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Cavalieri's principle

In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows: 2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in line segments of equal length the two regions have equal areas. 3-dimensional case: Suppose two regions in three-space are included between two parallel planes. If every plane parallel to these two planes intersects both regions in cross-sections of equal area the two regions have equal volumes. Today Cavalieri's principle is seen as an early step towards integral calculus, while it is used in some forms, such as its generalization in Fubini's theorem, results using Cavalieri's principle can be shown more directly via integration. In the other direction, Cavalieri's principle grew out of the ancient Greek method of exhaustion, which used limits but did not use infinitesimals. Cavalieri's principle was called the method of indivisibles, the name it was known by in Renaissance Europe.

Cavalieri developed a complete theory of indivisibles, elaborated in his Geometria indivisibilibus continuorum nova quadam ratione promota and his Exercitationes geometricae sex. In the 3rd century BC, using a method resembling Cavalieri's principle, was able to find the volume of a sphere given the volumes of a cone and cylinder in his work The Method of Mechanical Theorems. In the 5th century AD, Zu Chongzhi and his son Zu Gengzhi established a similar method to find a sphere's volume; the transition from Cavalieri's indivisibles to Evangelista Torricelli's and John Wallis's infinitesimals was a major advance in the history of the calculus. The indivisibles were entities of codimension 1, so that a plane figure was thought as made out of an infinity of 1-dimensional lines. Meanwhile, infinitesimals were entities of the same dimension as the figure. Applying the formula for the sum of an arithmetic progression, Wallis computed the area of a triangle by partitioning it into infinitesimal parallelograms of width 1/∞.

If one knows that the volume of a cone is 1 3 one can use Cavalieri's principle to derive the fact that the volume of a sphere is 4 3 π r 3, where r is the radius. That is done as follows: Consider a sphere of radius r and a cylinder of radius r and height r. Within the cylinder is the cone whose apex is at the center of one base of the cylinder and whose base is the other base of the cylinder. By the Pythagorean theorem, the plane located y units above the "equator" intersects the sphere in a circle of area π; the area of the plane's intersection with the part of the cylinder, outside of the cone is π. As we can see, the area of every intersection of the circle with the horizontal plane located at any height y equals the area of the intersection of the plane with the part of the cylinder, "outside" of the cone; the aforementioned volume of the cone is 1 3 of the volume of the cylinder, thus the volume outside of the cone is 2 3 the volume of the cylinder. Therefore the volume of the upper half of the sphere is 2 3 of the volume of the cylinder.

The volume of the cylinder is base × height = π r 2 ⋅ r = π r 3 Therefore the volume of the upper half-sphere is 2 3 π r 3 and that of the whole sphere is 4 3 π r 3. The fact that the volume of any pyramid, regardless of the shape of the base, whether circular as in the case of a cone, or square as in the case of the Egyptian pyramids, or any other shape, is × base × height, can be established by Cavalieri's principle if one knows only that it is true in one case. One may establish it in a single case by partitioning the interior of a triangular prism into three pyramidal components of equal volumes. One may show the equality of those three volumes by means of Cavalieri's principle. In fact, Cavalieri's principle or similar infinitesimal argument is necessary to compute the volume of cones and pyramids

Settimo Mineo

Settimo Mineo is an Italian member of the Sicilian Mafia Pagliarelli mandamento from Palermo. Settimo Mineo, known as "Tonton Settimo", was born in Palermo in 1938, he owns a jewelry shop in the Palermo, but is considered the oldest boss of the Sicilian Mafia. In 1982, he escaped an ambush that cost the life of his brother Giuseppe, while in 1976 his brother Antonino was murdered. Testified against by pentito Tommaso Buscetta, he was sentenced to five years in prison in the Maxi Trial. After he was released from prison, he was re-arrested in 2006 and sentenced in the "Gotha" trial, he was released in 2013 by decision of the Supreme Court of Cassation. Despite being an former associate of Antonio Rotolo, a historical ally of the Corleonesi Mafia clan, in recent years Mineo made alliances with the cousins Franco and Tommaso Inzerillo, members of the Inzerillo Mafia clan and had as his right-hand man, Salvatore Sorrentino, all of them known rivals of Rotolo and of the Corleonesi, showing that Settimo Mineo had changed sides inside the Cosa Nostra.

