History.

Classical antiquity.

The oldest piers of the bridge were probably laid when the Via Aurelia was constructed in the mid-2nd century BC. According to Titus Livius, there existed a bridge in the same location as the Pons Aemilius in 192 BC. The first stone bridge was constructed by Censor Marcus Fulvius Nobilior several years after that, in 179 BC (although it was not completed until 151 BC). The bridge's piers date from this early period, although its arches were constructed by Scipio Aemilianus and L. Mummius in 142 BC. The bridge kept its place for several hundred years, although it was repaired and rebuilt both by Augustus, and later by Emperor Probus in AD 280.

Middle ages.

After the collapse of the Roman Empire, the bridge was damaged several times by floods, with each flood taking a greater and greater toll on the overall structure. It was first severely damaged in AD 1230, after which it was rebuilt by Pope Gregory XI. Later, the bridge was more seriously damaged by the flood of 1557, but again was later rebuilt by Pope Gregory XIII; the remnants of the bridge today still bear Latin inscriptions detailing Gregory XIII's renovation of the bridge. Finally, floods in 1575 and 1598 carried the eastern half away, resulting in its abandonment as a functioning bridge for several centuries. For many years, it was used as a fishing pier. In 1853, Pope Pius IX had the remnants of the bridge connected to the mainland via an iron footbridge, but the heavy metal weakened the structural integrity of the stone. The remaining half was demolished in 1887 to make room for the Ponte Palatino, leaving behind only one arch that remains to this day.

The Pons Aemilius (), today called Ponte Rotto, is the oldest Roman stone bridge in Rome, Italy. Preceded by a wooden version, it was rebuilt in stone in the 2nd century BC. It once spanned the Tiber, connecting the Forum Boarium with Trastevere; a single arch in mid-river is all that remains today, lending the bridge its name "Ponte Rotto" ("Broken bridge").

埃米利乌斯桥 (Pons Aemilius,),今天称为“断桥”(Ponte Rotto),是意大利罗马最古老的古罗马石桥。此前有一个木桥,在公元前2世纪改建为石桥。它曾经跨越台伯河,连接屠牛广场与特拉斯提弗列。今天仅存一个在河中央的桥拱。


Historical usage.

Not all states gave their naval commanders such a title. Athens, for instance, placed its fleet under the command of generals ("strategoi") holding the same title as those who commanded its land forces. Such command structures reflected the fact that, especially early in the Classical period, fleets operated in close conjunction with land forces, and indeed, the title of navarch did not begin to appear until the time of the Peloponnesian War, when fleets began to operate more independently. This separate title was originally used in cities that lacked an established naval tradition, Sparta being the most prominent, but entered broader use later, being adopted by the navies of the Hellenistic era states such as Macedon, Syracuse, Ptolemaic and Seleucid Empire, Achaean League, and Rhodes.  At Sparta and many other city-states, the position was held for one year only (a situation that compelled the Spartans to resort to an elaborate legal fiction when they wished to reinstate Lysander for more than one year in command). Admirals of despotic or monarchic states, however, could serve for years at a time. At Sparta, the position, unlike most high-level offices, was available to men from outside the Spartiate class; Lysander, the most famous occupant of the office, was a beneficiary of this rule.  The Latinisation'was used by the Roman Navy for its squadron commanders. The Greek-speaking Byzantines sometimes used the term to designate the captains of ships; the terms "drungarios" or'were used to designate their admirals.

Modern Greece.

In the modern Hellenic Navy, "" is the highest rank, equivalent to full admiral. All but one of the remaining flag ranks are also derivations of this word: (, "deputy-admiral") is the equivalent to vice admiral and (, "under-admiral"), equivalent to rear admiral, while is the equivalent of commodore. The same ranks are also used by the Hellenic Coast Guard. The rank of full is held in active service only by the Chief of the General Staff of National Defence, when he is a naval officer, and given to the Chiefs of the Hellenic Navy General Staff on retirement. Under the Greek monarchy, the five-star rank of (), equivalent to grand admiral or admiral of the fleet, existed, and was held only by the reigning monarch (Kings George II, Paul and Constantine II).

Navarch (, ) is an Anglicisation of a Greek word meaning "leader of the ships", which in some states became the title of an office equivalent to that of a modern admiral.

海军都统(Navarch),是赋予古希腊指挥军舰的军官的称号。它的古希腊语名为,源于(“船”)和(“指挥”)。在斯巴达,这是一个重要的官衔,可以指挥整只舰队。雅典也有同样称呼的军官。在马其顿和希腊化时期的各个王国,比如塞琉古王朝和托勒密王朝中,该职即为海军司令。例如在围攻提尔的时候,亚历山大大帝的称号就是马其顿舰队的海军都统。在古罗马时代,海军都统是海军一个连的指挥。


Biography.

Ulitskaya was born in the town of Davlekanovo in Bashkiria and grew up in Moscow where she received a degree in genetics from the Moscow State University. Having worked in the field of genetics and biochemistry, Ulitskaya began her literary career by joining the Jewish drama theatre as a literary consultant. Her first published short fiction appeared in 1990. Today, Lyudmila Ulitskaya divides her time between Moscow and Israel.

Fiction.

Style.

In her fiction, Ulitskaya seemingly describes and observes her characters at an equal distance from each one. Rather than going in for character development or delving into the tortured workings of her characters’ psyches otherwise perceived as the hallmark of Russian writing, Ulitskaya favors capsule descriptions, though she acknowledges that her characters are tortured. Generally speaking, she makes little use of dialogue. Masha Gessen, in her tribute article in "The New Yorker" in October 2014, finds that Ulitskaya's writing makes for compelling, addictive reading. Gessen reports that she was driven entirely by the desire to learn what happens next.

Themes.

Among her interlinked themes are: the need for religious and ethnic tolerance; the problem of the intelligentsia in Soviet culture; how women shape new gender roles in society; and everyday life as a literary subject.

Other activity.

Ulitskaya authored two movie scripts produced in the early 1990s: "The Liberty Sisters" (Сестрички Либерти, 1990) and "A Woman for All" (Женщина для всех, 1991). She regularly publishes commentary on social issues and is actively involved in philanthropic projects increasing access to literature. In March 2014 Ulitskaya was among the key speakers at the Moscow Anti-War demonstration.

Reception.

Ulitskaya's first novella, "Sonechka" (Сонечка), published in "Novy Mir" in 1992, almost immediately became extremely popular, and was shortlisted for the Russian Booker Award. Her works have been translated into several languages including English, and received several international and Russian literary awards, including the Russian Booker for "The Kukotsky Enigma" (Казус Кукоцкого; 2001). Ulitskaya was the first woman to receive this distinguished prize.  In Germany her novels have been added to bestseller lists thanks to the featuring of her works on a television program hosted by literary critic. Today her writing is much admired by the general reading public and critics in Russia and many other countries.

Lyudmila Evgenyevna Ulitskaya (, born February 21, 1943) is an internationally acclaimed modern Russian novelist and short-story writer who, in 2014, was awarded the prestigious Austrian State Prize for European Literature for her oeuvre. In 2006 she published "Daniel Stein, Interpreter" (Даниэль Штайн, переводчик), a novel dealing with the Holocaust and the need for reconciliation between Judaism, Christianity, and Islam. Ulitskaya herself belongs to a group of people formed by the realities of the former Soviet Union, who see themselves ethnically and culturally as Jews, while having adopted Christianity as their religion.

柳德米拉·乌利茨卡娅(,1943年-2月21日)是一位俄罗斯小说家和短篇小说家,她的作品在2014年获得奥地利国家欧洲文学奖。2006年,她出版《丹尼尔·斯坦》(Даниэль Штайн, переводчик),这本小说涉及大屠杀及犹太教、基督教和伊斯兰教之间的和解。 乌里特斯卡娅在族裔和文化上将自己视为犹太人,同时将基督教作为其宗教信仰。


第7号交响曲 (肖斯塔科维奇)

Length and form.

Shostakovich’s longest symphony, and one of the longest in the whole repertory, typically takes some 75 minutes to perform — but there have been wide interpretive differences over the years: Leonard Bernstein’s acclaimed 1988 recording stretches to 85 minutes. The work has four movements. Shostakovich at first gave each of them a title — "“War,” “Reminiscence,” “Home Expanses”" and "“Victory,”" respectively — but he soon withdrew these and left the movements with their tempo markings alone:

I. Allegretto.

This is in modified sonata form and lasts for around half an hour; there are the usual two contrasting subjects, but no development section, this being replaced by the 'invasion' theme. It begins with a rousing, majestic theme played by all the strings and later echoed by the woodwinds. The theme rises in pitch through the first moments of the piece, with octave-long runs in the strings. This is followed by a slower, more tranquil section driven by flutes and lower strings, which peters out only to be replaced — slyly — by the "invasion" march: a 22-bar, snare-drum-led, bolero-like ostinato that will pervade much of the movement. (The march is derived from "Da geh' ich zu Maxim" from Franz Lehár's "The Merry Widow" for its latter half and

II. Moderato (poco allegretto).

This is the symphony's shortest movement. Shostakovich referred to it as both a scherzo and a lyric intermezzo. It begins in the latter vein with a quiet, playful theme in the strings. Some aspects of the interplay of the violins are evocative of a fugue. Moments later, a solo oboe

III. Adagio.

The third movement (15–20 minutes) is structured much like the second, with a slow initial theme, a faster middle section that evokes the first movement, and a recapitulation of the initial theme. Shostakovich stated elsewhere that he had hoped to portray Leningrad by twilight, its streets and the embankments of the Neva River suspended in stillness. Woodwinds begin with slow, sustained notes, accentuated by the horns. This simple theme cadences, and is

IV. Allegro non troppo.

This begins with a quiet, searching melody in the strings that slowly rises in pitch. The high strings hold the high notes, and are joined briefly by woodwinds. The low strings suddenly begin a quick march-like tune that is answered by increasingly frantic violins and point-like interjections from the rest of the orchestra. This section gathers frenzy for several minutes. A brief break comes in the form of a transition passage with repetitive three-note figures played by high strings, accented by slap "pizzicati" in the cellos

Instrumentation.

