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thirteenth century a wealth on details and did not belong to any distinct type of division fig 24 the central part of the ebstorf mappa mundi shows the square city of jerusalem the original map was destroyed in world war ii during the bombing of hanover a set of black and white photographs of the original map was taken in 1891 several color copies were made before its destruction in 1943 wikipedia 4 the last period has an overlap with the previous one and runs from 1209 to 1400 it is dominated by the work of franciscan monks influential names were roger bacon c 1214 1294 john duns scotus c 1265 1306 and william of occam c 1290 c 1349 the small but very important book de sphaera of john sacrobosco john of holywood is dated between 1220 30 and is therefore earlier than a book with the same title by robert grosseteste 1175 1253 the idea of a spherical world was well established it contradicts the opinion of nineteenth century authorities that the earth of the thirteenth century scholars was thought of as flat an exceptional relict of the fourfold conceptual approach to map making can be found in a schoolbook for young clergyman printed in 1475 in germany fig 25 fig 25 a late conceptual four fold world view from a woodcut in the rudimentum novitiorium published in 1475 by lucas brandiss in lübeck the top of the map is to the east oriens with the four rivers of paradise flowing from it at the center the holy land palestine and judea but no special reference is made to jerusalem the land ophir is in the south to the right auster and the pillars of hercules are visible to the bottom of the map west in strauss 1981 the rudimentum novitiorum lübeck 1475 in a colored version the book was re issued from new blocks from paris in 1488 and lyons in 1491 in shirley 2001 all these endeavors in map making reflected the basic need of humanity to locate themselves in a seemingly boundless space and draws attention to the problem of relation in the end it is the concept of division which shapes this relation and which makes it possible to bring structure in an otherwise incomprehensible environment the four directions north east south and west are now generally accepted as the basic division of place they are which is much less understood the living examples of the possibility to think in a structural spatial fourfold pattern andrews michael c 1925 the study and classification of medieval mappae mundi pp 61 76 in archeologia oxford lxxv 1925 26 arentzen jorg geerd 1984 imago mundi cartographica studien zur bildlichkeit mittelalterlicher welt und oekumene karten unter besonderer berucksichtigung des zusammenwirkens von text und bild wilhelm fink verlag munchen isbn 3 7705 2258 3 brincken von den anna dorothee 1970 ut describeretur univer sus orbis zur universal kartographie des mittelalters pp 249 278 in zimmermann albert hoffmann rudolf ed miscellanea mediaevalia band 7 methoden in wissenschaft und kunst des mittelalters walter de gruyter co berlin brown hanbury 1978 man and the stars oxford university press oxford isbn 0 19 851001 2 ann ronan library destombes marcel ed 1964 mappemondes ad 1200 1500 catalogue préparé par la commission des cartes anciennes de l union geographique internationale n israel amsterdam essling prince d 1909 les livres a figures venitiens de la fin du xve siecle et du commencement du xvie librairie leo s olschki florence librairie henri leclerc paris groenewegen frankfort h a 1951 arrest and movement an essay on space and time in the representational art of the ancient near east faber and faber limited london harley j b woodward david 1987 the history of cartography vol i cartography in prehistoric ancient and medieval europe and the mediterramean the university of chicago press chicago london haskins charles h 1924 1960 studies in the history of mediaeval science frederick ungar publishing co new york 1927 the renaissance of the twelfth century harvard university press cambridge mass miller konrad 1926 1986 mappae arabicae beihefte zum tübinger atlas des vorderen orients reihe b geisteswissenschaften nr 65 gaube heinz ed dr ludwig reichert verlag wiesbaden isbn 3 88226 293 1 shirley rodney w 2001 mapping of the world early printed world maps 1472 1700 early world press ltd riverside usa isbn 0 970351801 strauss l ed 1981 the illustrated bartsch 80 part i anonymous artists 1457 1475 abaris books new york isbn 0 91 3870 50 1 geplaatst in geen categorie tags de natura rerum geographic orientation plaats een reactie 8 orientation geplaatst op 1 juli 2013 door quadralectics the directions of the wind the orientation by the four winds is very old but its origin cannot be precisely indicated the greek seafarers used them and erathosthenes in his book geography mentioned the boreas apeliotes notos and zepyros he subdivided the earth by parallel east west and north south lines and could measure the circumference of the earth by these directions and the height of the sun hipparchus of nicaea