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77-523: The points of the compass are a set of horizontal, radially arrayed compass directions (or azimuths ) used in navigation and cartography . A compass rose is primarily composed of four cardinal directions — north , east , south , and west —each separated by 90 degrees , and secondarily divided by four ordinal (intercardinal) directions—northeast, southeast, southwest, and northwest—each located halfway between two cardinal directions. Some disciplines such as meteorology and navigation further divide

154-410: A Cartesian system ) is called the pole , and the ray from the pole in the fixed direction is the polar axis . The distance from the pole is called the radial coordinate or radius , and the angle is the angular coordinate , polar angle , or azimuth . In the cylindrical coordinate system, there is a chosen reference axis and a chosen reference plane perpendicular to that axis. The origin of

231-637: A meridian drawn between the north ( arctos ) and its opposite could be used to divide East from West. Homer already spoke of Greeks sailing with Ursa Major (or "Wagon"/"Wain") for orientation. The identification of the Pole Star (at that time, Kochab in the Ursa Minor ) as the better indicator of the North seems to have emerged a little later (it is said Thales introduced this, probably learned from Phoenician seafarers). Distinct from these cardinal points,

308-454: A branch of meteorology , the classical wind rose had only a tentative relationship with actual navigation . The Classical 12-point wind rose was eventually displaced by the modern compass rose (8-point, 16-point and 32-point), adopted by seafarers during the Middle Ages . It is uncertain when or why the human sense of geographic orientation and direction became associated with winds . It

385-462: A collective of north winds, the Boreae . It is said that the geographer Eratosthenes of Cyrene (c. 200 BCE), realizing that many winds presented only slight variations, reduced twelve winds down to eight principal winds. Eratosthenes's own work has been lost, but the story is reported by Vitruvius , who goes on to say Eratosthenes came to this conclusion in the course of measuring the circumference of

462-503: A guide for helmsmen. Prior to the modern three-figure method of describing directions (using the 360° of a circle), the 32-point compass was used for directions on most ships, especially among European crews. The smallest unit of measure recognized was 'one point', 1/32 of a circle, or 11 + 1 ⁄ 4 °. In the mariner's exercise of "boxing the compass", all thirty-two points of the compass are named in clockwise order. This exercise became more significant as navigation improved and

539-607: A later chapter, Pliny goes on to say that Aquilo, in the summer, turns into the Etesian winds, the periodic wind already referred to by Aristotle. Pliny also mentions, for the other half-winds, Phoenicias (for SSE, not Euronotus), Libonotus (SSW), and Thrascias (NNW). It is apparent Pliny had recently read Aristotle and sought to resurrect some of the abandoned Aristotelean names (Boreas/Aparctias, Meses, Etesian winds, Phoenicias, he even mentions Olympias and Sciron as local Greek winds), albeit they appear rather awkwardly when inserted into

616-629: A later note that "Caecias" is mentioned in Aristotle (but does not give it a position). Aquilo/Boreas seem well-enthroned at NE. Another surprise is the re-emergence of Eurus in the East, where it has not been seen since Homer. He seems to treat Eurus as a Latin name, giving the Aristotelean Apeliotes as the Greek equivalent, and reducing Subsolanus to a mere variant "from Roman sailors". With Eurus now absent in

693-499: A northwest wind and a southwest wind. Some have taken this to imply that Homer may have had as many as eight winds. However, others remain unconvinced, and insist Homer only had a four wind-rose. Writing several centuries later, Strabo (c. 10 BC) notes that some contemporaries took Homer's ambiguity to imply that the Homeric system may already anticipate the summer and winter distinction later made famous by Aristotle . This refers to

770-555: A reference plane that passes through the origin and is orthogonal to the zenith, and a fixed reference direction in that plane. Classical compass winds In the ancient Mediterranean world , the classical compass winds were names for the points of geographic direction and orientation, in association with the winds as conceived of by the ancient Greeks and Romans . Ancient wind roses typically had twelve winds and thus twelve points of orientation, sometimes reduced to eight or increased to twenty-four. Originally conceived as