The work is written

Overview.

Composition.

"Music about terror".

There are conflicting accounts as to when Shostakovich began the symphony. Officially, he was said to have composed it in response to the German invasion. Others, such as Rostislav Dubinsky, say that he had already completed the first movement a year earlier. The composer stated, according to "Testimony", that he had planned the symphony before the German attack and that he had "other enemies of humanity" in mind when he composed the "invasion theme" of the first movement. He had no problem calling the work the "Leningrad" Symphony. "Which Leningrad?" became the question after the publication of "Testimony" in the West. The Leningrad that Shostakovich reportedly had in mind was not the one that withstood the German siege. Rather, it was the one "that Stalin destroyed and Hitler merely finished off." However, the authenticity of the US-published book is very much disputed.  The Leningrad Symphony Orchestra announced the premiere of the Seventh Symphony for its 1941–1942 season. The fact this announcement was made before the German invasion would seem to confirm the statement in "Testimony". Shostakovich did not like talking about what he called "creative plans,"

"Inquisition for blood".

Regardless of when Shostakovich initially conceived the symphony, the Nazi attack and consequent relaxing of Soviet censorship gave Shostakovich the hope of writing the work for a mass audience. A model on how to do this was Igor Stravinsky's "Symphony of Psalms." Stravinsky's compositions held considerable influence over Shostakovich and he had been deeply impressed with this particular work. Moreover, Stravinsky had initially set the Russian text of the Psalms, only later switching to Latin. As soon as Shostakovich received the score, he transcribed it for piano four-hands. He often performed this arrangement with students in his composition class at Leningrad Conservatory.  Shostakovich's plan was for a single-movement symphony, including a chorus and a requiem-like passage for a vocal soloist, with a text taken from the Psalms of David. With the help of his best friend, critic Ivan Sollertinsky, who was

"Invasion" theme.

Something else Shostakovich played for his composition students were the 12 variations of what later became known as the "invasion" theme. This has been taken historically, especially in the West, as portraying the invading "Wehrmacht", and was listed as such in the official program. For many years this was considered irrefutable. New information now casts some doubt. For instance, musicologist Ludmila Mikheyeva (who is also Ivan Sollertinsky's daughter in law) maintains that Shostakovich played the theme and its variations for his students before the war with Germany began.  While the word "invasion" was used by commentators in numerous articles and reviews, Shostakovich never used it to describe the episode or theme. He tried to evade the point in his

Tensions not resolved.

Two weeks before he planned to complete the symphony-requiem, Shostakovich played what he had finished to date for Sollertinsky, who was being evacuated with the Leningrad Philharmonic. While playing the music, Shostakovich realized that what he had written was not a complete work in itself but actually the beginning of something much larger, since the tensions brought up in the symphony-requiem had not been resolved. The question now became whether to stay in the city to continue working or to evacuate and resume the work after a long hiatus. By the time he decided to evacuate, it was too late—the Germans had cut off the rail link to the city. He and his family were trapped.  On 2 September, the day the Germans

Premières.

The world première was held in Kuybyshev on 5 March 1942. The Bolshoi Theatre Orchestra, conducted by Samuil Samosud, gave a rousing performance that was broadcast across the Soviet Union and later in the West as well. The Moscow première took place on 29 March 1942 in the Columned Hall of the House of Unions, by a joined orchestra of the Bolshoi Orchestra and the All-Union Radio Orchestra.  The microfilmed score was flown to Tehran and travelled to the West in April 1942. The symphony received its broadcast première in Europe by Sir Henry J. Wood and the London Philharmonic Orchestra on 22 June 1942 in London, and concert

Reception.

In Russia.

At the first hearings of the Seventh, most listeners wept. This was true even when Shostakovich played the piece on the piano for friends. The requiem pages of the first movement made a special impression, much as the Largo of his Fifth Symphony had done. Some scholars believe that, as he had done in the Fifth, Shostakovich gave his audience a chance to express thoughts and suffering that, in the context of the Great Purges, had remained hidden and accumulated over many years. Because these previously hidden emotions were expressed with such power and passion, the Seventh became a major public event. Alexei Tolstoy, who played a pivotal role in the life of the Fifth Symphony, was the first to note the significance of the spontaneous reaction to the Seventh. After hearing an orchestral rehearsal of it, Tolstoy wrote a highly positive review of the work for "Pravda".  Tolstoy's actions became instrumental in the life of the

In the West.

Shostakovich had been known in the West before the war. When news of the Seventh quickly spread in the British and American press, the composer's popularity soared. During the war, the work was very popular both in the West and in the Soviet Union as the embodiment of the fighting Russian spirit. The American premiere, in July 1942, was by the NBC Symphony Orchestra conducted by Arturo Toscanini, broadcast on radio by NBC and preserved on transcription discs; RCA issued the recording on LP in 1967 and later reissued it on CD. The symphony was played 62 times in the United States in

Decline in appreciation.

Once the novelty of the Seventh Symphony had worn away, audience interest in the West quickly dissipated. One reason may have been the work's length. At about 70 minutes, it was longer than any previous Shostakovich symphony. While it could be argued that he could have made the symphony 30 minutes shorter by condensing his message, the long passages of sparsely accompanied solos for wind instruments present listeners with the opportunity to study them, appreciate the inner character of the music as each instrument soliloquises on a given mood. To utilize this to the extent that Shostakovich did, combined with a wordless narrative style of mood-painting, necessitated an expansive time frame. Even so, this extended time span may have seemed excessive to some critics, especially since Western critics were unaware of the anti-Stalinist subtext hidden in the work. Hearing it only in the context of wartime propaganda, Western critics dismissed the symphony as a series of bombastic platitudes, and as such not worth serious consideration. The critic Ernest Newman famously remarked that, to find

Re-evaluation.

When "Testimony" was published in the West in 1979, Shostakovich's overall anti-Stalinist tone and specific comments about the anti-totalitarian content hidden in the Fifth, Seventh and Eleventh Symphonies were held suspect initially. They were in some ways a complete about-face from the comments the West had received over the years, many times in the composer's words. Questions also arose over Solomon Volkov's role—to what degree he was a compiler of previously written material, a transcriber of the composer's actual words from interviews, or an author essentially putting words into the composer's mouth.  Two things happened.

In popular culture.

It has been alleged that Béla Bartók quoted the march theme of the first movement in the "Intermezzo Interotto" of his "Concerto for Orchestra" in response to the Hungarian composer's frustration about the positive reception of the piece. The quotation is clearly the "invasion" theme, and the manner in which it is presented seems very much a parody. Bartók interjects his very romantic and lyrical melody in the movement with a much slower, dimwitted interpretation of Shostakovich's invasion ostinato. The resemblance has been variously interpreted by later commentators as an accusation of tastelessness, as a commentary on the symphony's over-popularity in Bartók's eyes, and as an acknowledgement of the position of the artist in a totalitarian society. However, it is much more likely

Film version.

On 31 January 2005 a film version of the Symphony was premiered in St. Petersburg, with the St. Petersburg Academic Symphony Orchestra, conducted by Maxim Shostakovich accompanying a film directed by Georgy Paradzhanov, constructed from documentary materials, including

Notable recordings.

Recordings of this symphony include:

Dmitri Shostakovich’s Symphony No. 7 in C major, Op. 60, titled Leningrad, was completed in Samara in December 1941 and premiered in that city on March 5, 1942. At first dedicated to Lenin, it was eventually submitted in honor of the besieged city of Leningrad, where it was first played under dire circumstances on August 9, 1942, with the siege by Axis and Finnish forces ongoing. The "Leningrad" soon became popular in both the Soviet Union and the West as a symbol of resistance to fascism, thanks in part to the composer’s microfilming of the score in Samara and its clandestine delivery, via Tehran and Cairo, to New York, where Arturo Toscanini led a broadcast performance (July 19, 1942) and "Time" magazine placed Shostakovich on its cover. That popularity faded somewhat after 1945, but the work is still regarded as a major musical testament to the 27 million Soviet people who lost their lives in World War II, and it is often played at Leningrad Cemetery, where half a million victims of the 900-day Siege of Leningrad are buried.

C大调第七交响曲,作品60,是俄国作曲家季米特里·肖斯塔科维奇的作品。创作于1941年第二次世界大战期间,并于同年12月27日完成。作曲家将乐曲题献给自己的出生和成长地-受德军所围困的列宁格勒,因此本曲亦加有副题「列宁格勒」(Leningrad)。


Statement of the problem.

The general statement of Apollonius' problem is to construct one or more circles that are tangent to three given objects in a plane, where an object may be a line, a point or a circle of any size. These objects may be arranged in any way and may cross one another; however, they are usually taken to be distinct, meaning that they do not coincide. Solutions to Apollonius' problem are sometimes called "Apollonius circles", although the term is also used for other types of circles associated with Apollonius.  The property of tangency is defined as follows. First, a point, line or circle is assumed to be tangent to itself; hence, if a given circle is already tangent to the other two given objects, it is counted as a solution to Apollonius' problem. Two distinct geometrical objects are said to "intersect" if they have a point in common. By definition, a point is tangent to a circle or a line if it intersects them, that is, if it lies on them; thus, two distinct points cannot be tangent. If the angle between lines or circles at an intersection point is zero, they are said to be "tangent"; the intersection point is called a "tangent point" or a "point of tangency". (The word "tangent" derives from the Latin present participle, "tangens", meaning "touching".) In practice, two distinct circles are tangent if they intersect at only one point; if they intersect at zero or two points, they are not tangent. The same holds true for a line and a circle. Two distinct lines cannot be tangent in the plane, although two parallel

History.