c 165 c 127 bc amended erathothenes division of the earth in sixty parts by drawing climata lines at regular intervals 360 parts the modern degrees in that way it was possible to locate every place on earth by co ordinates ptolemy ad 90 168 provided in his geography the latitude and longitude of eight thousand places the importance of the winds was emphasized by andronicus of cyrrhus who built around 50 bc the octagonal tower of the winds in athens also called the horlogeion fig 26 fig 26 the tower of the winds or horlogium in athens greece photo in boardman 1993 orientation is fairly well documented in the maritime and shipping history every ship leaving a harbor and sailing at an empty sea away from the shoreline is comparable with a human mind on a tabula rasa the observer has to invent some sort of dynamic structural framework for guidance alternatively like daniel boorstin 1983 p 47 rightly put it in his book the discoverers when people set out to explore the oceans they found it more than ever necessary to know the heavens but to approach the heaven in an orderly way one has to take decisions over the type of division in a comprehensive composition fig 27 this wooden quadrant was built by paul hainzel burgomaster of augsburg and a friend of tycho brahe it is an illustration from tycho brahe s work astronomia instaurate mechanica 1598 many types of quadrants were built during the development of navigation and surveying tools in the sixteenth century a star was focused through the small rings e and d and the angle could be read at the quarter circle with a graduated scale h the whole contraption of the nineteen foot radius quadrant and a brass scale could turn from a platform without a reliable quadrant it was impossible to fix any of the cardinal points of the sky the position and movement of the sun and the stars were the most obvious points of references in maritime orientation the sun comes up at a certain point reaches it height and sinks to another point on the horizon the operative line was not that from n to s but that from e to w said eva taylor 1937 1957 p 23 a seaman oriented himself by facing the north the pole of heavens and spreading out his arms to east and west instruments were made to measure angles the simplest one is the measuring staff but more elaborated forms are the quadrant fig 27 the theodolite and the astrolabe fig 28 in the late sixteenth century these instruments found their apex in the armillary or a small scale model of the universe fig 28 the four parts of an astrolabe 1 mater round disc with graduation on the outer edge limbus divided in 360 degrees or 24 hours 2 the planisphere or tympana tables for different pole elevations 3 rete disk with fixed stars from zodiac 4 alhidade al hidada indicator turning around a fixed point not shown here the illustration to the lower right shows the backside of the astrolabe with additional tables from a manual made for the spanish king alfonso the sage around 1300 the astrolabe or star shooter is a quadrant to measure the height of stars compared to the earthly horizon dreier 1979 lehr 1981 one of the oldest descriptions of the instrument is by hermann the lame from reichenau who died in 1054 chaucer 1340 1400 wrote in 1391 a treatise for the astrolabium for his ten year old son lewis this is the oldest early scientific work in english the drawings in fig 28 were prepared for king alfonso the sage at the end of the thirteenth century in the thirteenth and fourteenth century the use of the astrolabe was sporadic but this changed drastically when the spirit of discovery took hold in the fifteenth century orontius fine 1532 issued many treatises and construction rules in the sixteenth century like the beautiful book protomathesis fig 29 this astrolabe is from the seventh tablet of the series sapihal al afakiyah pictures of the horizon a description of a persian astrolabe constructed for shah husain safawi around 1700 the seafarer could apart from the sun and the stars also rely on the winds as a sailing aid the spanish sailors on columbus crew says boorstin 1983 p 217 thought of direction not as degrees of compass bearings but as los vientos the winds portuguese sailors continued to call their compass card a rosa dos ventos a wind rose before the general use of the compass a direction was understood to be a certain wind blowing from a given direction windroses flowered even before the introduction of the compass as detailed indicators of direction based on a division of the circle in four eight twelve sixteen or even thirty two parts the ancient system of winds or plagae was essentially a system of division the greek geographer timosthenes a direct predecessor of erathosthenes knew the so called twelve wind system taylor 1937 noted in an article over matthew paris de ventis written on the last folio of the historia s albani cotton mss nero d 5 dated after 1250 the twelve fold division associated with the name of aristotle and later with that of the sea admiral timosthenes is