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Page "Euler's sum of powers conjecture" ¶ 15
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From and initial
From an initial investment of $1,200 in 1943, it has grown, with no additional capital investment, to a present value estimated by some as exceeding $10,000,000 ( we don't disclose financial figures to the public ).
From his blood sprang a red flower, as at the death of Hyacinthus, which bore on its leaves the initial letters of his name Ai, also expressive of lament.
From this initial collection of filmmakers with left-wing political agendas, Marker created the group S. L. O. N.
From the eigenvalues and the eigenvectors of A it is possible to determine if an initial point will converge or diverge to the equilibrium point at the origin.
From an estimated initial population of 250, 000 in 1492, 14, 000 Arawaks were left by 1517.
From late 1947 to May 1949, Fuchs gave Alexander Feklisov, his case officer, the principal theoretical outline for creating a hydrogen bomb and the initial drafts for its development as the work progressed in England and America.
From almost all initial conditions we can no longer see any oscillations of finite period.
From his initial capital Ambohimanga, and later from the Rova of Antananarivo, this Merina king rapidly expanded his rule over neighboring principalities.
From an initial twelve acres, Al-Fayed has since built the estate up to sixty five thousand acres.
From an initial design point of view, engineers often use a quantity termed the specific speed to identify the most suitable pump type for a particular combination of flow rate and head.
From his initial monastery, demand quickly grew and, by the time of his death in 346, one count estimates there were 3000 monasteries dotting Egypt from north to south.
From the initial syllables of the first verses of the resultant setting he then took the names of the first notes of the musical scale.
From the initial two Yugoslav-built cargo vessels, the line had grown by the mid-1970s to seven ships, totaling about 52, 340 deadweight tons.
From the early years of his life, Shoghi Effendi was greatly influenced by ` Abdu ' l-Bahá, who provided much of his initial training.
From five initial bulls, all current European bison bulls have one of only two remaining Y-chromosomes.
From the initial colonization ( s ) the Lucayans expanded throughout the Bahamas Islands in some 800 years ( c. 700 – c. 1500 ), growing to a population of about 40, 000.
From an initial aerial victory over a Focke-Wulf Fw 190 on 5 April their tally rose dramatically and the squadron became the focus of Soviet propaganda, so much so that Generalfeldmarschall Wilhelm Keitel decreed that any French pilot captured would be executed.
From the 13th to 15th century, Baltic and Ukrainian lands were consolidated into the Grand Duchy of Lithuania, with its initial capital unknown, but which presumably could have been either Navahrudak, Voruta, Trakai, Kernavė or Vilnius.
From its initial public announcement, Murphy's law quickly spread to various technical cultures connected to aerospace engineering.
From the initial synthesis of PCB until 1914, large amounts of PCB were released into the environment.
The initial release of the band's first album, From Genesis to Revelation, used a plain black sleeve with Genesis written in a green gothic typeface.
From 1895 to 1950, the Olmsted Brothers ( his successors ) added to some of their father's initial projects, as well as designing new ones.
From the 7th century it spread rapidly from the Arabian Peninsula to the rest of the world through the initial Muslim conquests, and subsequently with traders and explorers after the death of the Prophet Muhammad.
From these initial connections, Gelli was able to extend his network throughout the echelons of the Italian establishment.