A rich repertoire of geometrical and algebraic methods have been developed to solve Apollonius' problem, which has been called "the most famous of all" geometry problems. The original approach of Apollonius of Perga has been lost, but reconstructions have been offered by François Viète and others, based on the clues in the description by Pappus of Alexandria. The first new solution method was published in 1596 by Adriaan van Roomen, who identified the centers of the solution circles as the intersection points of two hyperbolas. Van Roomen's method was refined in 1687 by Isaac Newton in his "Principia", and by John Casey in 1881.  Although successful in solving Apollonius' problem, van Roomen's method has a drawback. A prized property in classical Euclidean geometry is the ability to solve problems using only a compass and a straightedge. Many constructions are impossible using only these tools, such as dividing an angle in three equal parts. However, many such "impossible" problems can be solved by intersecting curves such as hyperbolas, ellipses and parabolas (conic sections). For example, doubling the cube (the problem of constructing a cube of twice the volume of a given cube) cannot be done using only a straightedge and compass, but Menaechmus showed that the problem can be solved by

Solution methods.

Intersecting hyperbolas.

The solution of Adriaan van Roomen (1596) is based on the intersection of two hyperbolas. Let the given circles be denoted as "C", "C" and "C". Van Roomen solved the general problem by solving a simpler problem, that of finding the circles that are tangent to "two" given circles, such as "C" and "C". He noted that the center of a circle tangent to both given circles must lie on a hyperbola whose foci are the centers of the given circles. To

Viète's reconstruction.

As described below, Apollonius' problem has ten special cases, depending on the nature of the three given objects, which may be a circle (C), line (L) or point (P). By custom, these ten cases are distinguished by three letter codes such as CCP. Viète solved all ten of these cases using only compass and straightedge constructions, and used the solutions of simpler cases to solve the more complex cases.  Viète began by solving the PPP case (three points) following the method of Euclid in his "Elements". From this, he derived a lemma corresponding to the power of a point theorem, which he used to solve the LPP case (a line and two points). Following Euclid a second time, Viète solved the LLL case (three lines) using the angle bisectors. He then derived a lemma for constructing the line perpendicular to an angle bisector that passes through a point, which he used to solve the LLP problem (two lines and

Algebraic solutions.

Apollonius' problem can be framed as a system of three equations for the center and radius of the solution circle. Since the three given circles and any solution circle must lie in the same plane, their positions can be specified in terms of the ("x", "y") coordinates of their centers. For example, the center positions of the three given circles may be written as ("x", "y"), ("x", "y") and ("x", "y"), whereas that of a solution circle can be written as ("x", "y"). Similarly, the radii of the given circles and a solution circle can be written as "r", "r", "r" and

Lie sphere geometry.

The same algebraic equations can be derived in the context of Lie sphere geometry. That geometry represents circles, lines and points in a unified way, as a five-dimensional vector "X" = ("v", "c", "c", "w", "sr"), where c = ("c", "c") is the center of the circle, and "r" is its (non-negative) radius. If "r" is not zero, the sign "s" may be positive or negative; for visualization, "s" represents the orientation of the circle, with counterclockwise circles having a positive "s" and clockwise circles having a negative "s". The parameter "w" is zero for a straight line, and one otherwise.  In this five-dimensional world, there is a bilinear product similar to the dot product:  The Lie quadric is defined as those vectors whose product with themselves (their square norm) is zero, ("X"|"X") = 0. Let "X" and "X" be two vectors belonging to this quadric; the norm of their difference equals  The product distributes over addition and subtraction

Inversive methods.

A natural setting for problem of Apollonius is inversive geometry. The basic strategy of inversive methods is to transform a given Apollonius problem into another Apollonius problem that is simpler to solve; the solutions to the original problem are found from the solutions of the transformed problem by undoing the transformation. Candidate transformations must change one Apollonius problem into another; therefore, they must transform the given points, circles and lines to other points, circles and lines, and no other shapes. Circle inversion has this property and allows the center and radius of the inversion circle to be chosen judiciously. Other candidates include the Euclidean plane isometries; however, they do not simplify the problem, since they merely shift, rotate, and mirror the original problem.  Inversion in a circle with center O and radius "R" consists of the following operation (Figure 5): every point P

Pairs of solutions by inversion.

Solutions to Apollonius's problem generally occur in pairs; for each solution circle, there is a conjugate solution circle (Figure 6). One solution circle excludes the given circles that are enclosed by its conjugate solution, and vice versa. For example, in Figure 6, one solution circle (pink, upper left) encloses two given circles (black), but excludes a third; conversely, its conjugate solution (also pink, lower right) encloses that third given circle, but excludes the other two. The two conjugate solution circles are related by inversion, by the following argument.  In general, any

Inversion to an annulus.

If two of the three given circles do not intersect, a center of inversion can be chosen so that those two given circles become concentric. Under this inversion, the solution circles must fall within the annulus between the two concentric circles. Therefore, they belong to two one-parameter families. In the first family (Figure 7), the solutions do "not" enclose the inner concentric circle, but rather revolve like ball bearings in the annulus. In the second family (Figure 8), the solution circles enclose the inner concentric circle. There are generally four solutions for each family, yielding eight possible solutions, consistent with the algebraic solution.  When two of the given circles are concentric, Apollonius's problem can be solved easily using a method of Gauss. The radii of the three given circles are known, as is the distance "d" from the common concentric center to the non-concentric circle (Figure 7). The solution circle can be determined from its radius "r", the angle θ, and the distances "d" and "d" from its center to the

Resizing and inversion.

The usefulness of inversion can be increased significantly by resizing. As noted in Viète's reconstruction, the three given circles and the solution circle can be resized in tandem while preserving their tangencies. Thus, the initial Apollonius problem is transformed into another problem that may be easier to solve. For example, the four circles can be resized so that one given circle is shrunk to a point; alternatively, two given circles can often be resized so that they are tangent to one another. Thirdly, given circles that intersect can be resized so that they become non-intersecting, after which the method for inverting to an annulus can be applied. In all such cases, the solution of the original Apollonius problem is obtained from the solution of the transformed problem by undoing the resizing and inversion.

Gergonne's solution.

Gergonne's approach is to consider the solution circles in pairs. Let a pair of solution circles be denoted as "C" and "C" (the pink circles in Figure 6), and let their tangent points with the three given circles be denoted as A, A, A, and B, B, B, respectively. Gergonne's solution aims to locate these six points, and thus solve for the two solution circles.  Gergonne's insight was that if a line "L" could be constructed such that A and B were guaranteed to fall on it, those two points could be identified as the intersection points of "L" with the given circle "C" (Figure

Intersection theory.

The techniques of modern algebraic geometry, and in particular intersection theory, can be used to solve Apollonius's problem. In this approach, the problem is reinterpreted as a statement about circles in the complex projective plane. Solutions involving complex numbers are allowed and degenerate situations are counted with multiplicity. When this is done, there are always eight solutions to the problem.  Every quadratic equation in,, and determines a unique conic, its vanishing locus. Conversely, every conic in the complex projective plane has an equation, and that equation is unique up to an overall scaling factor (because rescaling an equation does not change its vanishing locus). Therefore, the set of all conics may be parametrized by five-dimensional projective space, where the correspondence is  A "circle" in the complex projective plane is defined to be a conic that passes through the two points and, where denotes a square root of. The points and are called the "circular points". The projective variety of all circles is the subvariety of

Radii.

In the generic problem with eight solution circles, The reciprocals of the radii of four

Special cases.

Ten combinations of points, circles, and lines.

Apollonius problem is to construct one or more circles tangent to three given objects in a plane, which may be circles, points, or lines. This gives rise to ten types of Apollonius' problem, one corresponding to each combination of circles, lines and points, which may be labeled with three letters, either C, L, or P, to denote whether the given elements are a circle, line or point, respectively (Table 1). As an example, the type of Apollonius problem with a given circle, line, and point is denoted as CLP.  Some of these special cases are much easier to solve than the general case of three given circles. The two simplest cases are the problems of drawing a circle through three given points (PPP) or tangent to three lines (LLL), which were solved first by Euclid in his "Elements". For example, the PPP problem can be solved as

Number of solutions.

The problem of counting the number of solutions to different types of Apollonius' problem belongs to the field of enumerative geometry. The general number of solutions for each of the ten types of Apollonius' problem is given in Table 1 above. However, special arrangements of the given elements may change the number of solutions. For illustration, Apollonius' problem has no solution if one circle separates the two (Figure 11); to touch both the solid given circles, the solution circle would have to cross the dashed given circle; but that it cannot do, if it is to touch the dashed circle tangentially. Conversely, if three given circles are all tangent at the same point, then "any" circle tangent at the same point is a solution; such Apollonius problems

Mutually tangent given circles: Soddy's circles and Descartes' theorem.

If the three given circles are mutually tangent, Apollonius' problem has five solutions. Three solutions are the given circles themselves, since each is tangent to itself and to the other two given circles. The remaining two solutions (shown in red in Figure 12) correspond to the inscribed and circumscribed circles, and are called "Soddy's circles". This special case of Apollonius' problem is also known as the four coins problem. The three given circles of this Apollonius problem form a Steiner chain tangent to the two Soddy's circles.  Either Soddy circle, when taken together with the three given circles, produces a set of four circles that are mutually tangent at six points. The radii of these four circles are related

Generalizations.