847-665: A reference to Mount Olympus and the Sciros rocks in Megara . The remaining winds also seem to be geographical. Caecias ( καικίας ) means from Caicus, a river in Mysia , a region northeast of the Aegean. Lips ( λίψ ) means "from Libya ", to the southwest of Greece (although an alternative theory connects it to "leibo", λείβω , same root as libation , meaning pouring, because this wind brought rain). Phoenicias ( φοινικίας ) comes "from Phoenicia " (to

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924-602: A reference to the Mistral ) He also notes Iapyx (already mentioned, but first here explained as a local wind from Iapygia in Apulia ) and periodic regional Etesian winds and the "Prodromi" (NW fore-winds, in Greek, πρόδρομοι ). The "Vatican table" is a marble Roman anemoscope (wind-vane) dating from the 2nd or 3rd Century CE, held by the Vatican Museums . Divided into twelve equal sides, on each of its sides, it has inscribed

1001-487: A reference to the warm rains and storms brought from the south). Eurus and Zephyrus seem to come from "brightness" (q.v. Eos ) and "gloominess" ("zophos") respectively, doubtlessly a reference to sunrise and sunset . The archaic Greek poet Homer (c. 800 BC) refers to the four winds by name – Boreas, Eurus, Notos, Zephyrus – in his Odyssey , and in the Iliad . However, at some points, Homer seems to imply two more:

1078-485: A significant step in the evolution of the compass rose. Depending on how Ventorum Situs is dated, Timosthenes can be credited with turning Aristotle's asymmetric ten-wind compass into a symmetric twelve-wind compass, by introducing the SSW wind (Leuconotos/Libonotos) omitted by Aristotle and Theophrastus and assigning the compound "Euronotos" (already alluded to by Aristotle, no mention of Theophrastus's Orthonotos here) in place of

1155-410: Is " Quarto di Tramontana verso Greco "; and northeast-by-north is " Quarto di Greco verso Tramontana ". The table below shows how the 32 compass points are named. Each point has an angular range of 11 + 1 ⁄ 4 degrees where the azimuth midpoint is the horizontal angular direction (clockwise from north) of the given compass bearing; minimum is the lower (counterclockwise) angular limit of

1232-411: Is "Greco-Levante"; SSE is "Ostro-Scirocco", etc. The quarter winds are expressed with an Italian phrase, " Quarto di X verso Y" ( pronounced [ˈkwarto di X ˈvɛrso Y ] one quarter from X towards Y), or "X al Y" (X to Y) or "X per Y" (X by Y). There are no irregularities to trip over; the closest principal wind always comes first, the more distant one second, for example: north-by-east

1309-532: Is already in Timosthenes, but Aparctias's demotion from the N is novel). When he goes on to discuss half-winds, Pliny re-introduces Caecis as lying "between Aquilo and Subsolanus", thus restoring it effectively to its NE position. Evidently reading Aristotle, Pliny tries to insert long-lost Meses again "between Boreas (= Aquilo) and Caecis", thus placing Meses in a position that (in a modern 32-point compass) would be called " Northeast by north ". Confusing matters, in

1386-567: Is an attempt to derive the etymology of the winds. As they are often named after a particular locality from where they seem to blow, different places in the Hellenistic world have come up with variant local names for the winds. In the list given in the Ventorum Situs : The Greek-Roman physician Agathemerus (c. 250 CE), in his Geographia , gives the eight principal winds. But Agathemerus goes on to note that nearly five hundred years earlier,

1463-427: Is asymmetric. Specifically, the half-winds would be at 22½° on either side of the North, while the principal eight would be at 45° angles from each other. However, an alternative hypothesis is that they will be more equally spaced around 30° from each other. By way of guidance, Aristotle mentions that the easterly and westerly positions are that of the sun as seen on the horizon at dawn and at dusk at different times of

