A neusis construction might be performed by means of a 'Neusis Ruler': a marked ruler that is rotatable around the point "P" (this may be done by putting a pin into the point "P" and then pressing the ruler against the pin). In the figure, one end of the ruler is marked with a yellow eye with crosshairs: this is the origin of the scale division on the ruler. A second marking on the ruler (the blue eye) indicates the distance "a" from the origin. The yellow eye is moved along line "l", until the blue eye coincides with line "m". The position of the line element thus found is shown in the figure as a dark blue bar.
Point "P" is called the pole of the neusis, line "l" the directrix, or guiding line, and line "m" the catch line. Length "a" is called the "diastema" (διάστημα; Greek for "distance").
"Neuseis" have been important because they sometimes provide a means to solve geometric problems that are not solvable by means of compass and straightedge alone. Examples are the trisection of any angle in three equal parts, or the construction of a regular heptagon. Mathematicians such as Archimedes of Syracuse (287–212 BC) freely used "neuseis". Slowly, the Greeks stopped using it.
T. L. Heath, the historian of mathematics, thought that the Greek mathematician Oenopides (ca. 440 BC) was the first to put compass and straightedge constructions above "neuseis". Hippocrates of Chios (ca. 430 BC) may have spread the idea that mathematicians should avoid "neuseis" whenever possible. He came from the same island as Oenopides, and who was—as far as we know—the first to write a systematically ordered geometry textbook. One hundred years after him, Euclid also said bad things about "neuseis" in his very influential textbook, "The Elements".
The next attack on the neusis came when, from the fourth century BC, Plato's idealism gained ground. Under its influence, a hierarchy of three classes of geometrical constructions was developed. Descending from the "abstract and noble" to the "mechanical and earthly", the three groups were:
In the end, the Greek mathematicians thought that using a neusis was acceptable only when the two other, higher groups of constructions did not offer a solution. Neusis became a kind of last resort that was invoked only when all other, more respectable, methods had failed. Using neusis where other construction methods might have been used, was branded by the late Greek mathematician Pappus of Alexandria (ca. 325 AD) as "a not inconsiderable error".
Eishō
Eishō or Eisho may mean:
Acute accent
The acute accent ( ´ ) is a mark in many written languages. It is usually added above a vowel to show how to say it. Acute accents are sometimes added to consonants too. Sometimes, the acute accent changes the sound of the whole word by giving it stress in a sentence. This accent is part of many modern languages that use Latin, Cyrillic, and Greek alphabets. The acute accent is one of many similar marks called diacritics.
The acute accent was first used in Ancient Greece. It told the speaker when to say a syllable with a high pitch. Another early accent mark was the apex. In Latin the apex marked long vowels.
The acute accent is mainly used to tell readers about the sound of vowels in words. Sometimes it is very important to the meaning because it shows the difference between two similar words. For example, "resume" may mean to start again, but "résumé" is a summary of someone's work and school experience. Some languages use the accent to show the same changes in sounds, but others use it differently. The acute accent may show:
Some languages use the accent to actually make new letters. Both Faroese and Icelandic add the acute accent to all of their vowels to make new letters. These letters, á, í, ó, ú and ý (plus é in Icelandic) are separate letters with different pronunciations. In Turkmen, the letter is a consonant: .
Many languages have borrowed words from French. Many Norwegian words which came from French keep an acute accent. Some examples are: "allé", "kafé", "idé", "komité". Swedish examples include "café" and "resumé" (noun). Examples in English include: "attaché", "canapé", "cliché", "communiqué", "café", "décor", "fiancé", "passé", "toupée" and "touché". However, sometimes writers forget or choose not to use the accent mark.
Some languages such as Arabic, Persian, or Japanese do not use alphabets. Some writers use the acute accent to tell how the words should sound when words from these languages are written in English. This is more common in older books and less common today.
The ISO-8859-1 and Windows-1252 character encodings included "á", "é", "í", "ó", "ú", "ý". They also had how letters and accents looked when they were written as capital letters. Unicode has many more letters with the acute accent.
To make an accented letter in a Microsoft Office software (Word, PowerPoint, Excel, etc.), users hold the key and press the apostrophe key once. Then, let the key go, and press the letter they want.
On Apple Macintosh computers, users press "option-e" and then the vowel. Vowels can also be capitalised. For example, users make á by pressing "option-e" and then 'a'. Pressing "Option-e" and then "Shift-a" makes Á.
On Wikipedia, users make these symbols by clicking on a link in a box. Some other websites work the same way.
Sonitpur
Sonitpur is a major district of Assam, India.
The name "Sonitpur" as well as "Tezpur" literally means "the city of blood".
It reminds of the romantic legend of Usha and Anirudha. The legend revolves around Banasura, the great Asura king of ancient Tezpur, his beautiful daughter Usha and her friend Chitralekha. The princess saw a handsome prince in her dreams and fell in love with him. Chitralekha, a talented artist, not only painted his portrait from Usha's description but recognised him to be Aniruddha, the grandson of Lord Krishna and ruler of Dwarka. Using her magical powers, Chitralekha spirited Aniruddha away to the princess' boudoir where the two married each other according to Gandharva rites, without the knowledge of the king. When Banasura learnt of the clandestine romance, he imprisoned Aniruddha, which led to the arrival of Lord Krishna to rescue his grandson. A fierce battle followed and the entire city was drenched in human blood, hence the name Sonitpur or Tezpur, i.e. ‘the city of blood’ .
The story of eternal love between Usha and Aniruddha finds expression in many stories, novels, dramas, dance-dramas, movies.
Sir Edward A. Gait ( 1897) had made reference to the nine line inscription of Harjjar Varma in his ‘’A History of Assam.’’ The inscription is the first recorded history of Assam and dates back to 829 A.D. The inscription was found engraved on a massive
stone some two kms away from Tezpur town situated near a temple called Rudrapad.
Salastambha dynasty ruled Kamrupa from seventh to Tenth century A.D. The accurate boundary of their kingdom is debatable. But the erstwhile Darrang was certainly a part of the kingdom. They shifted their capital from Pragjyotishpur to Haruppeswara, or Hatappeswara- the present day Tezpur. The famous King of the dynasty Harjjar Varma, besides other things had excavated a large pond in 70 acres of land, later came to be known as Hajara Pukhuri ( Harjjara Pukhuri ).Pal dynasty ruled Haruppeswara till the 12th century. The most famous ruler of the Pal dynasty was Brahmapal.