Apollonius' problem can be extended to construct all the circles that intersect three given circles at a precise angle θ, or at three specified crossing angles θ, θ and θ; the ordinary Apollonius' problem corresponds to a special case in which the crossing angle is zero for all three given circles. Another generalization is the dual of the first extension, namely, to construct circles with three specified tangential distances from the three given circles.  Apollonius' problem can be extended from the plane to the sphere and other quadratic surfaces. For the sphere, the problem is to construct all the circles (the boundaries of spherical caps) that are tangent to three given circles on the sphere. This spherical problem can be rendered into a corresponding planar problem using stereographic projection. Once the solutions to the planar problem have been constructed, the corresponding solutions to the spherical problem can be determined by inverting the stereographic projection. Even more generally, one can consider the problem of four tangent curves that result from the intersections of an arbitrary quadratic surface and four planes, a problem first considered by Charles Dupin.  By solving Apollonius' problem repeatedly to find the inscribed circle, the interstices between mutually tangential circles can be

Applications.

The principal application of Apollonius' problem, as formulated by Isaac Newton, is hyperbolic trilateration, which seeks to determine a position from the "differences" in distances to at least three points. For example, a ship may seek to determine its position from the differences in arrival times of signals from three synchronized transmitters. Solutions to Apollonius' problem were used in World War I to determine the location of an artillery piece from the time a gunshot was heard at three different positions, and hyperbolic trilateration is the principle used by the Decca Navigator System and LORAN. Similarly, the location of an aircraft may be determined from the difference in arrival times of its transponder signal at four receiving stations. This multilateration problem is equivalent to the three-dimensional generalization of Apollonius' problem and applies to global navigation satellite systems (see GPS#Geometric interpretation). It is also used to determine the position of calling animals (such as birds and whales), although Apollonius' problem does not pertain if the speed of sound varies with direction (i.e., the transmission medium not isotropic).  Apollonius' problem has other applications. In Book 1, Proposition 21 in his "Principia", Isaac Newton used his solution of Apollonius' problem to construct an orbit in celestial mechanics from the center of attraction and observations of tangent lines to the orbit corresponding to instantaneous velocity. The special case of the problem of Apollonius when all three circles are tangent is used in the Hardy–Littlewood circle method of analytic number theory to construct Hans Rademacher's contour for complex integration, given by the boundaries of an infinite set of Ford circles each of which touches several others. Finally, Apollonius' problem has been applied to some types of packing problems, which arise in disparate fields such as the error-correcting codes used on DVDs and the design of pharmaceuticals that bind in a particular enzyme of a pathogenic bacterium.

In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c. 262 190 BC) posed and solved this famous problem in his work ("", "Tangencies"); this work has been lost, but a 4th-century AD report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them (Figure 2), a pair of solutions for each way to divide the three given circles in two subsets (there are 4 ways to divide a set of cardinality 3 in 2 parts).

阿波罗尼奥斯问题是一道有名的几何题:「平面上给定三个圆周,如何用尺规作图构造出和这三个已知圆都相切的圆(图1 )?」


Etymology and nomenclature.

"Anattā" is a composite Pali word consisting of "an" (not, without) and "attā" (soul). The term refers to the central Buddhist doctrine that "there is in humans no permanent, underlying substance that can be called the soul." It is one of the three characteristics of all existence, together with "dukkha" (suffering, dissatisfaction) and "anicca" (impermanence).  "Anattā" is synonymous with "Anātman" (an + ātman) in Sanskrit Buddhist texts. In some Pali texts, "ātman" of Vedic texts is also referred to with the term "Attan", with the sense of soul. An alternate use of "Attan" or "Atta" is "self, oneself, essence of a person", driven by the Vedic era Brahmanical belief that the soul is the permanent, unchangeable essence of a living being, or the true self.  In Buddhism-related English literature, "Anattā" is rendered as "not-Self", but this translation expresses an incomplete meaning, states Peter Harvey; a more complete rendering is "non-Self" because from its earliest days, "Anattā" doctrine denies that there is anything called a 'Self' in any person or anything else, and that a belief in 'Self' is a source of "Dukkha" (suffering, pain, unsatisfactoriness). It is also incorrect to translate "Anattā" simply as "ego-less", according to Peter Harvey, because the Indian concept of "ātman" and "attā" is different from the Freudian concept of ego.  "Anatta" or "Anatma-vada" is also referred to as the "no-soul or no-self doctrine" of Buddhism.

Anattā in early Buddhist texts.

The concept of "Anattā" appears in numerous Sutta(Pali)/Sutra(Sanskrit) of the ancient Buddhist Nikāya texts (Pali canon). It appears, for example, as a noun in "Samyutta Nikaya" III.141, IV.49, V.345, in Sutta II.37 of "Anguttara Nikaya", II.37–45 and II.80 of "Patisambhidamagga", III.406 of "Dhammapada". It also appears as an adjective, for example, in "Samyutta Nikaya" III.114, III.133, IV.28 and IV.130–166, in Sutta III.66 and V.86 of "Vinaya".  The ancient Buddhist texts discuss "Attā" or "Attan" (soul, self), sometimes with alternate terms such as "Atuman", "Tuma", "Puggala", "Jiva", "Satta", "Pana" and "Nama-rupa", thereby providing the context for the Buddhist "Anattā" doctrine. Examples of such "Attā" contextual discussions are found in "Digha Nikaya" I.186-187, "Samyutta Nikaya" III.179 and IV.54, "Vinaya" I.14, "Majjhima Nikaya" I.138, III.19, and III.265–271 and "Anguttara Nikaya" I.284.  The contextual use of "Attā" in Nikāyas is two sided. In one, it directly denies that there is anything called a self or soul in a human being that is a permanent essence of a human being, a theme found in Brahmanical (proto-Hindu) traditions. In another, states Peter Harvey, such as at "Samyutta Nikaya" IV.286, the Sutta considers the materialistic concept in pre-Buddhist Vedic times of "no afterlife, complete annihilation" at death to be a denial of Self, but still "tied up with belief in a Self". "Self exists" is a false premise, assert the early Buddhist texts. However, adds Peter Harvey, these texts do not admit the premise "Self does not exist" either because the wording presumes the concept of "Self" prior to denying it; instead, the early Buddhist texts use the concept of "Anattā" as the implicit premise. According to Steven Collins, the doctrine of anatta and "denial of self" in the canonical Buddhist texts is "insisted on only in certain theoretical contexts", while they use the terms "atta, purisa, puggala" quite naturally and freely in various contexts. The elaboration of the anatta doctrine, along with identification of the words such as "puggala" as "permanent subject or soul" appears in later Buddhist literature.  "Anattā" is one of the main bedrock doctrines of Buddhism, and its discussion is found in the later texts of all Buddhist traditions. For example, the Buddhist philosopher Nagarjuna (~200 CE), extensively wrote about rejecting the metaphysical entity called "attā" or "ātman" (self, soul), asserting in chapter 18 of his "Mūlamadhyamakakārikā" that there is no such substantial entity and that "Buddha taught the doctrine of no-self". The texts attributed to the 5th-century Buddhist philosopher Vasubandhu of the Yogachara school similarly discuss "Anatta" as a fundamental premise of the Buddha. The Vasubandhu interpretations of no-self thesis were challenged by the 7th-century Buddhist scholar Candrakirti, who then offered his own theories on its importance.

Existence and non-existence.

"Anattā" (non-self, no enduring soul or essence) is the nature of all things, and this is one of the three marks of existence in Buddhism, along with "Anicca" (impermanence, nothing lasts) and "Dukkha" (suffering, unsatisfactoriness is innate in birth, aging, death, rebirth, redeath – the Saṃsāra cycle of existence). It is found in many texts of different Buddhist traditions, such as the "Dhammapada" – a canonical Buddhist text. Buddhism asserts with Four Noble Truths that there is a way out of this Saṃsāra.

Eternalism and annihilationism.

While the concept of soul in Hinduism (as atman) and Jainism (as jiva) is taken for granted, which is different from the Buddhist concept of no-soul, each of the three religions believed in rebirth and emphasized moral responsibility in different ways in contrast to pre-Buddhist materialistic schools of Indian philosophies. The materialistic schools of Indian philosophies, such as Charvaka, are called annihilationist schools because they posited that death is the end, there is no afterlife, no soul, no rebirth, no karma, and death is that state where a living being is completely annihilated, dissolved.  Buddha criticized the materialistic annihilationism view that denied rebirth and karma, states Damien Keown. Such beliefs are inappropriate and dangerous, stated Buddha, because they encourage moral irresponsibility and material hedonism. Anatta does not mean there is no afterlife, no rebirth or no fruition of karma, and Buddhism contrasts itself to annihilationist schools. Buddhism also contrasts itself to other Indian religions that champion moral responsibility but posit eternalism with their premise that within each human being there is an essence or eternal soul, and this soul is part of the nature of a living being, existence and metaphysical reality.

Karma, rebirth and anattā.

The Buddha emphasized both karma and anatta doctrines.  The Buddha criticized the doctrine that posited an unchanging soul as a subject as the basis of rebirth and karmic moral responsibility, which he called "atthikavāda". He also criticized the materialistic doctrine that denied the existence of both soul and rebirth, and thereby denied karmic moral responsibility, which he calls "natthikavāda". Instead, the Buddha asserted that there is no soul, but there is rebirth for which karmic moral responsibility is a must. In the Buddha's framework of karma, right view and right actions are necessary for liberation.

