It was the first American war in which the death rate from disease was lower than that from battle, due to the provision of trained medical personnel ( of the 200,000 officers, 42,000 were physicians ), compulsory vaccination, rigorous camp sanitation, and adequate hospital facilities.

This article was the first to provide a rigorous proof that there was more than one kind of infinity.

The first scientifically rigorous theory was the Gaia hypothesis by James Lovelock, a UK chemist.

Thus, contrary to the first impression its name might convey, and as realized in specific approaches and disciplines ( e. g. Fuzzy Sets and Systems ), intuitionist mathematics is more rigorous than conventionally founded mathematics, where, ironically, the foundational elements which Intuitionism attempts to construct / refute / refound are taken as intuitively given.

Unfortunately not a whole lot of very old buildings are left in town: first the Americans carpet-bombed it in February 1944, later the Germans shelled it for about five months after the liberation in September 1944, and finally there were a lot of very rigorous city planners in the 1950s, 60's and 70's who finished what the Americans and Germans started.

In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.

Roman Catholics view the first day as a day for assembly for worship ( 2178, ), but consider a day of rigorous rest not obligatory on Christians (, ).

One of the defining classical works of horror, Mary Shelley's novel Frankenstein, is the first fully realized work of science fiction, where the manufacture of the monster is given a rigorous science-fictional grounding.

Durkheim sought to create one of the first rigorous scientific approaches to social phenomena.

Williams was privy to the plans of the Puritan leaders to migrate to the New World, and while he did not join the first wave in the summer of 1630, before the end of the year, he decided he could not remain in England under Archbishop William Laud's rigorous ( and High church ) administration.

Grimm's law was the first non-trivial systematic sound change to be discovered in linguistics ; its formulation was a turning point in the development of linguistics, enabling the introduction of a rigorous methodology to historical linguistic research.

Working with Gérard Debreu, Arrow produced the first rigorous proof of the existence of a market clearing equilibrium, given certain restrictive assumptions.

A rigorous proof was published by Argand in 1806 ; it was here that, for the first time, the fundamental theorem of algebra was stated for polynomials with complex coefficients, rather than just real coefficients.

This informal analysis can be formalized to make a rigorous proof of the incompleteness theorem, as described in the section " Proof sketch for the first theorem " below.

Komarov was later chosen for the rigorous task of commanding Soyuz 1 as part of the Soviet Union's bid to reach the Moon first.

Initially, for his first year under Leschetizky, he was given rigorous preparatory technical tuition from Anna Yesipova ( Leschetizky ’ s second wife and a famous pianist in her own right ) and also from Malwine Bree who was Leschetizky's assistant.

The first is an informal proof, a rigorous natural-language expression that is intended to convince the audience of the truth of a theorem.

Though Heaven's Gate was not the first film to have animals killed during its production, it is believed that the film was largely responsible for sparking the now common use of the " No animals were harmed ..." disclaimer and more rigorous supervision of animal acts by the AHA, which had been inspecting film production since the 1940s.

Radiography started in 1895 with the discovery of X-rays, also referred to as Röntgen rays after Wilhelm Conrad Röntgen who first described their properties in rigorous detail.

In 1874, on the first attempt, Sargent passed the rigorous exam required to gain admission to the École des Beaux-Arts, the premier art school in France.

On each occasion the allegation that there had been a policy of ' recruit to dilute ' was rejected, however, at first instance the judge described the Names as the innocent victims [...] of staggering incompetence and at appeal the Court found that representations that Lloyd's had a rigorous auditing system were false ( 376 of the judgment: [...] the answer to the question [...] whether there was in existence a rigorous system of auditing which involved the making of a reasonable estimate of outstanding liabilities, including unknown and unnoted losses, is no.

At first, there were no disputes, but soon the monks felt that Theobald was cheating them and imposing too rigorous a definition of poverty, and asked that the stewardship of the estates be restored to Parvus.

The Greek mathematician Archimedes ( c. 287 BC – c. 212 BC ), in The Method of Mechanical Theorems, was the first to propose a logically rigorous definition of infinitesimals.

During the last years of the 18th century, Sir George Cayley started the first rigorous study of the physics of flight.

Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae ( Latin, Arithmetical Investigations ), which, among things, introduced the symbol ≡ for congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, stated the class number problem for them, and showed that a regular heptadecagon ( 17-sided polygon ) can be constructed with straightedge and compass.

A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.

* Elements of Theology: A systematic work, with 211 propositions and proofs, describing the universe from the first principle, the One, to the descent of souls into bodies

Probably no English minister ever received in so short a time so many proofs of the confidence and admiration of the public, the capital and all the chief towns voting him addresses and the freedom of their corporations ( e. g., London presented him with the first ever honorary Freedom of the City awarded in history ).

First page of the first proofs of Béatrix ( Balzac ) | Béatrix

The mathematical aspects of the first two books were so clearly consistent that they were easily accepted ; for example, Locke asked Huygens whether he could trust the mathematical proofs, and was assured about their correctness.

He carried his enquiries so far into the occult sciences of abstruse and hidden nature, that, after having given most ample proofs, by his writings concerning physiognomy, geomancy, and chiromancy, he moved on to the study of philosophy, physics, and astrology ; which studies proved so advantageous to him, that, not to speak of the two first, which introduced him to all the popes of his time, and acquired him a reputation among learned men, it is certain that he was a great master in the latter, which appears not only by the astronomical figures he had painted in the great hall of the palace at Padua, and the translations he made of the books of the most learned rabbi Abraham Aben Ezra, added to those he himself composed on critical days, and the improvement of astronomy, but by the testimony of the renowned mathematician Regiomontanus, who made a fine panegyric on him, in quality of an astrologer, in the oration he delivered publicly at Padua when he explained there the book of Alfraganus.

The first of these was the trial of Sir Walter Raleigh ; according to one of Coke's biographers, " There is, perhaps, no reported case in which the proofs against the prisoner were weaker than in this trial ... never was an accused person condemned on slighter grounds ".

With a definition of effective calculation came the first proofs that there are problems in mathematics that cannot be effectively decided.

One genre is concerned with stories of prophetic miracles, called aʿlām al-nubuwa ( literally, proofs of prophethood — the first word is sometimes substituted for amārāt or dalāʾil ).

The collection includes autograph scores, sketches, composer-emended proofs and first editions of major works by Mozart, Bach, Beethoven, Brahms, Schumann, Chopin, Schubert, Liszt, Ravel, Stravinsky, Copland and other masters of the classical music canon.

Yet there are sufficient proofs and examples from nature that such flights can take place without danger, although when the first trials are made you may have to pay for the experience, and not mind an arm or leg.

Gödel specifically used this scheme at two levels: first, to encode sequences of symbols representing formulas, and second, to encode sequences of formulas representing proofs.

The first proofs of class field theory used substantial analytic methods.

For example, college studies now include linear algebra, topology, and graph theory where the subject is developed from first principles, and propositions are deduced by elementary proofs.

He lent his name to his sister's first romances, but did little beyond correcting the proofs.

Many proofs of the irrationality of the square roots of non-square natural numbers implicitly assume the fundamental theorem of arithmetic, which was first proven by Carl Friedrich Gauss in his Disquisitiones Arithmeticae.

Their first published proof replaced the cobordism theory of the first proof with K-theory, and they used this to give proofs of various generalizations in the papers.

After a short account of the incidents preceding the conversion of the king, and of his conversations with a philosopher, a Christian, and a Muslim concerning their respective beliefs, a Jew appears on the stage, and by his first statement startles the king ; for, instead of giving him proofs of the existence of God, he asserts and explains the miracles performed by Him in favor of the Israelites.

At the time of his death, Reznikoff was correcting proofs of the first volume of the Black Sparrow Collected Poems.

" This act was praised by the Latin Christians of the county ; " Such ", William continues, " were the first proofs of valor which were given by the young count, whereby he won the affection of all his people and universal approval.

This shows that he was unaware of two different proofs of this statement that Schönemann had given, one in either part of a two-part article, the second of which being the one based on the criterion cited above ; this is all the more surprising given the fact that two pages further Eisenstein actually refers ( for a different matter ) to the first part of Schönemann's article.

It performed an important role, historically speaking, in developments in topology in the 1950s and early 1960s, in particular in the Hirzebruch – Riemann – Roch theorem, and in the first proofs of the Atiyah – Singer index theorem.