On 29 May 2018, Mineo was elected the new head of the Sicilian Mafia Commission after the death of Salvatore Riina. On 4 December 2018, he was re-arrested in the operation "Cupola 2.0" conducted by the Carabinieri, on charges to be the new head of the "Dome" of Cosa Nostra. Before his arrest, Mineo was known for his mediation skills. Mineo and his wife would go to mass at the Church of San Giovanni Decollato in Ballarò, for a year participated in a volunteer project of the church, involved in an after-school program for children at the church


Nicocodeine is an opioid analgesic and cough suppressant, an ester of codeine related to dihydrocodeine and the codeine analogue of nicomorphine. It is not used in most countries, but has activity similar to other opiates. Nicocodeine and nicomorphine were introduced in 1957 by Lannacher Heilmittel of Austria. Nicocodeine is metabolised in the liver by demethylation to produce nicomorphine known as 6-nicotinoylmorphine, subsequently further metabolised to morphine. Side effects are similar to those of other opiates and include itching and respiratory depression. Related opioid analogues such as nicomorphine and nicodicodeine were first synthesized; the definitive synthesis, which involves treating anhydrous codeine base with nicotinic anhydride at 130 °C, was published by Pongratz and Zirm in Monatshefte für Chemie in 1957 with the two analogues in an article about amides and esters of various organic acids. Nicocodeine is always used as the hydrochloride salt, which has a free base conversion ratio of.917.

In the past, the tartrate, phosphate, methiodide and sulfate were used in research or as pharmaceuticals. Nicocodeine is regulated in most cases as is codeine and similar weak opiate drugs like ethylmorphine, benzylmorphine and its other close derivatives like acetyldihydrocodeine and others of this class in the laws of countries and the Single Convention On Narcotic Drugs. One notable example is the fact that nicocodeine is a Schedule I/Narcotic controlled substance in the United States along with heroin as nicocodeine was never introduced for medical use in the United States. Nicodicodeine is a similar drug, to nicocodeine as dihydrocodeine is to codeine; the metabolites of nicodicodeine include dihydromorphine where nicocodeine is turned into morphine as noted above. Nicocodeine cough medicines are available as syrups, extended-release syrups, sublingual drops. Analgesic preparations are in the form of sublingial drops and tablets for oral administration. Nicocodeine is the same strength as hydrocodone.

The 2013 DEA annual production quota for nicocodeine and its two related drugs are zero. Nicocodeine's ACSCN is 9309. Nicodicodeine is not assigned an ACSCN and is controlled as either an ester of dihydromorphine or derivative of nicomorphine


Naim is a male given name and surname. Notable persons with the name include: Naim ibn Hammad, Hadith collector Naeem Ahmed, Pakistani cricketer Na'im Akbar, American psychologist Naïm Aarab, Belgian football player Naim Araidi, Israeli writer Naim Ateek, Palestinian priest Naim Attallah, Palestinian businessman Naeem Ashraf, Pakistani cricketer Naim Bey, Ottoman bureaucrat Naeem Bokhari, Pakistani television host and lawyer Naim Dangoor, British businessman Naim Farouqi, Afghan detainee Naim Frashëri, Albanian romantic poet Naim Frashëri, Albanian actor Naeem Hashmi, Pakistani film actor Na'im ibn Musa, Iraqi mathematician Na'eem Jeenah, South African political activist Naeem Khan, American fashion designer Naïm Kattan, Jewish Iraqi-born Canadian writer Niam Kuchi, Afghan detainee Naim Krieziu, Albanian football player Naim Maloku, Kosovar politician Naeem Murr, British novelist Naim Popal, Afghan musician Naeim Saadavi, Iranian football player and coach Naim Süleymanoğlu, Turkish weightlifter Naim Talu, Turkish politician and Prime Minister Naim Terbunja, Swedish boxer Abdullahi Ahmed An-Na'im, Sudanese lawyer and writer Armon Ben-Naim, Israeli football player C. M. Naim, American writer Hussein Naeem, Lebanese football player Mohammad Naeem, several people Moisés Naím, Venezuelan writer Omar Naim, Lebanese film director and screenwriter Ra'anan Naim, Israeli politician Yael Naim, Israeli singer Yuval Naim, Israeli former football player and manager Yuval Naimy, Israeli basketball player Nicole Naim, A legend