1540-462: Is centered at Athens , it has been calculated that this construction would yield a symmetric compass rose with approximately 30° angles all around. If set out on a compass card, Aristotle's system could be conceived of as a twelve-wind rose with four cardinal winds (N, E, S, W), four "solstitial winds" (loosely speaking, NW, NE, SE, SW), two "polar winds" (roughly NNW, NNE) and two "non-winds" (SSW, SSE). Aristotle explicitly groups Aparctias (N) and

1617-496: Is frequent reference to four cardinal directions . The names of the directions seem to be associated with physical landmarks for the ancient Israelites living in the region of Judea , e.g. East is referred to as kedem , which may derive from "edom" ("red"), and may be a reference to the color of the rising dawn , or the red sandstone cliffs of the Land of Edom to the east; North is referred to as saphon , from Mount Zaphon on

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1694-641: Is given by where θ is the angle ∠ P 1 P 2 P 3 . This formula uses the law of sines . If the three points are given by their coordinates ( x 1 , y 1 ) , ( x 2 , y 2 ) , and ( x 3 , y 3 ) , the radius can be expressed as The radius r of a regular polygon with n sides of length s is given by r = R n s , where R n = 1 / ( 2 sin ⁡ π n ) . {\displaystyle R_{n}=1\left/\left(2\sin {\frac {\pi }{n}}\right)\right..} Values of R n for small values of n are given in

1771-579: Is implied at several places in the Old Testament. "Four winds" are referred to in the Bible in several places. Kedem (East) is used frequently as the name of a scorching wind that blows from the east. It is related to the modern word קדימה‬ " kadima ", meaning "forward". There are several passages referring to the scattering of people "to all the winds". Unlike the Biblical Israelites,

1848-425: Is probable that for ancient settled populations, local physical landmarks (e.g. mountains, deserts, settlements) were the initial and most immediate markers of general direction ("towards the coast", "towards the hills", "towards the lands of Xanadu", etc.). Astral phenomena, in particular the position of the sun at dawn and dusk, were also used to denote direction. The association of geographic direction with wind

1925-634: Is said to have been built by Andronicus of Cyrrhus , of uncertain dates. From the style of the sculptures the tower is usually dated around 50 BC, not long before Varro and Vitruvius mention it. An alternative possibility is that it was part of the generosity of Attalus III of Pergamon (d. 131 BC) who built the Stoa of Attalus in the city. Either way, it is after Eratosthenes. It gives as its eight winds Boreas (not Aparctias, N), Caecias (NE), Apeliotes (E), Eurus (SE), Notos (S), Lips (SW), Zephyrus (W) and Sciron (NW, variant of Argestes). Boreas' reappearance in

2002-425: Is uncertain. Among tentative propositions is that Boreas might come from "boros", an old variant of "oros" ( Greek for "mountains", which were to the north geographically). An alternative hypothesis is that it may come from "boros" meaning "voracious". Another is that it comes from the phrase ἀπὸ τῆς βοῆς ("from the roar"), a reference to its violent and loud noise. Notos probably comes from "notios" ("moist",

2079-575: The Middle Ages (with no obvious connection to the twelve classical compass winds of the ancient Greeks and Romans). The traditional mariner's wind names were expressed in Italian , or more precisely, the Italianate Mediterranean lingua franca common among sailors in the 13th and 14th centuries, which was principally composed of Genoese ( Ligurian ), mixed with Venetian , Sicilian , Provençal , Catalan , Greek , and Arabic terms from around

2156-485: The Peripatetic school , in his On Weather Signs and "On Winds" (c. 300 BCE), adopted the same wind system as Aristotle, with only some slight differences, e.g. Theophrastus misspelled Thrascias as "Thracias" and seemed to distinguish between Apractias and Boreas (perhaps as " North by west " and "North" wind respectively). In the pseudo-Aristotelean fragment Ventorum Situs (often attributed to Theophrastus ), there