Developing the self.

According to Peter Harvey, while the "Suttas" criticize notions of an eternal, unchanging Self as baseless, they see an enlightened being as one whose empirical self is highly developed. This is paradoxical, states Harvey, in that "the Self-like "nibbana" state" is a mature self that knows "everything as Selfless". The "empirical self" is the "citta" (mind/heart, mindset, emotional nature), and the development of self in the Suttas is the development of this "citta".  One with "great self", state the early Buddhist "Suttas", has a mind which is neither at the mercy of outside stimuli nor its own moods, neither scattered nor diffused, but imbued with self-control, and self-contained towards the single goal of "nibbana" and a 'Self-like' state. This "great self" is not yet an "Arahat", because he still does small evil action which leads to karmic fruition, but he has enough virtue that he does not experience this fruition in hell.  An "Arahat", states Harvey, has a fully enlightened state of empirical self, one that lacks the "sense of both 'I am' and 'this I am'", which are illusions that the "Arahat" has transcended. The Buddhist thought and salvation theory emphasizes a development of self towards a Selfless state not only with respect to oneself, but recognizing the lack of relational essence and Self in others, wherein states Martijn van Zomeren, "self is an illusion".

Anatta in Theravada Buddhism.

Theravada Buddhism scholars, states Oliver Leaman, consider the "Anattā" doctrine as one of the main theses of Buddhism.  The Buddhist denial of "any Soul or Self" is what distinguishes Buddhism from major religions of the world such as Christianity and Hinduism, giving it uniqueness, asserts the Theravada tradition. With the doctrine of "Anattā", stands or falls the entire Buddhist structure, asserts Nyanatiloka.  According to Collins, "insight into the teaching of anatta is held to have two major loci in the intellectual and spiritual education of an individual" as s/he progresses along the Path. The first part of this insight is to avoid "sakkayaditthi" (Personality Belief), that is converting the "sense of I which is gained from introspection and the fact of physical individuality" into a theoretical belief in a self. "A belief in a (really) existing body" is considered a false belief and a part of the Ten Fetters that must be gradually lost. The second loci is the psychological realisation of anatta, or loss of "pride or conceit". This, states Collins, is explained as the conceit of "asmimana" or "I am"; (...) what this "conceit" refers to is the fact that for the unenlightened man, all experience and action must necessarily appear phenomenologically as happening to or originating from an "I". When a Buddhist gets more enlightened, this happening to or originating in an "I" or sakkdyaditthi is less. The final attainment of enlightenment is the disappearance of this automatic but illusory "I".  The Theravada tradition has long considered the understanding and application of the "Anatta" doctrine to be a complex teaching, whose "personal, introjected application has always been thought to be possible only for the specialist, the practising monk". The tradition, states Collins, has "insisted fiercely on anatta as a doctrinal position", while in practice it may not play much of a role in the daily religious life of most Buddhists. The Suttas present the doctrine in three forms. First, they apply the "no-self, no-identity" doctrine to all phenomena as well as any and all objects, yielding the idea that "all things are not-self" ("sabbe dhamma anatta"). Second, states Collins, the Suttas apply the doctrine to deny self of any person, treating conceit to be evident in any assertion of "this is mine, this I am, this is myself" ("etam mamam eso 'ham asmi, eso me atta ti"). Third, the Theravada texts apply the doctrine as a nominal reference, to identify examples of "self" and "not-self", respectively the Wrong view and the Right view; this third case of nominative usage is properly translated as "self" (as an identity) and is unrelated to "soul", states Collins. The first two usages incorporate the idea of soul. The Theravada doctrine of "Anatta", or not-self not-soul, inspire meditative practices for monks, states Donald Swearer, but for the lay Theravada Buddhists in Southeast Asia, the doctrines of "kamma", rebirth and "punna" (merit) inspire a wide range of ritual practices and ethical behavior.  The "Anatta" doctrine is key to the concept of nirvana (nibbana) in the Theravada tradition. The liberated nirvana state, states Collins, is the state of "Anatta", a state that is neither universally applicable nor can be explained, but can be realized.

Current disputes.

The dispute about "self" and "not-self" doctrines has continued throughout the history of Buddhism. It is possible, states Johannes Bronkhorst, that "original Buddhism did not deny the existence of the soul", even though a firm Buddhist tradition has maintained that the Buddha avoided talking about the soul or even denied its existence. French religion writer André Migot also states that original Buddhism may not have taught a complete absence of self, pointing to the works of Buddhist and Pali scholars Jean Przyluski and Caroline Rhys Davids, whom Migot states showed early Buddhism generally believed in a self. Migot argues that Buddhist schools that admit an existence of a "self" are not heretical, but conservative, adhering to ancient beliefs. While there may be ambivalence on the existence or non-existence of self in early Buddhist literature, it is clear from these texts that seeking self-knowledge is not the Buddhist path for liberation, but turning away from what might erroneously be regarded as the self is, states Bronkhorst. This is a reverse position to the Vedic traditions which recognized the knowledge of the self as "the principal means to achieving liberation".  In Thai Theravada Buddhism, for example, states Paul Williams, some modern era Buddhist scholars have claimed that "nirvana is indeed the true Self", while other Thai Buddhists disagree. For instance, the Dhammakaya Movement in Thailand teaches that it is erroneous to subsume nirvana under the rubric of "anatta" (non-self); instead, nirvana is taught to be the "true self" or "dhammakaya". The Dhammakaya Movement teaching that nirvana is atta, or true self, was criticized as heretical in Buddhism in 1994 by Ven. Payutto, a well-known scholar monk, who stated that 'Buddha taught nibbana as being non-self". The abbot of one major temple in the Dhammakaya Movement, Luang Por Sermchai of Wat Luang Por Sodh Dhammakayaram, argues that it tends to be scholars who hold the view of absolute non-self, rather than Buddhist meditation practitioners. He points to the experiences of prominent forest hermit monks to support the notion of a "true self". Similar interpretations on the "true self" were put forth earlier by the 12th Supreme Patriarch of Thailand in 1939. According to Williams, the Supreme Patriarch's interpretation echoes the "tathāgatagarbha" sutras.  Several notable teachers of the Thai Forest Tradition have also described ideas in contrast to absolute non-self. Ajahn Maha Bua, a well known meditation master, described the citta (mind) as being an indestructible reality that does not fall under "anattā." He has stated that not-self is merely a perception that is used to pry one away from infatuation with the concept of a self, and that once this infatuation is gone the idea of not-self must be dropped as well. American monk Thanissaro Bhikkhu of the Thai Forest Tradition describes the Buddha's statements on non-self as a path to awakening rather than a universal truth. Thanissaro Bhikkhu states that the Buddha intentionally set the question of whether or not there is a self aside as a useless question, and that clinging to the idea that there is no self at all would actually "prevent" enlightenment. Bhikkhu Bodhi authored a rejoinder to Thanissaro, claiming that "The reason the teaching of anatta can serve as a strategy of liberation is precisely because it serves to rectify a misconception about the nature of being, hence an ontological error."  Buddhist scholars Richard Gombrich and Alexander Wynne argue that the Buddha's descriptions of non-self in early Buddhist texts do not deny that there is a self. Gethin claims that anatta is often mistranslated as meaning "not having a self", but in reality meant "not the self". Wynne claims early Buddhist texts such as the "Anattalakkhana Sutta" do not deny that there is a self, stating that the five aggregates that are described as not self are not descriptions of a human being but descriptions of the human experience. Wynne and Gombrich both argue that the Buddha's statements on anattā were originally a "not-self" teaching that developed into a "no-self" teaching in later Buddhist thought.  Thanissaro Bhikkhu points to the Ananda Sutta (SN 44.10), where the Buddha stays silent when asked whether there is a'self' or not, as a major cause of the dispute. In Thailand, this dispute on the nature of teachings about'self' and 'non-self' in Buddhism has led to arrest warrants, attacks and threats.

Anatta in Mahayana Buddhism.

There are many different views of Anatta (; Japanese: 無我 "muga"; Korean: 무아 "mu-a") within various Mahayana schools.  Nagarjuna, the founder of Madhyamaka (middle way) school of Mahayana Buddhism, analyzed dharma first as factors of experience. He, states David Kalupahana, analyzed how these experiences relate to "bondage and freedom, action and consequence", and thereafter analyzed the notion of personal self ("attā", "ātman").  Nagarjuna asserted that the notion of a self is associated with the notion of one's own identity and corollary ideas of pride, selfishness and a sense of psychophysical personality. This is all false, and leads to bondage in his Madhyamaka thought. There can be no pride nor possessiveness, in someone who accepts "Anattā" and denies "self" which is the sense of personal identity of oneself, others or anything, states Nagarjuna. Further, all obsessions are avoided when a person accepts emptiness ("sunyata"). Nagarjuna denied there is anything called a self-nature as well as other-nature, emphasizing true knowledge to be comprehending emptiness. Anyone who has not dissociated from his belief in personality in himself or others, through the concept of self, is in a state of "Avidya" (ignorance) and caught in the cycle of rebirths and redeaths.  The early Mahayana Buddhism texts link their discussion of "emptiness" ("shunyata") to "Anatta" and "Nirvana". They do so, states Mun-Keat Choong, in three ways: first, in the common sense of a monk's meditative state of emptiness; second, with the main sense of "Anatta" or 'everything in the world is empty of self'; third, with the ultimate sense of "Nirvana" or realization of emptiness and thus an end to rebirth cycles of suffering. The Anatta doctrine is another aspect of "shunyata", its realization is the nature of the "nirvana" state and to an end to rebirths.

