Since Michel Chasles cited this book of Pappus in his history of geometric methods, it has become the object of considerable attention.

Since 4 % can be expressed as. 04, gives the amount of alcohol in terms of ml — which, when divided by, shows the number of units.

Since then it has been eroding, creating dramatic incised valleys, and providing the sediment that gives the Yellow River its yellow color and that causes the flooding of the river in the lower reaches ( hence the river's nickname ' China's sorrow ').

Since the tucked shape is the most compact, it gives the most control over rotational speed, and dives in this position are easier to perform.

Since the larger of the two numbers is reduced, repeating this process gives successively smaller numbers until one of them is zero.

Since the 2. 4 GHz band is heavily used to the point of being crowded, using the relatively unused 5 GHz band gives 802. 11a a significant advantage.

Since 2 < sup >( q − 1 )</ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power x gives 2 < sup >( q − 1 ) x </ sup > ≡ 1, and since 2 < sup > p </ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power k gives 2 < sup > kp </ sup > ≡ 1.

Since adjoint functors exist in abundance, this gives numerous examples of continuous and cocontinuous functors.

Since Eddie was headed deeper into addiction ( at the hands of his brother Henry ) or prison ( at the hands of the government ), or worse ( at the hands of his drug lord ), he decides to throw his lot in with Roland, although with deep misgivings that he occasionally gives vent to in the form of angry outbursts.

From the 1990s to the present, the majority of communications from “ one fixed location to another have moved by fiber .” Since these fiber communications are “ wired ,” U. S. law “ gives them greater protection .”

Since constitutional law cannot be altered by state legislatures, this direct democracy component gives the people an automatic superiority and sovereignty, over representative government ( Magelby, 1984 ).

Since then, the Mission has been repaired and restored, and has one of the best-preserved interiors ( which gives one of the best examples of old mission life ).

Since the pressure on top of the engine is ambient, this means that base gives no overall thrust ( but it also means that this part of the nozzle doesn't lose thrust by forming a partial vacuum, thus the base part of the nozzle can be ignored at low altitude ).

Since Ferdinando is still doing nothing, she spits in his face in front of the entire town, which gives him all that he needed: an open insult to the family's honor due to his wife's elopement.

Since 1822, rather than ordinary money, the Sovereign gives out Maundy coins, which are specially minted 1, 2, 3 and 4 penny pieces, and are legal tender.

Since the determinant of a unitary matrix is a complex number with norm 1, the determinant gives a group homomorphism

Since F and g are differentiable, the chain rule gives

Since 2002, the Sun has run an approximately annual contest called " Page 3 Idol " that gives amateur models an opportunity to win Page Three modelling contracts.

Since every formula in the antecedent ( the left side ) must be true to conclude the truth of at least one formula in the succedent ( the right side ), adding formulas to either side results in a weaker sequent, while removing them from either side gives a stronger one.

Since 4 and 6 are congruent modulo 2, a function defined on the integers modulo 2 must give the same output when the input is 6 that it gives when the input is 4.

A simple version of this runs as follows: Since the brain in a vat gives and receives exactly the same impulses as it would if it were in a skull, and since these are its only way of interacting with its environment, then it is not possible to tell, from the perspective of that brain, whether it is in a skull or a vat.

Since her retirement in 1999, she has stayed away from the public eye and rarely gives interviews to talk about her past with Sierra On-Line.

Since aslan (" lion ") is a Turkish colloquial metaphor for a strong, courageous man, this gives the term a meaning close to " the milk of the strong.

Since metabolic conditions change rapidly, as a result of any of several factors, this is delayed news and gives no warning of a developing condition.

Since the complicated process of establishing new communes and reviewing the rudimentary plan left by the French did not even begin until the fall of 1957, this goal appears somewhat ambitious.

Since the evolution of the Aramaic alphabet out of the Phoenician one was a gradual process, the division of the world's alphabets into those derived from the Phoenician one directly and those derived from Phoenician via Aramaic is somewhat artificial.

Since the Roman consular fasti make it somewhat easy to confuse 87 – 57 BC with 84 – 54 BC, many scholars accept the dates 84 BC – 54 BC, supposing that his latest poems and the publication of his libellus coincided with the year of his death.

Since the 1960s, applied ethics has revived the ideas of casuistry in applying ethical reasoning to particular cases in law, bioethics and business ethics, so the reputation of casuistry is somewhat rehabilitated.

Since then McLean has stated that the lyrics are also somewhat autobiographical and present an abstract story of his life from the mid-1950s until the time he wrote the song in the late 1960s.

Since the 1960s the Chief rabbinate of Israel has moved somewhat closer to the positions of Haredi Judaism.

Since the Mishnah and all of the Baraitas and verses of Tanakh quoted and embedded in the Gemara are in Hebrew, Hebrew constitutes somewhat less than half of the text of the Talmud.

Since the 1970s Baldwin's reputation has recovered somewhat.

Since cotton is somewhat salt and drought tolerant, this makes it an attractive crop for arid and semiarid regions.

Since the pitch of each note is largely affected by the temperature of the steam, accurate tuning is nearly impossible ; however, the off-pitch notes ( particularly in the upper register ) have become somewhat of a trademark of the steam calliope.

Since the uncertainty is so high, the above formulas can be simplified to give a somewhat less cumbersome one.

Since then the movement has consolidated, and its views have emerged as somewhat more acceptable to Swedish free churches.

Since October 2010, programming on both night's schedules has been somewhat fluid as while all series have a permanent place on the Friday and Sunday primetime schedules, episode premieres of all Disney Channel original series are subject to being rotated on and off the schedule depending on the schedule for that given week as they usually air as part of a 90-minute block from 8 – 9: 30 p. m. ET / PT on Friday evenings and 7: 30 – 9 p. m. ET / PT on Sunday evenings.

Since rounded bricks are somewhat unstable, Mesopotamian bricklayers would lay a row of bricks perpendicular to the rest every few rows.

Since the cloudy appearance is due to nonuniform glass dissolution, it is ( somewhat paradoxically ) less marked if dissolution is higher, i. e. if a silicate-free detergent is used ; also, in certain cases, the etching will primarily be seen in areas that have microscopic surface cracks as a result of the items ' manufacturing.

Since the Guaraní people were a somewhat nomadic, decentralized society, there is little in the way of a reliable historical record.

Since the 1970s, the cladoceran populations have somewhat recovered, but not to former levels.

Since that nadir, the League Cup has recovered somewhat, embracing the ' youth ' football ethic, and maintaining its niche as an early season trophy.

Since the original FCC report, further improvements to VSB reception technologies as well as the introduction of E-VSB option to ATSC have reduced this challenge somewhat.

Since the strip of parchment hints strongly at the method, the ciphertext would have to be transferred to something less suggestive, somewhat reducing the advantage noted.

Since April 24, 2006, the band ( primarily Sean Dolan ) has kept somewhat in contact with their fanbase with their MySpace profile.

Since knitted fabrics are generally somewhat elastic and have a softer hand ( feel or drape ) than woven fabric, sweaters that are more tightly fitted or have a soft drape may conform well to the body without requiring tailoring necessary in a woven garment such as darts, flares and gores.

Since 2007 the South Stand has been made officially accessible to over-18s only, due to its hyper and somewhat provocative atmosphere.

Since then, very little has been spent on renovating the building, leaving parts of it somewhat tattered and outdated.

Since human habitation and subsequent forest fragmentation of their home island of Mindoro, the habitat preferences of the tamaraw have somewhat expanded to lower-altitude grassy plains.