By dividing V2 / V1, we get: r

By dividing the Cenozoic Era into three ( arguably two ) periods ( Paleogene, Neogene, Quaternary ) instead of 7 epochs, the periods are more closely comparable to the duration of periods in the Mesozoic and Paleozoic eras.

By successively dividing out factors x − a, one sees that any polynomial with complex coefficients can be written as a constant ( its leading coefficient ) times a product of such polynomial factors of degree 1 ; as a consequence the number of ( complex ) roots counted with their multiplicities is exactly equal to the degree of the polynomial.

By dividing the Tertiary Period into two periods instead of five epochs, the periods are more closely comparable to the duration of ' periods ' in the Mesozoic and Paleozoic Eras.

By dividing the difference in y-coordinates by the difference in x-coordinates, one can obtain the slope of the line:

By dividing the board into smaller pieces, constructing tours on each piece, and patching the pieces together, one can construct tours on most rectangular boards in polynomial time.

By dividing the illocutionary act into two subparts, Searle is able to explain that we can understand two meanings from the same utterance all the while knowing which is the correct meaning to respond to.

By dividing the total sail area into only two sails, the individual sails of a sloop are larger than those of a similar sized cutter or yawl or ketch.

By dividing reservation lands into privately-owned parcels, legislators hoped to complete the assimilation process by forcing the deterioration of the communal lifestyle of the Native societies and imposing Western-oriented values of strengthening the nuclear family and values of economic dependency strictly within this small household unit.

By dividing chess programs into these two pieces, developers can write only the user interface, or only the engine, without needing to write both parts of the program.

By this point, not only was Licinius the official Augustus of the west, but he also possessed part of the eastern provinces as well, as the Hellespont and the Bosporus became the dividing line, with Licinius taking the European provinces and Daia taking the Asian.

By 1969 ELDO was beginning to realise that dividing work up by country led to not enough overall collaboration, with a disjointed framework of planning.

By dividing Caswell County into two squares – each side measuring approximately twenty ( 20 ) miles in length, the settlers formed two counties of each.

By further dividing the 72-54-54 triangles of the pentaflexagon into 36-54-90 right triangles produces one variation of the 10-sided decaflexagon ().

By timing the delay between the morse signal and the peak / null, then dividing by the known rotational rate of the station, the bearing of the station could be calculated.

By this time, Casella was dividing his time between Los Angeles and Boston.

By tracking the closing stock prices of twelve companies, adding up their stock prices, and dividing by twelve, Dow came up with his average.

* By dividing the lands of the Terra Mariana between the crusading order of Livonian Brothers of the Sword and the Church five principalities were created:

By the end of the third century, Emperor Diocleatian administratively reordered Tarraconesis, dividing it into three separate territories ( Tarraconensis, Carthaginensis and Callaecia ), the latter comprising the northern Portugal, Galizia and Austurias.

By contrast, species of the family Dendrocerotaceae may begin dividing within the spore, becoming multicellular and even photosynthetic before the spore germinates.

A spousal RRSP is a means of splitting income in retirement: By dividing investment properties between both spouses each spouse will receive half the income, and thus the marginal tax rate will be lower than if one spouse earned all of the income.

By the time comic books came of age in the 1940s, the huge volume of work demanded by publishers had encouraged an assembly-line process, dividing the creative process into distinct tasks: writer, penciller, letterer, inker, and colorist.

By dividing each column by its length, it can be seen that the result is equivalent to the special case where each column has length 1, in other words if e < sub > i </ sub > are unit vectors and M is the matrix having the e < sub > i </ sub > as columns then

By counting the number of lines that cross a certain segment of a stream, multiplying this by the contour interval, and dividing that quantity by the length of the stream segment you can determine the stream gradient.

By the late 1970s, while she still interpreted love tunes, Magool also began singing Islamic songs that criticized Somalia's then ruling military government.