Tathagatagarbha Sutras: Buddha is True Self.

Some 1st-millennium CE Buddhist texts suggest concepts that have been controversial because they imply a "self-like" concept. In particular are the "Tathāgatagarbha sūtras", where the title itself means a "garbha" (womb, matrix, seed) containing "Tathagata" (Buddha). These Sutras suggest, states Paul Williams, that 'all sentient beings contain a Tathagata' as their 'essence, core or essential inner nature'. The "Tathagatagarbha" doctrine, at its earliest probably appeared about the later part of the 3rd century CE, and is verifiable in Chinese translations of 1st millennium CE. Most scholars consider the "Tathagatagarbha " doctrine of an 'essential nature' in every living being is equivalent to 'Self', and it contradicts the Anatta doctrines in a vast majority of Buddhist texts, leading scholars to posit that the "Tathagatagarbha Sutras" were written to promote Buddhism to non-Buddhists.  The "Mahayana" "Mahaparinirvana Sutra" explicitly asserts that the Buddha used the term "Self" in order to win over non-Buddhist ascetics. The "Ratnagotravibhāga" (also known as "Uttaratantra"), another text composed in the first half of 1st millennium CE and translated into Chinese in 511 CE, points out that the teaching of the "Tathagatagarbha" doctrine is intended to win sentient beings over to abandoning "self-love" ("atma-sneha") – considered to be one of the defects by Buddhism. The 6th-century Chinese "Tathagatagarbha" translation states that "Buddha has "shiwo" (True Self) which is beyond being and nonbeing". However, the "Ratnagotravibhāga" asserts that the "Self" implied in "Tathagatagarbha" doctrine is actually "not-Self".  According to some scholars, the Buddha-nature discussed in these sutras does not represent a substantial self; rather, it is a positive language and expression of śūnyatā "emptiness" and represents the potentiality to realize Buddhahood through Buddhist practices. Other scholars do in fact detect leanings towards monism in these tathagatagarbha references. Michael Zimmermann sees the notion of an unperishing and eternal self in the Tathagatagarbha Sutra. Zimmermann also avers that 'the existence of an eternal, imperishable self, that is, buddhahood, is definitely the basic point of the Tathagatagarbha Sutra'. He further indicates that there is no evident interest found in this sutra in the idea of Emptiness ("sunyata"). Williams states that the "Self" in "Tathagatagarbha Sutras" is actually "non-Self", and neither identical nor comparable to the Hindu concepts of Brahman and Self.

Anatta in Vajrayana Buddhism.

The Anatta or Anatman doctrine is extensively discussed in and partly inspires the ritual practices of the Vajrayana tradition. The Tibetan terms such as "bdag med" refer to "without a self, insubstantial, anatman". These discussions, states Jeffrey Hopkins, assert the "non-existence of a permanent, unitary and independent self", and attribute these ideas to the Buddha.  The ritual practices in Vajrayana Buddhism employs the concept of deities, to end self-grasping, and to manifest as a purified, enlightened deity as part of the Vajrayana path to liberation from rebirths. One such deity is goddess Nairatmya (literally, non-soul, non-self). She symbolizes, states Miranda Shaw, that "self is an illusion" and "all beings and phenomenal appearances lack an abiding self or essence" in Vajrayana Buddhism.

Anatta – a difference between Buddhism and Hinduism.

Anatta is a central doctrine of Buddhism. It marks one of the major differences between Buddhism and Hinduism. According to the anatta doctrine of Buddhism, at the core of all human beings and living creatures, there is no "eternal, essential and absolute something called a soul, self or atman". Buddhism, from its earliest days, has denied the existence of the "self, soul" in its core philosophical and ontological texts. In its soteriological themes, Buddhism has defined nirvana as that blissful state when a person, amongst other things, realizes that he or she has "no self, no soul".  The traditions within Hinduism believe in Atman. The pre-Buddhist Upanishads of Hinduism assert that there is a permanent "Atman", and is an ultimate metaphysical reality. This sense of self, is expressed as "I am" in Brihadaranyaka Upanishad 1.4.1, states Peter Harvey, when nothing existed before the start of the universe. The Upanishadic scriptures hold that this soul or self is underlying the whole world. At the core of all human beings and living creatures, assert the Hindu traditions, there is "eternal, innermost essential and absolute something called a soul, self that is atman." Within the diverse schools of Hinduism, there are differences of perspective on whether souls are distinct, whether Supreme Soul or God exists, whether the nature of Atman is dual or non-dual, and how to reach moksha. However, despite their internal differences, one shared foundational premise of Hinduism is that "soul, self exists", and that there is bliss in seeking this self, knowing self, and self-realization.  Both Buddhism and Hinduism distinguish ego-related "I am, this is mine", from their respective abstract doctrines of "Anatta" and "Atman". This, states Peter Harvey, may have been an influence of Buddhism on Hinduism.

Anatman and Niratman.

The term "niratman" appears in the "Maitrayaniya Upanishad" of Hinduism, such as in verses 6.20, 6.21 and 7.4. "Niratman" literally means "selfless". The "niratman" concept has been interpreted to be analogous to "anatman" of Buddhism. The ontological teachings, however, are different. In the Upanishad, states Thomas Wood, numerous positive and negative descriptions of various states – such as "niratman" and "sarvasyatman" (the self of all) – are used in "Maitrayaniya Upanishad" to explain the nondual concept of the "highest Self". According to Ramatirtha, states Paul Deussen, the "niratman" state discussion is referring to stopping the recognition of oneself as an individual soul, and reaching the awareness of universal soul or the metaphysical Brahman.

Correspondence in Pyrrhonism.

The Greek philosopher Pyrrho traveled to India as part of Alexander the Great's entourage where he was influenced by the Indian gymnosophists, which inspired him to create the philosophy of Pyrrhonism. Philologist Christopher Beckwith has demonstrated that Pyrrho based his philosophy on his translation of the three marks of existence into Greek, and that "adiaphora" (not logically differentiable, not clearly definable, negating Aristotle's use of "diaphora") reflects Pyrrho's understanding of the Buddhist concept of anatta.

In Buddhism, the term anattā (Pali) or anātman (Sanskrit) refers to the doctrine of "non-self", that there is no unchanging, permanent self, soul or essence in phenomena. It is one of the seven beneficial perceptions in Buddhism, and one of the three marks of existence along with "dukkha" (suffering) and "anicca" (impermanence).

无我(,,),佛教术语,指对于我的否定,为佛教根本思想之一。这个名词有二方面的意思,一方面,它可以解释为,没有我,我不存在,大乘佛教又称我空;另一方面,则可解释为,这不是我,也称为非我()。这两种含义间的争论,成为佛教各宗派间的重要课题。 否定世界上有物质性的实在自体(即所谓“我”)的存在,有两类:


Early life.

Haig was born in Fresno, California, and was raised in an Armenian community. He was the son of Roxy (Mooradian) and Haig Mosesian, an electrician. Haig's career began somewhat by accident. As a young man, his rapid growth interfered with his motor coordination, prompting him to take dancing lessons. At the age of seven years, he was a paid dancer in a children's Christmas show, and later joined a vaudeville revival show.  Haig also displayed musical talent particularly for the drums, prompting his parents to buy him a drum set, on which he mastered a wide range of music styles, including swing, country, jazz, blues and rock and roll. He found it easy to earn money with his music, and signed a recording contract one year out of high school. Still a teenager, Haig went on to record the single "Full House" with the T-Birds in 1958, which reached No. 4 on the charts.

The Pasadena Playhouse.

When Haig was in high school, the head of the drama department was Alice Merrill, who encouraged him to pursue an acting career. Merrill had been a Broadway actress who maintained her contacts in the business. During his senior year, a play was produced in which Merrill double cast the show, to have one of her Hollywood friends assess the actors in order to select the final cast.  The Hollywood contact who saw Haig perform was Dennis Morgan, a big musical comedy star from the 1940s, who chose Haig for a prominent role in the play. Two weeks later, he returned to see the show and advised Haig to continue his education in the San Fernando Valley and consider acting as a career. Two years later, Haig enrolled in the Pasadena Playhouse, the school that trained such noted actors as Robert Preston, Gene Hackman, and Dustin Hoffman. He later moved to Hollywood with longtime friend and Pasadena Playhouse roommate Stuart Margolin.

Acting career.

