Since Af and P divides Af for Af, we have Af.

Since a ruled surface of order N with N concurrent generators is necessarily a cone, it follows finally that every line through a point, P, of **zg meets its image at P, as asserted.

** Hays, Samuel P. ' A History of Environmental Politics Since 1945 ( 2000 ), abridged version

Since the light is turned through 90 degrees by the reflection, the slope of the parabola at P must be 1.

Since the ideal windings have no impedance, they have no associated voltage drop, and so the voltages V < sub > P </ sub > and V < sub > S </ sub > measured at the terminals of the transformer, are equal to the corresponding EMFs.

Since Petermann v. International Brotherhood of Teamsters, 344 P. 2d 25 ( Cal. App.

Since E and P are defined separately, this equation can be used to define D. The physical interpretation of D is not as clear as E ( effectively the field applied to the material ) or P ( induced field due to the dipoles in the material ), but still serves as a convenient mathematical simplification, since Maxwell's equations can be simplified in terms of free charges and currents.

Since his plans for an early-morning coordinated attack were now infeasible, Lee instead ordered Longstreet to coordinate a massive assault on the center of the Union line, employing the division of George Pickett and brigades from A. P.

Every prime ideal P in a Boolean ring R is maximal: the quotient ring R / P is an integral domain and also a Boolean ring, so it is isomorphic to the field F < sub > 2 </ sub >, which shows the maximality of P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.

Since there are other countries that are exporting the same widgets at a price of P < sub > world </ sub >, Japan's industry is threatened to go out of business should widgets be imported into their country without a tariff.

Since point P and O < sub > 2 </ sub > have only one velocity,

Since the point P ( and thus ) is arbitrary, it follows that

Since failure probabilities on fault trees tend to be small ( less than. 01 ), P ( A ∩ B ) usually becomes a very small error term, and the output of an OR gate may be conservatively approximated by using an assumption that the inputs are mutually exclusive events:

Since the power dissipation, P = I < sup > 2 </ sup > R, increases with the square of the current but only increases approximately linearly with the number of windings, the power lost in the windings can be minimized by reducing I and increasing the number of turns N proportionally.

Since furnaces had to be constantly burning, there were night shifts from 5: 00 P. M. to 3: 00 A. M.

Since the 1981 National Scout Jamboree, all Jamborees have been held at Fort A. P.

Since some indices, such as the S & P 500 and FTSE 100, are dominated by large company stocks, an index fund may have a high percentage of the fund concentrated in a few large companies.

Since HOU is used for William P. Hobby Airport, the new Houston-Intercontinental became IAH.

Since χ is a tensor, P is not necessarily colinear with E.

Since Rhode Island at that time did not have such sanction, his opinion was not popular.

Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.

Those famous lines of the Greek Anthology with which a fading beauty dedicates her mirror at the shrine of a goddess reveal a wise attitude: `` Venus, take my votive glass, Since I am not what I was, What from this day I shall be, Venus, let me never see ''.

Since it was issued in the spring of 1611, the King James Version has been most generally considered the most poetic and beautiful of all translations of the Bible.

Since she could not act, one part suited her as well as any other, and so she was the first person to offer Mr. Lincoln a glass of water, holding it up to the box, high above her head, to Miss Harris, who had asked for it.

Since ordinary breakfast-table conversation was impossible, it was at least something that they were able to offer Eugene the sugar bowl with their sugar in it, and the plate of bread and butter, and that Eugene could return the pitcher of hot milk to them handle first.

Since his Christ was to be life size, how was Mary to hold him on her lap without the relationship seeming ungainly??

Since the writer had established this democratic procedure in the beginning he had to go along with their decision -- after, of course, pointing out whether he thought their decision was a wise or an unwise one.

Since this type of item was not in the statute when section 381 was enacted in 1954, one cannot say with certainty what effect the enactment of that section should have.

Since writing was practiced in the Aegean before the end of the century, we may hope that the details of tradition will now be occasionally useful.

Since the strength of the Mexicans had been underrated, too small a posse had been collected, and since the deputy had not been provided with search warrants, MacPherson and his men decided it was much wiser to withdraw.

Since experience indicates that effluents from oxidation ponds do not create major problems at these BOD concentrations, the goal for the effluent quality of the accelerated treatment system was the same as from conventional oxidation ponds.

Since the psychiatric interview, like any other interview, depends on communication, it is significant to note that the therapist in this interview was a man of marked skill and long experience.

Since Fogg's was a one-man, one-plane flying service, this meant that he would have to do both trips, flying alone 600 miles a day, under sub-freezing temperature conditions.

Since the 1946 disaster there have been 15 tsunami in the Pacific, but only one was of any consequence.

Since a fall or blow might have caused it, a cold pack was usually first aid.

Since then he had worked at this and that, though some said his main interest was gambling.

Since 1949, the only National League club that got off to a hot start and made a runaway of the race was the '55 Dodger team.

Since Russian was being spoken instead of Spanish, there is no violation of artistry or logic here.

Since the organization was created thirteen years ago, it is obvious that this is not the original company ; ;

Since they did not glance curiously at us once, I guessed that there was a penalty for distraction.

Since 30 June 2012 when the last leap second was added, TAI has been exactly 35 seconds ahead of UTC.