Children's Park, Kollam

Asramam Children's Park is a park for children, situated at Asramam in Kollam city, Kerala. The park is owned by India, it is called Children’s Traffic Park. This park is considered as a part of Asramam Picnic Village, main centre for recreational activities in Kollam city. A model Adventure Park and a 200-year-old British Residency are situated close to this park. Kollam KSRTC Bus Station – 1.2 km Kollam Junction railway station – 3.8 km Chinnakada – 1.2 km Kollam Port – 3.4 km Kollam Ferry Terminal – 1.2 km Andamukkam City Bus Stand – 2.6 km The Children's Park in Asramam is one of the major attractions of Kollam city. The Government of Kerala modernized the park with Central Government aid in 2009–2010, it got another facelift in 2014, with the addition of new rides. Nowadays, this children's park is a regular exhibition ground for the Kollam Flower Show

Maximilian Karl Albert, Prince of Löwenstein-Wertheim-Rochefort

Maximilian Karl Albert, Prince of Löwenstein-Wertheim-Rochefort was an Austrian military officer and the first Prince of Löwenstein-Wertheim-Rochefort. Maximilian Karl Albert was the fourth child and the first son of Ferdinand Karl, Count of Löwenstein-Wertheim-Rochefort and his wife Countess Anna Maria of Fürstenberg. Maximilian Karl, entered the emperor's service at an early age, was an acting imperial advisor since 1684 and was named privy councilor of the empire in 1699. After Prince Elector Max Emanuel of Bavaria was forced into exile in 1704, Maximilian Karl became the imperial administrator of Bavaria and, in his new rank as a prince, assumed the honorable position of a principle commissioner, the permanent representative of the emperor in the imperial diet from 1712 on. On 3 April 1711 he was elevated to the status of a prince by Emperor Joseph I, he was granted principality for all his legitimate descendants by the emperor's brother and successor, Emperor Karl VI, on 8 January 1712.

His last office in the imperial service, which he held from 1717 until his death was the governorship of the Duchy of Milan, which Prince Eugene of Savoy had conquered for the House of Habsburg. Maximilian Karl was buried in Milan. On 26 August 1678, Maximilian Karl Albert married the Tyrolean Countess Maria Polyxena Khuen von Lichtenberg und Belasi; the marriage produced ten children: Princess Maria Theresia Franziska zu Löwenstein-Wertheim-Rochefort Wilhelm Karl Magnus Anton, Erbgraf zu Löwenstein-Wertheim-Rochefort Maximilian Karl Anton, Erbgraf zu Löwenstein-Wertheim-Rochefort Count Wolfgang Philipp Eberhard Joseph zu Löwenstein-Wertheim-Rochefort Count Felix Albert zu Löwenstein-Wertheim-Rochefort Princess Eleonore Maria Anna zu Löwenstein-Wertheim-Rochefort married in Frankfurt on 9 November 1704 Ernest Leopold, Landgrave of Hesse-Rotenburg and had issue Count Franz Joseph zu Löwenstein-Wertheim-Rochefort Princess Maria Leopoldine Theresia Renata Dorothea zu Löwenstein-Wertheim-Rochefort married in Alt-Otting on 1 September 1710 Conrad Sigismund, Count von Starhemberg and had issue Dominik Marquard Sebastian Christian Ernst, 2.

Fürst zu Löwenstein-Wertheim-Rochefort married Landgravine Christine of Hesse-Wanfried a daughter of Charles, Landgrave of Hesse-Wanfried and had issue Count Franz Carl zu Löwenstein-Wertheim-Rochefort Karl-Heinz Zuber, "Löwenstein-Wertheim-Rochefort, Maximilian Karl Fürst zu", Neue Deutsche Biographie, 15, Berlin: Duncker & Humblot, pp. 98–99.