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.

Since all anchors that embed themselves in the bottom require the strain to be along the seabed, anchors can be broken out of the bottom by shortening the rode until the vessel is directly above the anchor ( at this point the anchor chain is " up and down " in naval parlance ).

Since one DSL termination point can support multiple ISPs, the economic feasibility of DSL is substantially improved.

Since the maximum aperture of the pencils issuing from O is the angle u subtended by the entrance pupil at this point, the magnitude of the aberration will be determined by the position and diameter of the entrance pupil.

Since lead has a lower melting point than the other constituents of the brass, it tends to migrate towards the grain boundaries in the form of globules as it cools from casting.

Since 1980, each voter names three rookies: a first-place choice is given five points, a second-place choice three points, and a third-place choice one point.

Since the conclusion of Calvin and Hobbes, Watterson has taken up painting, at one point drawing landscapes of the woods with his father.

Since the Persian force obviously contained a high proportion of missile troops, a static defensive position would have made little sense for the Athenians ; the strength of the hoplite was in the melee, and the sooner that could be brought about, the better, from the Athenian point of view.

Since the second half of the 20th century, computers have been programmed to play chess with increasing success, to the point where home computers can play chess at a very high level.

Since helium remains a liquid even at absolute zero at atmospheric pressure, it has only a boiling point, and not a melting point, in conventional presentations.

Since this curl is not the same at every point, its plot is a bit more interesting:

( Since there is no citation for this exegesis, readers will need to analyse for themselves whether the " exact parallel " is addressed elsewhere and is generally accepted, or might represent a personal point of view, and readers will also need to discern for themselves what exactly is the " illumination ".

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since the direction of an electric field is defined as the direction of the force on a positive charge, electric field lines point away from a positive charge and toward a negative charge.

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.

Since the fundamental group is a homotopy invariant, the theory of the winding number for the complex plane minus one point is the same as for the circle.

Since these people would have to be descended from Adam, they would have had to travel to the other side of the Earth at some point ; Augustine continues:

Since half of the particles at point move right and half of the particles at point move left, the net movement to the right is:

Since King Kong was seen as the bigger draw ( at the time, he was even more popular in Japan than Godzilla ), and since Godzilla was still a villain at this point in the series, it led to the decision to not only give King Kong top billing, but also to present him as the winner of the climactic fight.

Since classical general relativity and quantum mechanics seem to be incompatible at such energies, from a theoretical point of view this situation is not tenable.

Since, by the second law of thermodynamics, this is statistically improbable to the point of exclusion, the Carnot efficiency is a theoretical upper bound on the reliable efficiency of any process.

Since honey normally exists below its melting point, it is a supercooled liquid.

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

Since P was never asserted as the only sufficient condition for Q, other factors could account for Q ( while P was false ).

** 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 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.