2233-595: The Phoenicias wind for the SSE (blows locally in some places), but suggests nothing for SSW. So, seen this way, Aristotle really has an asymmetric windrose of ten winds, as two winds are effectively missing or only local. (Variants: Olympias ( ὀλυμπίας ), Sciron ( σκίρων ) Notice that in the Aristotelean system, old Eurus is shunted from its traditional position in the cardinal East by Apeliotes ( ἀπηλιώτης ), meaning "from

2310-474: The clockwise direction and "CCW" counterclockwise . The final three columns show three common naming conventions: No "by" avoids the use of "by" with fractional points. Colour coding shows whether each of the three naming systems matches the "CW" or "CCW" column. The traditional compass rose of eight winds (and its 16-wind and 32-wind derivatives) was invented by seafarers in the Mediterranean Sea during

2387-585: The meteorological properties of the winds, e.g. that the winds on the NW-SE axis are generally dry, while the NE-SW winds are wet (NE producing heavier clouds than SW). N and NNE bring snow. Winds from the whole northwestern sector (NW, NNW, N) are described as cold, strong, cloud-clearing winds that can bring lightning and hurricanes with them. Aristotle also makes special note of the periodic bending summer Etesian winds, which comes from different directions depending on where

Points of the compass - Misplaced Pages Continue

2464-403: The radial distance or radius , while the angular coordinate is sometimes referred to as the angular position or as the azimuth . The radius and the azimuth are together called the polar coordinates , as they correspond to a two-dimensional polar coordinate system in the plane through the point, parallel to the reference plane. The third coordinate may be called the height or altitude (if

2541-468: The radius of a graph is the minimum over all vertices u of the maximum distance from u to any other vertex of the graph. The radius of the circle with perimeter ( circumference ) C is For many geometric figures, the radius has a well-defined relationship with other measures of the figure. The radius of a circle with area A is The radius of the circle that passes through the three non- collinear points P 1 , P 2 , and P 3

2618-465: The true north ( Pole Star , Septentrio). Pliny the Elder in his Natural History (C. 77 CE) after noting that twelve was an exaggeration, goes on to note that the "moderns" have reduced it to eight. He lists them as Septentrio (N), Aquilo (NNE), Subsolanus (E), Vulturnus (SE), Auster (S), Africus (SW), Favonius (W) and Corus (NW). Notice that Caecias (NE) is not part of this octet. Instead, Pliny puts

2695-510: The 32-wind compass rose comes from the eight principal winds, eight half-winds, and sixteen quarter-winds combined, with each compass point at an 11 + 1 ⁄ 4 ° angle from the next. By the middle of the 18th century, the 32-point system had been further extended by using half- and quarter-points to give a total of 128 directions. These fractional points are named by appending, for example, ⁠ 1 / 4 ⁠ east, ⁠ 1 / 2 ⁠ east, or ⁠ 3 / 4 ⁠ east to

2772-503: The Elder , are adamant that Homer mentioned only four winds. Hesiod (c. 700 BCE) in his Theogony (c. 735) gives the four winds mythical personification as gods, the Anemoi ( Ἄνεμοι ), the children of the Titan gods Astraeus (stars) and Eos (dawn). But Hesiod himself refers to only three winds by name – Boreas , Notos and Zephyrus – which he called the "good winds" and the "children of

2849-544: The Mediterranean basin. This Italianate patois was used to designate the names of the principal winds on the compass rose found in mariners' compasses and portolan charts of the 14th and 15th centuries. The traditional names of the eight principal winds are: Local spelling variations are far more numerous than listed, e.g. Tramutana, Gregale, Grecho, Sirocco, Xaloc, Lebeg, Libezo, Leveche, Mezzodi, Migjorn, Magistro, Mestre, etc. Traditional compass roses will typically have