Haig's first acting role was in a 1960 short student film titled "The Host", directed by Jack Hill at UCLA. This launched Haig's more-than-four-decade acting career in over fifty films and 350 television episodes. Haig became a staple in Hill's films, such as "Spider Baby", "Coffy" and "Foxy Brown". In 1971, Haig appeared in "THX 1138", the feature film directorial debut of George Lucas, as well as the James Bond film "Diamonds Are Forever".  Haig's television debut was a role in a 1962 episode of "The Untouchables". He also appeared in a number of other television programs, including "Batman", "The Man From U.N.C.L.E.", "Gunsmoke", "", "", "Get Smart", "The Flying Nun", "Mary Hartman, Mary Hartman", Emergency!, "Charlie's Angels", "Jason of Star Command", "Fantasy Island", "Buck Rogers in the 25th Century", "The Dukes of Hazzard", "The A-Team", "MacGyver", and "Just the Ten of Us".  Haig temporarily retired from acting in 1992, feeling typecast: "I just didn't want to play stupid heavies anymore. They just kept giving me the same parts but just putting different clothes on me. It was stupid, and I resented it, and I wouldn't have anything to do with it". Haig did not work in acting for five years, instead training and becoming a certified hypnotherapist. During this time, he was offered the role of Marsellus Wallace (later to be played by Ving Rhames) in "Pulp Fiction", the second feature film directed by Quentin Tarantino. At the time, Haig was concerned that low-budget television had been detrimental to his career and, at seeing the shooting script and the short number of days dedicated for each locale, he reportedly passed on the project; he is said to have later regretted this decision. Haig later appeared as a judge in Tarantino's 1997 film "Jackie Brown", a part written specifically for Haig by Tarantino.  In 2003, Haig starred in Rob Zombie's debut film "House of 1000 Corpses", as a psychotic clown named Captain Spaulding. The role revived Haig's acting career, earning him a "Best Supporting Actor" award in the 13th Annual Fangoria Chainsaw Awards, and an induction into Fangoria's Horror Hall of Fame. Haig reprised his role as Spaulding in the 2005 film "The Devil's Rejects", a continuation of "House of 1000 Corpses", in which Spaulding is portrayed as the patriarch of the murderous Firefly family. Captain Spaulding has since been considered a modern icon of horror cinema, and Haig himself has been called a "horror icon". For his reprisal of the role in "The Devil's Rejects", he received the award for "Best Actor" in the 15th Annual Fangoria Chainsaw Awards, and shared the award for "Most Vile Villain" at the First Annual Spike TV Scream Awards with Leslie Easterbrook, Sheri Moon, and Bill Moseley as the Firefly family. Haig was also nominated as "Best Butcher" in the Fuse/Fangoria Chainsaw Awards, but lost to Tobin Bell's Jigsaw from "Saw II".  Haig reunited with Rob Zombie for the director's "Halloween" remake, released in 2007, with Haig playing the role of cemetery caretaker Chester Chesterfield. Haig again reprised his role as Captain Spaulding for Zombie's 2009 animated film "The Haunted World of El Superbeasto". Haig also appeared in Zombie's 2013 film "The Lords of Salem", as well as in the films "Hatchet III" and "Devil in My Ride".  In 2019, Haig appeared as Captain Spaulding for the final time in the Rob Zombie film "3 from Hell", a sequel to "House of 1000 Corpses" and "The Devil's Rejects". He is set to posthumously appear in the 2020 slasher film "Hanukkah", as well as in the 2021 film "Abruptio".

Personal life and death.

On November 2, 2007, Haig married Susan L. Oberg.  In early September 2019, Haig was hospitalized after falling at his home in Thousand Oaks, CA. While recovering, he began to suffer from Aspergillus Pneumonia after aspirating vomit in his sleep. He died on September 21, 2019, from Aspiration Pneumonitis triggered by Aspergillus Pneumonia (caused by the Aspiration of said vomit), which resulted in cardiopulmonary arrest at the age of 80. Celebrity gossip site TMZ, in a move that infuriated Haig's family, put Haig's official Death Certificate on their site, free to download as a PDF document.

Sidney Eddie Mosesian (July 14, 1939 – September 21, 2019), known professionally as Sid Haig, was an American actor, film producer, and musician. He is known for his roles in several of Jack Hill's blaxploitation films from the 1970s, as well as for his appearances in horror films, most notably his role as Captain Spaulding in the Rob Zombie films "House of 1000 Corpses", "The Devil's Rejects" and "3 from Hell". Haig's Captain Spaulding, and Haig himself, have been called icons of horror cinema. Haig had a leading role on the television series "Jason of Star Command" as the villain Dragos. He appeared in many television programs, including "The Untouchables", "Batman", "Gunsmoke", "", "", "Get Smart", "Charlie's Angels", "Fantasy Island", "Buck Rogers in the 25th Century", "The Dukes of Hazzard", "The A-Team", and "MacGyver".

雪梨·艾迪·摩西安(英语:Sidney Eddie Mosesian,1939年-7月14日-2019年-9月21日)或称作席德·海格(英语:Sid Haig),是一名美国男演员、制片人和音乐家。海格时常出演恐怖片,以及在1970年代间于杰克·希尔的黑人剥削电影中演出。他较著名的是在罗伯·僵尸电影《猛鬼1000》(2003年)、《猎杀猛鬼公路》(2005年)、《鬼界超级混蛋》(2009年)和《地狱3人行》(2019年)中饰演史伯汀队长 (罗伯·僵尸角色)一角,这使海格和该角称为了恐怖片界的著名偶像。


Features.

It has a 23.7 mm by 15.6 mm DX format image sensor with 6.1 million effective pixels. It also has a 2.0" (50 mm) polysilicon TFT LCD with 130,000 pixels. The camera uses a through-the-lens full-aperture exposure metering system. It can simultaneously record NEF and JPEG data to a Secure Digital storage device. Like its newer, higher-end sibling (the D80), the D50 uses Secure Digital instead of CompactFlash cards found on previous Nikon digital SLRs. The camera is powered by a rechargeable lithium-ion battery which is claimed to be able to take up to 2,000 shots on a single charge. The camera is compatible with PictBridge printers and can shoot 2.5 frames per second in continuous mode. The camera's dimensions are 133 mm in width, 102 mm in height, and 76 mm in depth.  The D50 is the only entry-level Nikon DSLR to have the autofocus motor ('screw drive') built into the camera body, making the camera backwards-compatible with mechanical-drive autofocus lenses (Nikkor AF series) dating back to 1989. This feature has been eliminated on later entry-level models and is currently only available on mid-range and advanced models. This makes the D50 the lightest Nikon DSLR to have the autofocus motor.  This camera has many settings that can only be accessed by selecting a detailed menu view. One such feature is the ability to a make series of differently-exposed images for processing into HDRI photographs. The camera menu refers to this setting as BKT (Bracketed Set).

Market.

The D50 was announced on April 20, 2005 and went on sale in June 2005. When introduced, the camera carried a suggested retail price of US$799 for the body only or $899 with a new 18-55 mm F3.5-5.6 G AF-S DX lens. Another variant of the D50 kit containing both the 18–55 mm and a 55–200 mm F4-5.6 G AF-S DX lens was available. Competitors of the D50 included the Canon EOS 350D, the Pentax *ist DS, the Konica Minolta Dynax 5D, and the Olympus E-300.  The website Digital Photography Review rated the D50 highly and noted its improved noise performance over the D70s it was largely derived from, although it had fewer hobbyist features (making the D50 the first de-specified entry-level DSLR camera thus lowering the MSRP) and a lower price than the D70s. In depth testing by the Images Resources website and the October 2005 "Hoshi Nabi" (Star Navigator) Magazine, indicated that the D50 achieved its low noise through exceptionally good performance at the sensor level. Testing by Roger Clark confirmed that the D50 had higher gain and lower noise than the D70. Tests of the D50 at all ISO levels indicated that it did offer low noise without loss of contrast or detail.

The D50 is a 6.1-megapixel entry-level digital single-lens reflex camera, sold from June 2005 until November 2006 by Nikon. It was Nikon's first DSLR aimed at the consumer market, and sold for US$899. It uses the Nikon F mount. The D50 was succeeded by the Nikon D40 in November 2006.

Nikon D50是尼康在2005年4月20日和Nikon D70s一起发表的数码单反相机,采取APS-C规格。D50与Nikon以往的数码单反相机最大的不同点在于,D50简化了部分功能,并且针对家庭用途加强了小孩、宠物等情境模式,同时色调呈现上也与Nikon以往的照相机不同,较为偏暖。


History of the concept.

The Caucasus as the origin of humanity and the peak of beauty.

In the eighteenth century, the prevalent view amongst European scholars was that the human species had its origin in the region of the Caucasus Mountains. This view was based upon the Caucasus being the location for the purported landing point of Noah's Ark – from whom the Bible states that humanity is descended – and the location for the suffering of Prometheus, who in Hesiod's myth had crafted humankind from clay.  In addition, the most beautiful humans were reputed to be the stereotypical "Circassian beauties" and the Georgian people; both Georgia and Circassia are in the Caucasus region. The "Circassian beauty" stereotype had its roots in the Middle Ages, whilst the reputation for the attractiveness of the Georgian people was developed by early modern travellers to the region such as Jean Chardin.

Göttingen School of History.

The term "Caucasian" as a racial category was first introduced in the 1780s by members of the Göttingen School of History – notably Christoph Meiners in 1785 and Johann Friedrich Blumenbach in 1795 – it had originally referred in a narrow sense to the native inhabitants of the Caucasus region.  In his "The Outline of History of Mankind" (1785), the German philosopher Christoph Meiners first used the concept of a "Caucasian" ("Kaukasisch") race in its wider racial sense. Meiners imagined that the Caucasian race encompassed all of the ancient and most of the modern native populations of Europe, the aboriginal inhabitants of West Asia (including the Phoenicians, Hebrews and Arabs), the autochthones of Northern Africa (Berbers, Egyptians, Abyssinians and neighboring groups), the Indians, and the ancient Guanches. It was Johann Friedrich Blumenbach, a colleague of Meiners', who later came to be considered one of the founders of the discipline of anthropology, who gave the term a wider audience, by grounding it in the new methods of craniometry and Linnean taxonomy. Blumenbach did not credit Meiners with his taxonomy, although his justification clearly points to Meiners' aesthetic viewpoint of Caucasus origins. In contrast to Meiners, however, Blumenbach was a monogenist – he considered all humans to have a shared origin and to be a single species. Blumenbach, like Meiners, did rank his Caucasian grouping higher than other groups in terms of mental faculties or potential for achievement.  Alongside the anthropologist Georges Cuvier, Blumenbach classified the Caucasian race by cranial measurements and bone morphology in addition to skin pigmentation. Following Meiners, Blumenbach described the Caucasian race as consisting of the native inhabitants of Europe, West Asia, the Indian peninsula, and North Africa. This usage later grew into the widely used color terminology for race, contrasting with the terms "Negroid", "Mongoloid", and "Australoid".