an astronomer s system harmonizing with the twelve hours of the day and of the night the twelve signs of the zodiac and the twelve houses used in prognostication i e in general with the duodecimal numeration the division is related to the 360 degrees circle and angles of 60 30 15 and 5 degrees and therefore finally based on a combination of three and fourfold division the romans although lesser seafarers than the greek also use the twelve division erathosthenes abandoned the twelve wind system in favour of the eight wind system because it was too difficult for mariners brown 1949 1979 and hapgood 1966 1979 this may be true but another consideration can be put forward maybe this change came about by a shift in division thinking from triple four to dual four the eight wind system or one step further the sixteen fold division was generally used on navigation charts known as portolan maps this particular type of map making flourished in the fourteenth century and was used by sailors mostly in the mediterranean to chart their way from harbor to harbor the maps were based on a sixteen fold division quadruple four of the circle fig 30 the construction of the eight wind system of the portolan charts as given by livengood estes and woitkowski in hapgood 1966 1979 a circle is bisected eight times resulting in sixteen lines from the centre to the periphery at equal angles of 22 5 degrees horizontal and vertical lines through the intersections form a grid of sixteen squares geographical details like a coastline are marked within this grid the stages to construct this system by bisecting the circle four times fig 30 results in angles of 22 5 degrees hapgood 1966 1979 p 14 15 this procedure displays the ratiocinationis quadrivium as mentioned earlier 1 division four times division of a circle results in angles of 22 5 degrees 2 definition horizontal and vertical lines are drawn from the intersections of the angle lines with the circle this results in a grid of sixteen squares a theoretical framework 3 demonstration geographical landmarks are indicated on this grid 4 resolution the procedure of sixteen directions or plagae within a theoretical framework filled with empirical data enables an observer to known a location in a given context the aforementioned scheme has little to do with the elaborate mathematical projections employed by later map makers like gerard mercator 1512 1594 abraham ortelius 1527 1598 and the blaeu family to catch the spherical earth in a convenient flat plane it is a strictly theoretical approach to the communication between an observer and the environment based on an a priori definition of division it has simultaneously a philosophical connotation inherent to this choice this aspect is much less obvious in the scientific map making of later centuries it is important to realize that the orientations of the great portuguese and spanish discoverers originated in a theoretical division framework and not in any form of mathematical projection pedro de medina published in 1545 in valladolid spain his book arte del navegar and gives a sketchy but remarkably complete picture of the earth encompassed by eight winds fig 31 here we see the merger of a well developed theoretical division idea with an emerging mathematical approach based on projection the book was translated in french german english and italian and the map figures in the editions printed in venice in the years 1554 1555 and 1609 but not due to rivalry in the french edition fig 31 the world with eight winds an illustration of pedro de medina s book arte del navegar valladolid 1545 this fairly complete world picture in some sort of fantasy projection is surrounded by eight winds as indicators for the main directions the compass although known from the twelfth century was in its initial stages a rather crude instrument and did not contribute substantially to the geographical discoveries of the fourteenth and fifteenth century in fact it was surrounded by superstition and seen as a magical force alexander neckam 1157 1217 could write when the mariners cannot see the sun clearly in murky weather or at night and cannot tell which way their prow is tending they put a needle above a magnet which revolves until its point looks north and then stands still there might have been other than mechanical reasons for the initiation of the great journeys which resulted in the discovery of new lands it could well be that this urge was caused by a desire for delimitation for finding the end of the earth this spirit could only develop in a mind that valuates an awareness of boundaries in the first place a world without fixed limits is incomprehensible and unacceptable in a mind that operates on the lower division level so towards the end of the fifteenth century in the renaissance as the identity crisis of the european cultural history these limits had to be found at all costs that might be the true reason columbus set sail and maybe it would...
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