2926-456: The North slot in place of Aparctias is notable. The winds are personified in stone reliefs as gods ( Anemoi ) at the top of the faces. Vitruvius says the tower was topped with a weather vane . The Greek wind system was adopted by the Romans, partly under their Greek nomenclature, but increasingly also under new Latin names. Roman poet Virgil , in his Georgics (c. 29 BCE) refers to several of

3003-548: The North, Boreas shunted to NNE, Euronotus instead of Phoenicias, Circius as alternate of Thrascias). The differences of De Mundo from Timosthenes are that (1) it introduces Libophoenix as another name for Libonotos (Leuconotos not mentioned); (2) two alternates to Argestes are mentioned – Iapyx (as in the Ventorum ) and Olympias (as in Aristotle) (Timosthenes mentions no variants for this wind), (3) like Aristotle, De Mundo refers to

3080-589: The SE, Euronotus (previously SSE) is promoted to the vacant SE position. Finally, a new name, Caurus , is introduced as the NW wind. This is almost certainly a misspelling of Corus (NW). Aulus Gellius gives some information about local winds. He mentions Circius as a local wind in Gaul , known for its dizzying, circular motion, and notes its alternate spelling Cercius in Hispania (probably

3157-690: The Sun" or from "the heat of the Sun". Old Boreas is mentioned only as an alternative name to Aparctias ( ἀπαρκτίας ), which means "from the Bear", that is, the Ursa Major , the Arctic Circle . Among the new winds are the Argestes ( ἀργέστης ) meaning "clearing" or "brightening", a reference to the northwest wind sweeping away clouds. Argestes's variants, Olympias ( ὀλυμπίας ) and Sciron ( σκίρων ) are local Athenian names,

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3234-489: The United States Navy to box from north and south toward east and west, with the exception that divisions adjacent to a cardinal or inter-cardinal point are always referred to that point." The Royal Navy used the additional "rule that quarter points were never read from a point beginning and ending with the same letter." Compass roses very rarely named the fractional points and only showed small, unlabelled markers as

3311-425: The ancient Greeks had four winds ( Anemoi ). The peoples of early Greece reportedly conceived of only two winds – the winds from the north, known as Boreas ( Βορέας ), and the winds from the south, known as Notus ( Νότος ). But two more winds – Eurus ( Εὖρος ) from the east and Zephyrus ( Ζέφυρος ) from the west – were added soon enough. The etymology of the names of the four archaic Greek winds

3388-444: The cardinal winds, e.g. as western winds bring rain, then when Homer says a "stormy Boreas" he means a different wind from a "loud Boreas" (i.e. wet north = NW, loud north = N) Nonetheless, while it seems that Homer may have realized that there were more than four winds, he did not use those epithets systematically enough to permit us to conclude that he also embraced a six- or eight-point windrose. Other classical writers, e.g. Pliny

3465-709: The compass point; and maximum is the upper (clockwise) angular limit of the compass point. Navigation texts dating from the Yuan , Ming , and Qing dynasties in China use a 24-pointed compass with named directions. These are based on the twelve Earthly Branches , which also form the basis of the Chinese zodiac. When a single direction is specified, it may be prefaced by the character 單 (meaning single) or 丹 . Headings mid-way in-between are compounds as in English. For instance, 癸子 refers to

3542-484: The compass with additional azimuths. Within European tradition, a fully defined compass has 32 "points" (and any finer subdivisions are described in fractions of points). Compass points or compass directions are valuable in that they allow a user to refer to a specific azimuth in a colloquial fashion, without having to compute or remember degrees. The names of the compass point directions follow these rules: In summary,

3619-673: The contemporary 12-wind compass schema. In his Attic Nights (written c. 159), the Athens -raised Latin writer Aulus Gellius , possibly inspired by the Tower of the Winds in that city, reduces the Latin rose to from twelve to eight winds, the principal winds, for which he gives both the Latin and Greek terms. He lists them as: Among the novelties is the disappearance of Caecias (NE, like in Pliny), although he does make