Carleton Coon.

There was never any consensus among the proponents of the concept the existence of a "Caucasoid race" with regard to how it would be delineated from other proposed groups such as the proposed Mongoloid race. Carleton S. Coon (1939) included the populations native to all of Central and Northern Asia, including the Ainu people, under the Caucasoid label. However, many scientists maintained the racial categorizations of color established by Meiners' and Blumenbach's works, along with many other early steps of anthropology, well into the late 19th and mid-to-late 20th centuries, increasingly used to justify political policies, such as segregation and immigration restrictions, and other opinions based in prejudice. For example, Thomas Henry Huxley (1870) classified all populations of Asian nations as Mongoloid. Lothrop Stoddard (1920) in turn classified as "brown" most of the populations of the Middle East, North Africa, the Horn of Africa, Central Asia and South Asia. He counted as "white" only European peoples and their descendants, as well as a few populations in areas adjacent to or opposite southern Europe, in parts of Anatolia and parts of the Rif and Atlas mountains.  In 1939 Coon argued that the Caucasian race had originated through admixture between "Homo neanderthalensis" and "Homo sapiens" of the "Mediterranean type" which he considered to be distinct from Caucasians, rather than a subtype of it as others had done. While Blumenbach had erroneously thought that light skin color was ancestral to all humans and the dark skin of southern populations was due to sun, Coon thought that Caucasians had lost their original pigmentation as they moved North. Coon used the term "Caucasoid" and "White race" synonymously.  In 1962, Coon published "The Origin of Races", wherein he proposed a polygenist view, that human races had evolved separately from local varieties of "Homo erectus". Dividing humans into five main races, and argued that each evolved in parallel but at different rates, so that some races had reached higher levels of evolution than others. He argued that the Caucasoid race had evolved 200,000 years prior to the "Congoid race", and hence represented a higher evolutionary stage.

Criticism based on modern genetics.

After discussing various criteria used in biology to define subspecies or races, Alan R. Templeton concludes in 2016: "[T]he answer to the question whether races exist in humans is clear and unambiguous: no."

Racial anthropology.

Physical traits.

Skull and teeth.

Drawing from Petrus Camper's theory of facial angle, Blumenbach and Cuvier classified races, through their skull collections based on their cranial features and anthropometric measurements. Caucasoid traits were recognised as: thin nasal aperture ("nose narrow"), a small mouth, facial angle of 100°–90°, and orthognathism, exemplified by what Blumenbach saw in most ancient Greek crania and statues. Later anthropologists of the 19th and early 20th century such as Pritchard, Pickering, Broca, Topinard, Morton, Peschel, Seligman, Bean, Ripley, Haddon and Dixon came to recognize other Caucasoid morphological features, such as prominent supraorbital ridges and a sharp nasal sill. Many anthropologists in the 20th century used the term "Caucasoid" in their literature, such as Boyd, Gates, Coon, Cole, Brues and Krantz replacing the earlier term "Caucasian" as it had fallen out of usage.  Caucasoids have small teeth, with the maxillary lateral incisors often shrunken in size or replaced with peg laterals. According to George W. Gill and other modern forensic anthropologists, physical traits of Caucasoid crania can be distinguished from those of the people from Mongoloid and Negroid racial groups based on the shapes of specific diagnostic anatomical features. They assert that they can identify a Caucasoid skull with an accuracy of up to 95%. However, Alan H. Goodman cautions that this precision estimate is often based on methodologies using subsets of samples. He also argues that scientists have a professional and ethical duty to avoid such biological analyses since they could potentially have sociopolitical effects.  Variation in craniofacial form between humans has been found to be largely due to differing patterns of biological inheritance. Modern cross-analysis of osteological variables and genome-wide SNPs has identified specific genes, which control this craniofacial development. Of these genes, DCHS2, RUNX2, GLI3, PAX1 and PAX3 were found to determine nasal morphology, whereas EDAR impacts chin protrusion and facial hair, both of which have been recently selected in Caucasians

Classification.

In the 19th century "Meyers Konversations-Lexikon" (1885–90), Caucasoid was one of the three great races of humankind, alongside Mongoloid and Negroid. The taxon was taken to consist of a number of subtypes. The Caucasoid peoples were usually divided into three groups on ethnolinguistic grounds, termed Aryan (Indo-European), Semitic (Semitic languages), and Hamitic (Hamitic languages i.e. Berber-Cushitic-Egyptian).  19th century classifications of the peoples of India were initially uncertain if the Dravidians and the Sinahalese were Caucasoid or a separate "Dravida" race, but in 1915, some anthropolgists declared Dravidians to be Caucasoid.  Historically, the racial classification of the Turkic peoples was sometimes given as "Turanid". Turanid racial type or "minor race", subtype of the Europid (Caucasian) race with Mongoloid admixtures, situated at the boundary of the distribution of the Mongoloid and Europid "great races".  There was no universal consensus of the validity of the "Caucasoid" grouping within those who attempted to categorize human variation. Thomas Henry Huxley in 1870 wrote that the "absurd denomination of 'Caucasian'" was in fact a conflation of his Xanthochroi (Nordic) and Melanochroi (Mediterranean) types.

Subraces.

The postulated subraces vary depending on the author, including but not limited to Mediterranean, Atlantid, Aryan Nordic, East Baltic, Alpine, Dinaric, Turanid, Armenoid, Iranid, Indid, Arabid, and Hamitic.  H. G. Wells argued that across Europe, North Africa, the Horn of Africa, West Asia, Central Asia and South Asia, a Caucasian physical stock existed. He divided this racial element into two main groups: a shorter and darker "Mediterranean" or "Iberian" race and a taller and lighter "Nordic" race. Wells asserted that Semitic and Hamitic populations were mainly of Mediterranean type, and Aryan populations were originally of Nordic type. He regarded the Basques as descendants of early Mediterranean peoples, who inhabited western Europe before the arrival of Aryan Celts from the direction of central Europe.  The "Northcaucasian race" is a sub-race proposed by Carleton S. Coon (1930). It comprises the native populations of the North Caucasus, the Balkars, Karachays and Vainakh (Chechens and Ingushs).

Origin.

Carleton Coon (1962) argued that Caucasoid traits emerged prior to the Cro-Magnons, and were present in the Skhul and Qafzeh hominids. However, these fossils and the Predmost specimen were held to be Neanderthaloid derivatives because they possessed short cervical vertebrae, lower and narrower pelves, and had some Neanderthal skull traits. Coon further asserted that the Caucasoid race was of dual origin, consisting of early dolichocephalic (e.g. Galley Hill, Combe-Capelle, Téviec) and Neolithic Mediterranean "Homo sapiens" (e.g. Muge, Long Barrow, Corded), as well as Neanderthal-influenced brachycephalic "Homo sapiens" dating to the Mesolithic and Neolithic (e.g. Afalou, Hvellinge, Fjelkinge).

Usage in the United States.

In the United States, the term "Caucasoid" is used in disciplines such as craniometry, epidemiology, forensic medicine, forensic anthropology, and forensic archaeology. It is also associated with notions of racial typology.  Besides its use in anthropology and related fields, the term "Caucasian" has often been used in the United States in a different, social context to describe a group commonly called "white people". "White" also appears as a self-reporting entry in the U.S. Census. Naturalization as a United States citizen was restricted to "free white persons" by the Naturalization Act of 1790, and later extended to other resident populations by the Naturalization Act of 1870, Indian Citizenship Act of 1924 and Immigration and Nationality Act of 1952. The Supreme Court in "United States v. Bhagat Singh Thind" (1923) decided that Asian Indians were ineligible for citizenship because, though deemed "Caucasian" anthropologically, they were not "white" like European descendants since most laypeople did not consider them to be "white" people. This represented a change from the Supreme Court's earlier opinion in "Ozawa v. United States", in which it had expressly approved of two lower court cases holding "high caste Hindus" to be "free white persons" within the meaning of the naturalization act. Government lawyers later recognized that the Supreme Court had "withdrawn" this approval in "Thind". In 1946, the U.S. Congress passed a new law establishing a small immigration quota for Indians, which also permitted them to become citizens. Major changes to immigration law, however, only later came in 1965, when many earlier racial restrictions on immigration were lifted. This resulted in confusion about whether American Hispanics are included as "white", as the term "Hispanic" originally applied to Spanish heritage but has since expanded to include all people with origins in Spanish speaking countries. In other countries, the term "Hispanic" is not nearly as associated with race, but with the Spanish language and cultural affiliation.  The United States National Library of Medicine often used the term "Caucasian" as a race in the past. However, it later discontinued such usage in favor of the more narrow geographical term "European", which traditionally only applied to a subset of Caucasoids.

References.

Notes Bibliography

The Caucasian race (also Caucasoid or Europid) is an outdated grouping of human beings historically regarded as a biological taxon, which, depending on which of the historical race classifications is used, has usually included ancient and modern populations from all or parts of Europe, Western Asia, Central Asia, South Asia, North Africa, and the Horn of Africa.

高加索人种(英语:Caucasian race, Caucasoid),或称欧罗巴人种,是在欧洲、北非、非洲之角、西亚、中亚、南亚、北美、南美和大洋洲的人口中常见的人种。这个术语在体质人类学中用于来自这些地域的很多人群,与人类肤色没有必然性关联。高加索人种的种族主要有雅利安人种、闪米特人种和含米特人种,还包括乌拉尔语系民族等。