The first explicit formulation of the principle of induction was given by Pascal in his Traité du triangle arithmétique ( 1665 ).

In this case the sequence is called a composition series for M. In order to prove a statement inductively using composition series, the statement is first proved for simple modules, which form the base case of the induction, and then the statement is proved to remain true under an extension of a module by a simple module.

Faraday performed the first experiments on induction between coils of wire, including winding a pair of coils around an iron ring, thus creating the first toroidal closed-core transformer.

The first type of transformer to see wide use was the induction coil, invented by Rev.

Stanley's first patented design was for induction coils with single cores of soft iron and adjustable gaps to regulate the EMF present in the secondary winding ( see image ).

The transformer is based on two principles: first, that an electric current can produce a magnetic field ( electromagnetism ) and second that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil ( electromagnetic induction ).

Stanley's first patented design was for induction coils with single cores of soft iron and adjustable gaps to regulate the EMF present in the secondary winding.

* 1889: Mikhail Dolivo-Dobrovolsky of Gatchina, Russian Empire created the first squirrel-cage induction motor.

* September 21 – William Stanley, Jr. patents the first practical alternating current transformer device, the induction coil.

In June 2006 Hanks was inducted as an honorary member of the United States Army Rangers Hall of Fame for his accurate portrayal of a Captain in the movie Saving Private Ryan ; Hanks, who was unable to attend the induction ceremony, was the first actor to receive such an honor.

These electrons interact with the radio-frequency magnetic field of the induction coil and are accelerated first in one direction, then the other, as the field changes at high frequency ( usually 27. 12 million cycles per second ).

These electrons interact with the radio-frequency magnetic field of the induction coil and are accelerated first in one direction, then the other, as the field changes at high frequency ( usually 27. 12 MHz ).

This issue arises in first order theories of arithmetic, such as Peano arithmetic, because the principle of mathematical induction is expressed as an infinite set of axioms ( an axiom schema ).

Prior to the first act, an induction frames the play as a " kind of history " played in front of a befuddled drunkard named Christopher Sly who is tricked into believing that he is a lord.

There is the same degree of licentiousness and error in forming Axioms, as in abstracting Notions: and that in the first principles, which depend in common induction.

1968 introduced the Endura ' rubber ' front bumper on the GTO, the precursor to modern cars ' integrated bumpers, and the first of a series " Ram Air " engines, which featured the induction of cold air to the carburetor ( s ) for more power, and took away some of the sting from deleting the famous Tri-Power multiple carburation option from the engine line up.

While it was believed for years that the first professional football game was played in Latrobe, the city refused induction into the Hall of Fame records.

One critical test is nevertheless to consider the induction from experience that the externally observable world does not seem, at first approach, to be directly manipulable purely by mental energies alone.

Grassmann ( 1861 ) set out the first axiomatic presentation of arithmetic, making free use of the principle of induction.

He chose to wear the Reds cap at his induction in honor of former GM Bob Howsam, who gave Anderson his first chance at a major-league managing job.

" Avicenna then adds two further methods for arriving at the first principles: the ancient Aristotelian method of induction ( istiqra ), and the method of examination and experimentation ( tajriba ).

The first term on the right hand side of the induction equation is a diffusion term.

We will first discuss several major candidates thought to be involved in the induction and maintenance of both embryonic stem cells and their differentiated progeny, and then turn to one example of specific signaling pathways in which more direct evidence exists for its role in epigenetic change.

On 21 October 2007, Whineray became the first New Zealander to earn induction to the IRB Hall of Fame.

We visited the Okamoto home -- where for the first time I saw the famous tea ceremony.

The first Academy Awards ceremony was held on May 16, 1929, at the Hotel Roosevelt in Hollywood to honor the outstanding film achievements of the 1927 / 1928 film season.

He had to return to Europe before the ceremony, so the Academy agreed to give him the prize earlier ; this made him the first Academy Award winner in history.

The first three C-295s, designated C-105A Amazonas in Brazilian service, were commissioned into service in a formal ceremony at Base Aérea de Manaus on March 31, 2007.

The second funeral differs from the first in that it is a cremation ceremony rather than a ship-burial.

She had ceased to attend the meetings when she was nominated to be the first woman Grand Master of the Science Fiction Writers of America, but the nomination was withdrawn at the request of her husband, Thomas Reggie, who said that due to the Alzheimer's progress the award and ceremony would be at best confusing and likely upsetting to her.

Rowan Atkinson makes his second appearance, this time as a fully fledged but gaffe-prone priest conducting his first wedding ceremony through his connection as a friend of the family.

The ceremony was first conducted with the Prince of Wales ( the future Edward VIII ) in 1927, then with King George VI in 1939, and last with his daughter, Queen Elizabeth II in 1959 and 1970.

However, according to some traditions, the announcement of the month of Aviv could also be postponed depending on the condition of roads used by families to come to Jerusalem for Passover, adequate numbers of lambs to be sacrificed at the Temple, and on the ripeness of the barley that was needed for the first fruits ceremony.

Although the practice of Holy Communion was first alluded to in the Christian Bible and defined by theologians in the 1st centuries AD, it was around the time of the appearance of the first Christianised Grail literature that the Roman church was beginning to add more ceremony and mysticism around this particular sacrament.

Today, a Kohen is the first one called up at the reading of the Torah, performs the Priestly Blessing, as well as complying with other unique laws and ceremonies, including the ceremony of redemption of the first-born.

The first line was opened in July 1942, the ceremony being disrupted by passively-resisting Jersey spectators.

" This name actually refers to a special " ceremony ": the last weekly Torah portion is read from Deuteronomy, completing the annual cycle, and is followed immediately by the reading of the first chapter of Genesis.

Louis Mountbatten, 1st Earl Mountbatten of Burma | Lord Mountbatten swears in Pandit Jawaharlal Nehru as the first Prime Minister of free India at the ceremony held at 8: 30 am Indian Standard Time | IST on 15 August 1947

Kaunda was appointed Chancellor and officiated at the first graduation ceremony in 1969.

On 18 March, the Polish Army re-enacted Poland's Wedding to the Sea ceremony, which had been celebrated for the first time in 1920 by General Józef Haller.

He has produced the Academy Awards ceremony twice, first in 1999 with the 72nd annual Academy Awards and second in 2004 with the 77th annual ceremony.

* 1964 – The opening ceremony at The 1964 Summer Olympics in Tokyo, Japan, is broadcast live in the first Olympic telecast relayed by geostationary communication satellite.

The Apostolic Tradition, attributed to Hippolytus of Rome ( died 235 ), describes how to perform the ceremony of baptism ; it states that children were baptised first, and if any of them could not answer for themselves, their parents or someone else from their family was to answer for them.

Strikingly, among the first uses of grounded floats — towed by horses — was a ceremony in memory of recently drowned parade oarsmen.

The first spade at the start of the Daimler-Benz development was turned by the Mayor of Berlin, Eberhard Diepgen, on 11 October 1993, and the finished complex was officially opened by the Federal President of Germany, Roman Herzog, on 2 October 1998, in a glittering ceremony featuring large-scale celebrations and musical performances.

Four years later, at the first commencement ceremony, 35 bachelor's degrees and one master's degree were awarded.

Later that year, he won first prize in the International Science Fair for the invention ; he was also recognized by the Westinghouse Talent Search and was personally congratulated by President Lyndon B. Johnson during a White House ceremony.