3696-407: The direction halfway between point 子 and point 癸 , or 7 + 1 ⁄ 2 °. This technique is referred to as a double-needle ( 雙針 ) compass. Radius If an object does not have a center, the term may refer to its circumradius , the radius of its circumscribed circle or circumscribed sphere . In either case, the radius may be more than half the diameter, which is usually defined as

3773-448: The early Greeks maintained two separate and distinct systems of cardinal directions and winds, at least for a while. Astral phenomena were used to define four cardinal points : arctos ( ἄρκτος , "bear", the Ursa Major , for North), anatole ( ἀνατολή , "sunrise" or eos "dawn", East), mesembria ( μεσημβρία , "noon", South) and dysis ( δύσις , "sunset" or hesperus , "evening", West). Heraclitus , in particular, suggests that

3850-411: The earth, and felt there were really only eight equally sized sectors, and that other winds were but local variations of these eight principal winds . If true, that would make Eratosthenes the inventor of the eight-wind compass rose . Eratosthenes was a disciple of Timosthenes and is said to have drawn principally from his work. But they part ways on this. Both recognized that Aristotle's ten-wind rose

3927-543: The fact that the "east" (sunrise) and "west" (sunset) are not stable on the horizon, but depend on the season, i.e. during the winter, the sun rises and sets a little further south than in the summer, Consequently, the Homeric system may have had six winds – Boreas (N) and Notos (S) on the meridian axis, and the other four on diagonals: Zephyrus (NW), Eurus (NE), Apeliotes (SE) and Argestes (SW). Strabo, quoting Posidonius notes that Homer sometimes used epithets of qualitative attributes to append ordinal directions to

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4004-562: The first Greek to go beyond treating these "winds" merely as meteorological phenomena and to begin viewing them properly as points of geographic direction. Timosthenes (through Agathemerus) assigns each of the 12 winds to geographical locations and peoples (relative to Rhodes ): Modern scholars to conjecture that Timosthenes, in his lost periplus , might have made ample use of these winds for sailing directions (which may help explain Agathemerus's eagerness to credit Timosthenes for "inventing"

4081-523: The half- and quarter-point system increased the number of directions to include in the 'boxing'. Points remained the standard unit until switching to the three-figure degree method. These points were also used for relative measurement, so that an obstacle might be noted as 'two points off the starboard bow', meaning two points clockwise of straight ahead, 22 + 1 ⁄ 2 ° This relative measurement may still be used in shorthand on modern ships, especially for handoffs between outgoing and incoming helmsmen, as

4158-480: The half-wind Aquilo (NNE) there instead. It seems Pliny is aware Aquilo is a half-wind, because since he says it lies "in between Septentrio and the summer sunrise" (although in a later chapter he places it at the summer sunrise). If the first version is taken, this means Pliny's eight-wind compass is asymmetric. Pliny goes on to mention that Aquilo is also "named Aparctias and Boreas" (the Boreas identification with NNE

4235-522: The half-winds Thrascias (NNW) and Meses (NNE) together as "north winds" and Argestes (NW) and Zephyrus (W) together as "west winds" — but he goes on to note that both the north and west winds could be classified as "generally northerly" ( Boreae ), since they all tend to be cold. Similarly Lips (SW) and Notos (S) are "south winds" and Eurus (SE) and Apeliotes (E) are "east winds", but once again, both south and east winds are "generally southerly" ( Notiae ) because are all relatively warm (Aristotle reasons that as

4312-399: The initials T, G, L, S, O, L, P, and M on the main points. Portolan charts also colour-coded the compass winds: black for the eight principal winds, green for the eight half-winds, and red for the sixteen quarter-winds. Each half-wind name is simply a combination of the two principal winds that it bisects, with the shortest name usually placed first, for example: NNE is "Greco-Tramontana"; ENE