By 1850, Luanda was one of the greatest and most developed Portuguese cities in the vast Portuguese Empire outside Mainland Portugal, full of trading companies, exporting ( together with Benguela ) palm and peanut oil, wax, copal, timber, ivory, cotton, coffee, and cocoa, among many other products.

By the time of Mesalim, whichever dynasty controlled the city of Kish was recognised as šar kiššati (= king of Kish ), and was considered preeminent in Sumer, possibly because this was where the two rivers approached, and whoever controlled Kish ultimately controlled the irrigation systems of the other cities downstream.

By the beginning of World War II, many towns and cities had built space, and there were numerous qualified pilots available.

By the end of Judges the Israelites are in a worse condition than they were at the beginning, with Yahweh's treasures used to make idolatrous images, the Levites ( priests ) corrupted, the tribe of Dan conquering a remote village instead of the Canaanite cities, and the tribes of Israel making war on the Benjamites, their own brothers.

Boroughs proliferated in the suburban areas of the larger cities: By the 1980s there were 19 boroughs and three cities in the area that is now the City of Auckland.

By 1920, Cambridge was one of the main industrial cities of New England, with nearly 120, 000 residents.

By late 1918, hundreds of Cheka committees had been created in various cities, at multiple levels including: oblast, guberniya (" Gubcheks "), raion, uyezd, and volost Chekas, with Raion and Volost Extraordinary Commissioners.

By then Delft was one of the leading cities of Holland and it was equipped with the necessary city walls to serve as a headquarters.

By virtue of National roads linking major cities in the country, they sometimes double as Regional and Inter-Regional roads.

By July, Goebbels was lamenting that Hitler had cut himself off from the people – it was noted, for example, that he never visited the bomb-ravaged cities of the Ruhr.

By mid-1860, he was playing in such cities as New York ; Boston ; Chicago ; Cleveland ; St. Louis ; Columbus, Georgia ; Montgomery, Alabama ; and New Orleans.

By the turn of the 19th century, the company had become the largest of the ‘’ hongs ’’ or foreign trading conglomerates with offices in all the important Chinese cities as well as Yokohama, Japan.

By this time, the Mamluks under Baibars were taking advantage of the kingdom's constant disputes, and began conquering the remaining crusader cities along the coast.

By the 9th century public libraries started to appear in many Islamic cities.

By late 569 they had conquered all the principal cities north of the Po River except Pavia, which fell in 572.

By 1850, Luanda was one of the greatest and most developed Portuguese cities in the vast Portuguese Empire outside Mainland Portugal, full of trading companies, exporting ( together with Benguela ) palm and peanut oil, wax, copal, timber, ivory, cotton, coffee, and cocoa, among many other products.

By the mid 1970s, Sweden experienced a recession that struck especially hard on the industrial sector ; shipyards and manufacturing industries were hard hit, which led to high unemployment in many cities of Scania.

By 1519, the Aztec capital, Mexico-Tenochtitlan, the site of modern-day Mexico City, was one of the largest cities in the world, with a population of 30, 000 ( estimates range as high as 60, 000 ).

By 1921, small groups of Marxists existed in six Chinese cities: Shanghai, Peking, Changsha, Wuhan, Canton and Tsinan, with a further group having been founded by Chinese students in Paris.

By 1985, Mecca, like other Saudi cities, possessed the most modern telephone, telex, radio and TV communications.

By the middle of the 19th century, Rotterdam was already one of the largest port cities in the world, mainly because of transshipment of goods from Germany to Great Britain.

By the 14th century the Ottoman Empire's prosperity made manuscript works available to merchants and craftsmen, and produced a flowering of miniatures that depicted pagentry, daily life, commerce, cities and stories, and chronicled events.

By the end of 2012, 8 of the 10 largest Polish cities ( Gdańsk, Poznań, Wrocław, Łódź, Warsaw, Kraków, Katowice, Szczecin ) will have a motorway connecting them with the motorway network of Europe.

By 1952 the principal telecommunications network centered on Beijing, and links to all large cities had finally been established.