From and rational
From this, it might be wondered why any rational government would engage in actions that cause or continue hyperinflation.
From the 8th century, the Mutazilite school of Islam, compelled to defend their principles against the orthodox Islam of their day, looked for support in philosophy, and are among the first to pursue a rational Islamic theology, called Ilm-al-Kalam ( scholastic theology ).
From this shared starting point social contract theorists seek to demonstrate, in different ways, why a rational individual would voluntarily consent to give up his or her natural freedom to obtain the benefits of political order.
From this premise, the Mu ' tazili school of Kalam proceeded to posit that the injunctions of God are accessible to rational thought and inquiry: because knowledge is derived from reason, reason is the " final arbiter " in distinguishing right from wrong.
From this it follows that eudaimonia, living well, consists in activities exercising the rational part of the psyche in accordance with the virtues or excellency of reason.
From the late 1940s onwards Ellis worked on REBT and by January 1953 his break with psychoanalysis was complete, and he began calling himself a rational therapist.
From another viewpoint, motives continue the sequence of generalizations from rational functions on varieties to divisors on varieties to Chow groups of varieties.
From nice and rational ( Sailor Neptune ) to hotheaded ( Tsunade, Ikari ) and playful ( Ceilia von Spitzweg, Maria ), she tends to mainly play strong, beautiful female characters.
From 1961 until his retirement in 1989, Truesdell was professor of rational mechanics at Johns Hopkins University.
From his ministry in Rome, he developed and supervised the new village map, completely rebuilding it along rational lines from 1927 to 1934.
From global climate change to earthquakes, volcanoes, nonrenewable resources, environmental hazards and beyond, Observatory scientists provide a rational basis for the difficult choices facing humankind in the planet ’ s stewardship.
From there, the author rebuilds a great part of Euclidean geometry on top of his new proposed measurements, using only rational equivalences, which allow him to avoid any assumptions about the underlying scalar field.

From and point
One, a reservation on the point I have just made, is the phenomenon of pseudo-thinking, pseudo-feeling, and pseudo-willing, which Fromm discussed in The Escape From Freedom.
From the point of view of popularity the best-known member of the Commission was Walter Camp, the Yale athlete whose sobriquet was `` the father of American football ''.
From this point of view the `` militant mobs '' of the past, stirred into action by one ideology or another, were all composed of `` intellectuals '' -- and this is not the level on which the essence of mankind can be discovered.
From the moment of the occupation Lublin became a focal point.
From this point, I paint in as direct a manner as possible, by flowing on the washes with as pure a color mixture as I can manage.
From the manufacturer's point of view, the increasing cost of advertising and promotion is a very real problem to be faced in the sixties.
From the point of view of the applicants, less time was wasted in being evaluated -- and they got a meal out of it as well as some insights into their performances.
From the point of view of syntactic analysis the head word in the statement is the predicator has broken, and from the point of view of meaning it would seem that the trouble centers in the breaking ; ;
From the point of view of word formation real might be expected to have two syllables.
From the rather tortuous history of electoral planning in Morocco an important point emerges concerning the first elections in a developing country and evaluating their results.
From that point on he said he went to the post office and then walked leisurely to where his niece was staying, more than a mile away.
From the lioness' point of view, this strange creature on the back of another creature, lashing out with its long thin paw, very likely appeared as something she could not at first cope with.
From an economic point of view, the order Asparagales is second in importance within the monocots to the order Poales ( which includes grasses and cereals ).
From this point on he establishes himself as a psychological detective who proceeds not by a painstaking examination of the crime scene, but by enquiring either into the nature of the victim or the psychology of the murderer.
From this point, his mother and stepfather took a more active role in raising him.
From an artistic point of view, he was most successful in portrait-statues and groups of children, where he was obliged to follow nature most closely.
From the most northerly point, Ras ben Sakka in Tunisia, in 37 ° 21 ′ N, to the most southerly point, Cape Agulhas in South Africa, 34 ° 51 ′ 15 ″ S, is a distance approximately of ; from Cape Verde, 17 ° 33 ′ 22 ″ W, the westernmost point, to Ras Hafun in Somalia, 51 ° 27 ′ 52 ″ E, the most easterly projection, is a distance ( also approximately ) of.
From a strictly aerodynamic point of view, the term should refer only to those side-effects arising as a result of the changes in airflow from an incompressible fluid ( similar in effect to water ) to a compressible fluid ( acting as a gas ) as the speed of sound is approached.
From that point on, the show was a success.
From a political point of view, there is a trade-off between Bulgaria's economic growth and the stability required for early accession to the monetary union.
From a philosophical point of view, what makes the brain special in comparison to other organs is that it forms the physical structure that generates the mind.
From south to north, Broadway at one point or another runs over or under the IRT Lexington Avenue Line, the BMT Broadway Line, the IRT Broadway – Seventh Avenue Line, and the IND Eighth Avenue Line:

2.340 seconds.