4389-520: The local Phoenicias (SSE). His highlighting of the Italian "Circius" as a major variant of Thrascias (NNW) could be the first indication of the notorious Mistral wind of the west Mediterranean. Another major change in Timoesthenes is that he shunts Boreas out of the North position and into NNE (replacing Meses) – which will become customary in later authors. Timosthenes is also significant for being perhaps

4466-408: The loss of granularity is less significant than the brevity and simplicity of the summary. The table below shows how each of the 128 directions are named. The first two columns give the number of points and degrees clockwise from north. The third gives the equivalent bearing to the nearest degree from north or south towards east or west. The "CW" column gives the fractional-point bearings increasing in

4543-402: The maximum distance between any two points of the figure. The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it. The inner radius of a ring, tube or other hollow object is the radius of its cavity. For regular polygons , the radius is the same as its circumradius. The inradius of a regular polygon is also called apothem . In graph theory ,

4620-518: The morning" (engendering a little confusion, as it might be read as they were all easterly winds – although curious that Eurus is not among them). Hesiod refers to other "bad winds", but not by name. The Greek physician Hippocrates (c. 400 BC), in his On Airs, Water and Places , refers to four winds, but designates them not by their Homeric names, but rather from the cardinal direction from which they blow (arctos, anatole, dusis, etc.) He does, however, recognize six geographic points – north, south and

4697-404: The name of one of the 32 points. Each of the 96 fractional points can be named in two ways, depending on which of the two adjoining whole points is used, for example, N ⁠ 3 / 4 ⁠ E is equivalent to NbE ⁠ 1 / 4 ⁠ N. Either form is easily understood, but alternative conventions as to correct usage developed in different countries and organisations. "It is the custom in

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4774-561: The navigator Timosthenes of Rhodes (c. 282 BCE) had developed a system of 12 winds by adding four winds to the eight. (Agathemerus is, of course, incorrect – Aristotle had at least ten winds, not eight). Timosthenes's list (according to Agathemerus) was Aparctias (N), Boreas (not Meses, NNE), Caecias (NE), Apeliotes (E), Eurus (SE), "Phoenicias is also called Euronotos" (SSE), Notos (S), "Leuconotos alias Libonotos" (first mention, SSW), Lips (SW), Zephyrus (W), Argestes (NW) and "Thrascias alias Circius" (NNW). In many ways, Timosthenes marks

4851-461: The northern edge of Syria, South is often negev , from the Negev desert to the south, and West is yam ("sea", meaning the Mediterranean Sea ). Orientation seems to be to the East, in the direction of the rising sun, with the result that the terms kedem , saphon and negev became generalized with "facing", "left" and "right" side of anything. The association of cardinal directions with winds

4928-442: The observer lives. Aristotle had aggrandized the wind system beyond Homer to ten winds, but he left it unbalanced. It would be left to subsequent geographers to either add two more winds (to SSW and SSE) to make it into a symmetric 12-wind compass (as Timosthenes would do), or subtract two winds (NNW and NNE) to make it into a symmetric 8-wind compass (as Eratosthenes would do). Theophrastus of Eresos, Aristotle's successor in

5005-475: The observer's position. This was likely furthered by sailors who, far from landmarks at sea, nonetheless recognized a particular wind by its qualities and referred to it by a familiar name. The final step, completing the circle, was to use the proper names of the winds to denote general cardinal directions of the compass rose . This would take a little longer to work itself through. In the Hebrew Bible , there

5082-411: The reference plane is considered horizontal), longitudinal position , or axial position . In a spherical coordinate system, the radius describes the distance of a point from a fixed origin. Its position if further defined by the polar angle measured between the radial direction and a fixed zenith direction, and the azimuth angle, the angle between the orthogonal projection of the radial direction on

5159-412: The southeast of Greece) and Thrascias ( θρασκίας ) from Thrace (in Aristotle's day, Thrace covered a larger area than today, including the north-northwest of Greece). Finally, Meses ( μέσης ) might simply mean "middle", presumably because it was a half-wind. The implication of reading Thrascias and Meses as half-winds, and the others as principal winds, is that this implies Aristotle's construction

