perpetuate false ideas.
It had been the subject of comment by Plato, while Aristotle had quoted a figure for the circumference of the earth from a€?the mathematiciansa€? at 400,000 stades; he does not explain how he arrived at this figure, which may have been Eudoxusa€™ estimate. It would appear from what is known about Pytheasa€™ journeys and interests that he may have undertaken his voyage to the northern seas partly in order to verify what geometry (or experiments with three dimensional models) have taught him. Not only had the known world been extended considerably through the Roman conquests - so that new empirical knowledge had to be adjusted to existing theories and maps - but Roman society offered a new educational market for the cartographic knowledge codified by the Greeks. Ptolemy owed much to Roman sources of information and to the extension of geographical knowledge under this growing empire: yet he represents a culmination as well as a final synthesis of the scientific tradition in Greek cartography that has been highlighted in this introduction. Yet it is perhaps in the importance accorded the map as a permanent record of ownership or rights over property, whether held by the state or by individuals, that Roman large-scale mapping most clearly anticipated the modern world. Viewed in its development through time, the map is a sensitive indicator of the changing thought of man, and few of these works seem to reflect such an excellent mirror of culture and civilization. Of a different order, but also of interest, are those maps made in comparatively recent times that are designed to illustrate the geographical ideas of a particular person or group in the past but are suggested by no known maps. Many solutions to this problem were put forward, but it was solved once and for all by the Madaba map, which showed, between Jerusalem and Hebron, a place called Beth Zachari: the house of Zacharias. The paucity of evidence of clearly defined representations of constellations in rock art, which should be easily recognized, seems strange in view of the association of celestial features with religious or cosmological beliefs, though it is understandable if stars were used only for practical matters such as navigation or as the agricultural calendar. Later we encounter itineraries, referring either to military or to trading expeditions and provide an indication of the extent of Babylonian geographical knowledge at an early date. The celestial globe had reinforced the belief in a spherical and finite universe such as Aristotle had described; the drawing of a circular horizon, however, from a point of observation, might have perpetuated the idea that the inhabited world was circular, as might also the drawing of a sphere on a flat surface.
Aristotle also believed that only the ocean prevented a passage around the world westward from the Straits of Gibraltar to India.
The result was that his observations served not merely to extend geographical knowledge about the places he had visited, but also to lay the foundation for the scientific use of parallels of latitude in the compilation of maps.
Many influential Romans both in the Republic and in the early Empire, from emperors downward, were enthusiastic Philhellenes and were patrons of Greek philosophers and scholars.
In this respect, Rome had provided a model for the use of maps that was not to be fully exploited in many parts of the world until the 18th and 19th centuries.
The maps of early man, which pre-date other forms of written communication, were attempts to depict earth distributions graphically in order to better visualize them; like those of primitive peoples, the earliest maps served specific functional or practical needs.
Excavations on this site revealed the foundations of a little church, with a fragment of a mosaic that contained the name a€?Zachariasa€?. What is certainly different is the place and prominence of maps in prehistoric times as compared with historical times, an aspect associated with much wider issues of the social organization, values, and philosophies of two very different types of cultures, the oral and the literate. They do not go so far as to record distances, but they do mention the number of nights spent at each place, and sometimes include notes or drawings of localities passed through. Another of a land, also in the north, where a man, who could dispense with sleep, might earn double wages, as there was hardly any night. There was, however, evidently no consensus between cartographic theorists, and there seems in particular to have been a gap between the acceptance of the most advanced scientific theories and their translation into map form. Maps were also frequently used purely for decoration; they furnished designs for Gobelins tapestries, were engraved on goblets of gold and silver, tables, and jewel-caskets, and used in frescoes, mosaics, etc. As in Greek and Roman inscriptions, some documents record the boundaries of countries or cities. He probably had the first account from some sailor who had visited the northern latitudes in summer; and the second from one who had done the like in winter. It was not until the 18th century, however, that maps were gradually stripped of their artistic decoration and transformed into plain, specialist sources of information based upon measurement.

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