The intuition about mankind conveyed in these opening pages is of crucial importance for understanding the remainder of the text ; ;

It is difficult to tabulate exactly what was meant in each individual situation, but the conclusion may be drawn that 21 towns do not assess movable personal property, and of the remainder only certain types are valued for tax purposes.

The Russian experimenters claim that only a small fraction of the impulse from the sensors is caused by the incident momentum with the remainder being momentum of ejected material from the sensor.

The major part of this collection is in the central headquarters building, and the remainder is divided among five libraries in the system designated as subject centers.

And to " measure " is to place a shorter measuring length s successively ( q times ) along longer length l until the remaining portion r is less than the shorter length s. In modern words, remainder r = l − q * s, q being the quotient, or remainder r is the " modulus ", the integer-fractional part left over after the division.

The remainder of the book is a collection of essays on the game, statistics for the new characters and an update of the older ones in light of their appearance in the second series, and ( perhaps most usefully for GMs ) plot summaries of each of the ten books.

In the remainder of this region, the southern portion, the most prominent feature is Little Mountain, extending about from east to west between two valleys, and rising precipitously on the north side above them or above the sea.

The remainder of the state is occupied by the Coastal Plain.

Similar to the view of Leopold Kronecker that " God made the integers ; all else is the work of man ," musicians drawn to the alphorn and other instruments that sound the natural harmonics, such as the natural horn, consider the notes of the natural harmonic series — particularly the 7th and 11th harmonics — to be God's Notes, the remainder of the chromatic scale enabled by keys, valves, slides and other methods of changing the qualities of the simple open pipe being an artifact of mere mortals.

The remainder of this article is about the carbonyl-nitrogen sense of amide.

The first half is based mainly on the Soliloquies of St Augustine of Hippo, the remainder is drawn from various sources, and contains much that is Alfred's own and highly characteristic of him.

Of the rest of the land, 55. 2 % is settled ( buildings or roads ) and the remainder ( 4. 5 %) is non-productive ( rivers or lakes ).

The clouds which strike Kathiawar and Kutch are deprived of a great deal of their moisture by the hills in those countries ( now the majority of this region is in Gujarat state within independent India ), and the greater part of the remainder is deposited on Mount Abu and the higher slopes of the Aravalli Range, leaving but little for Merwara, where the hills are lower, and still less for Ajmer.

For example, an estate is granted to A for life, with remainder to the heir of B.

During B's lifetime, the remainder is in abeyance, for until the death of B it is uncertain who is B's heir.

During the remainder of Nero's reign, Agrippina's grave was not covered or enclosed.

However, in 1766 of common land were enclosed at Ryton, and 4 years later enclosure was applied to the remainder of land in Bulkington, totalling.

Thus, the dentist would preserve healthy natural tooth structure that existed on the mesiobuccal corner of the tooth for aesthetic purposes, the remainder of the tooth would be enclosed in restorative material.

The remainder was divided and enclosed and passed to the commoners.

The 8051 microcontroller has two, a primary accumulator and a secondary accumulator, where the second is used by instructions only when multiplying ( MUL AB ) or dividing ( DIV AB ); the former splits the 16-bit result between the two 8-bit accumulators, whereas the latter stores the quotient on the primary accumulator A and the remainder in the secondary accumulator B.

He and Mary Anne alternated between Hughenden and several homes in London for the remainder of their marriage.

For the remainder of his life he spent time between Albuquerque, New Mexico and Florida, living the last 13 years of his life in Archer, Florida, a small farming town near Gainesville.

The final nonzero remainder r < sub > N − 1 </ sub > is the greatest common divisor of a and b. The number N cannot be infinite because there are only a finite number of nonnegative integers between the initial remainder r < sub > 0 </ sub > and zero.

For the remainder of the decade, Voight would alternate between feature films and television movies, including a starring role in the 1993 miniseries Return to Lonesome Dove, a continuation of Larry McMurtry's western saga, 1989's Lonesome Dove.

Of the remainder, four have runways 1, 524 to 2, 437 m length, and a further four of lengths between 914 and 1, 523 m. Of the airports without paved runways, 1 has runways of length above 1, 524m, 17 have runway lengths between 914 and 1, 523 m, leaving 25 with length below 914m.

During World War II, the Vardar Banovina was occupied between 1941 and 1944 by Italian-ruled Albania, which annexed the Albanian-populated western regions, and pro-German Bulgaria, which occupied the remainder.