5236-589: The summer and winter risings and settings – using the latter to set the boundaries for the four general winds. The ancient Greek philosopher Aristotle , in his Meteorology (c. 340 BCE), introduced a ten-to-twelve wind system. One reading of his system is that there are eight principal winds : Aparctias (N), Caecias (NE), Apeliotes (E), Eurus (SE), Notos (S), Lips (SW), Zephyrus (W) and Argestes (NW). Aristotle then goes on to add two half-winds , Thrascias (NNW) and Meses (NNE), noting that they "have no contraries". Later, however, Aristotle suggests

5313-448: The sun rises in the east, then it heats east winds longer than west winds). With this general classification, Aristotle manages to account for the archaic Greek two-wind system. The exception to this system is Caecias (NE), which Aristotle notes is "half north and half east", and thus neither generally northern nor generally southern. The local Phoenicias (SSE), is also designated as "half south and half east". Aristotle goes on to discuss

5390-417: The system is the point where all three coordinates can be given as zero. This is the intersection between the reference plane and the axis. The axis is variously called the cylindrical or longitudinal axis, to differentiate it from the polar axis , which is the ray that lies in the reference plane, starting at the origin and pointing in the reference direction. The distance from the axis may be called

5467-412: The table. If s = 1 then these values are also the radii of the corresponding regular polygons. The radius of a d -dimensional hypercube with side s is The polar coordinate system is a two - dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction. The fixed point (analogous to the origin of

5544-425: The twelve winds are: (for the derivation of the Latin etymologies, see the section on Isidore of Seville below). Oddly, Seneca says the meridian line arises from Euronotus (SSE), not Auster (S), and that the "highest" point in the north is Aquilo (NNE), not Septentrio (N). This might imply an awareness of magnetic declination , the difference between the magnetic north ( compass north, in this case Aquilo) and

5621-432: The twelve winds). (Timosthenes's geographic list above is reproduced almost verbatim centuries later, in the 8th-century work of John of Damascus and a Prague manuscript from the early 1300s.) The pseudo-Aristotelean work De Mundo (normally attributed to an anonymous copier of Posidonius , probably written between 50 BCE and 140 CE), the winds are named practically identically to Timosthenes (e.g. Aparctias alone in

5698-415: The winds by their old Greek names (e.g. Zephyrus, Eurus, Boreas), and introduces a few new Latin names – notably, "black Auster", "cold Aquilo" and "frigid Caurus". The Roman writer Seneca , in his Naturales quaestiones (c. 65 CE), mentions the Greek names of some of the major winds, and goes on to note that Roman scholar Varro had said there were twelve winds. As given by Seneca, the Latin names of

5775-404: The year. Using his alphabetical notation, Aristotle notes that during the summer solstice the sun rises at Z (Caecias) and sets at E (Argestes); during the equinox , it rises at B (Apeliotes) and sets at A (Zephyrus), and finally during the winter solstice it rises at Δ (Eurus) and sets at Γ (Lips). So drawn on a compass rose, Aristotle's explanation yields four parallels: Assuming the viewer

5852-408: Was another source. It was probably farming populations, attentive to rain and temperature for their crops, that noticed the qualitative differences in winds – some were humid, others dry, some hot, others cold – and that these qualities depended on where the wind was blowing from. Local directional names were used to refer to the winds, eventually giving the wind itself a proper name , irrespective of

5929-407: Was unbalanced, but while Timosthenes restored balance by adding two winds to make it a symmetric twelve, Eratosthenes deducted two winds to make it a symmetric eight. It seems that, in practical appeal, Eratosthenes's reduction may have won the day. The famous octagonal " Tower of the Winds " in Athens exhibits only eight winds rather than the ten of Aristotle or the twelve of Timosthenes. The tower

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