One study on genetic variations between different species of Drosophila suggests that if a mutation changes a protein produced by a gene, the result is likely to be harmful, with an estimated 70 percent of amino acid polymorphisms having damaging effects, and the remainder being either neutral or weakly beneficial.

Six of the remainder have strips between 1, 524 and 2, 437 m, while one is under 914 m. 18 additional airports have unpaved runways 15 of them with strips between 914 and 1, 523 m.

The remainder of their 2005 home games were split between the Alamodome in San Antonio, Texas, and LSU's Tiger Stadium in Baton Rouge, Louisiana.

Of the 348 hymns in the original published edition of 1779 some commentaries state that Cowper wrote just 66 between 1772 and 1773, and Newton the remainder, while other sources attribute 67 to Cowper.

The difference between an amnesty and a presidential pardon is that the former clears all subsequent effects of the sentencing, as though the crime had not been committed, while pardon simply relieves the sentenced individual from part or all of the remainder of the sentence.

The potential to criticise arises from the gap between the concept and the object, which can never go into the former without remainder.

During the remainder of Paley's life his time was divided between Bishopwearmouth and Lincoln, during which time he wrote Natural Theology, despite his increasingly debilitating illness.

A golden era of 95 years comes to an end for Norway as civil wars between the members of Harald Fairhair's family line rage for the remainder of the century.

Economically, however, the majority of Perot voters ( 57 %) were middle class, earning between $ 15, 000 and $ 49, 000 annually, with the bulk of the remainder drawing from the upper middle class ( 29 % earning more than $ 50, 000 annually ).

For example, a quartz arenite would be composed of mostly (> 90 %) quartz grains and have little / no clayey matrix between the grains, a lithic wacke would have abundant lithic grains (< 90 % quartz, remainder would have more lithics than feldspar ) and abundant muddy matrix, etc.

The friendship between the two men was irreversibly damaged and their bitterness would last for the remainder of their lives.

In a stratagem possibly devised by the veteran Andrew Trollope, half the Lancastrian army under Somerset and Clifford advanced openly towards Sandal Castle, over the open space known as " Wakefield Green " between the castle and the River Calder, while the remainder under Ros and the Earl of Wiltshire were concealed in the woods surrounding the area.

( Sketch of proof: let A, B, C be the sets of residue classes modulo-and-coprime-to m, n, mn respectively ; then there is a bijection between A × B and C, by the Chinese remainder theorem.

Schepmann did his best to run the SA for the remainder of the war, attempting to restore the group as a predominant force within the Nazi Party and to mend years of distrust and bad feelings between the SA and SS.

The remainder term R is most easily expressed using the periodic Bernoulli polynomials P < sub > n </ sub >( x ).

Then, in terms of P < sub > n </ sub >( x ), the remainder

The goal of the kth step is to find a quotient q < sub > k </ sub > and remainder r < sub > k </ sub > such that the equation is satisfied

In other words, multiples of the smaller number r < sub > k − 1 </ sub > are subtracted from the larger number r < sub > k − 2 </ sub > until the remainder is smaller than the r < sub > k − 1 </ sub >.

In the next step ( k = 1 ), the remainders equal b and the remainder r < sub > 0 </ sub > of the initial step, and so on.

For example, if a < b, the initial quotient q < sub > 0 </ sub > equals zero, and the remainder r < sub > 0 </ sub > is a.

Since the remainders decrease with every step but can never be negative, a remainder r < sub > N </ sub > must eventually equal zero, at which point the algorithm stops.

In the first step, the final nonzero remainder r < sub > N − 1 </ sub > is shown to divide both a and b. Since it is a common divisor, it must be less than or equal to the greatest common divisor g. In the second step, it is shown that any common divisor of a and b, including g, must divide r < sub > N − 1 </ sub >; therefore, g must be less than or equal to r < sub > N − 1 </ sub >.

since the final remainder r < sub > N </ sub > is zero.

Therefore, c divides the initial remainder r < sub > 0 </ sub >, since r < sub > 0 </ sub > = a − q < sub > 0 </ sub > b = mc − q < sub > 0 </ sub > nc = ( m − q < sub > 0 </ sub > n ) c. An analogous argument shows that c also divides the subsequent remainders r < sub > 1 </ sub >, r < sub > 2 </ sub >, etc.