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 the statement is a sūtra, it is necessarily compressed and what the ropes produce is not elaborated on, but the context clearly implies the square areas constructed on their lengths, and would have been explained so by the teacher to the student.

Since any Godlike object is necessarily existent, it follows that any Godlike object in one world is a Godlike object in all worlds, by the definition of necessary existence.

Since the Hun empire was not ethnically homogeneous, this proposal is not necessarily in conflict with others.

Since the root can always be changed from red to black, but not necessarily vice-versa, this rule has little effect on analysis.

Since the space concept doesn ’ t necessarily have to be economical in the traditional sense, it allows the enrichment to exceed that which would be acceptable for a terrestrial system.

Since a one sided maximal ideal A is not necessarily two-sided, the quotient R / A is not necessarily a ring, but it is a simple module over R. If R has a unique maximal right ideal, then R is known as a local ring, and the maximal right ideal is also the unique maximal left and unique maximal two-sided ideal of the ring, and is in fact the Jacobson radical J ( R ).

Since elements of W are necessarily elements of V, axioms 1, 2 and 5-8 of a vector space are satisfied.

Since God has made satisfaction for the sins of the elect, they can no longer be condemned for them, and through the help of the Holy Spirit, they must necessarily persevere as Christians and in the end be saved.

Since Iceland was not settled until about 870, anything composed before that time would necessarily have been elsewhere, most likely in Scandinavia.

Since every team has not necessarily had a chance to prove itself against every other team, a playoff is necessary every season.

Since the IP address itself does not necessarily provide location information presently, today a " best efforts " approach is to use an available database to find that user and the physical address the user chose to associate with that telephone number — clearly an imperfect solution.

Since many of the events were reused in the 2001 film Jay and Silent Bob Strike Back, not all the events depicted here are necessarily continuous with those depicted elsewhere in the View Askewniverse.

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

Since DSR generically ( though not necessarily ) implies an energy-dependence of the speed of light, it has further been predicted that, if there are modifications to first order in energy over the Planck mass, this energy-dependence would be observable in high energetic photons reaching Earth from distant gamma ray bursts.

Since these, both the FA Premier League and FIFA World Cup qualifying matches require all spectators to be seated ( though not necessarily in an all-seater stadium, if terraces are left empty ).

Since an everywhere defined self-adjoint operator is necessarily bounded, one needs be more attentive to the domain issue in the unbounded case.

Since existing DOS programs expected to be able to initiate host-controlled ISA DMA for producing sound, backward compatibility with the older Sound Blaster cards for DOS programs required a software driver work-around ; since this work-around necessarily depended on the virtual 8086 mode of the PC's CPU in order to catch and reroute accesses from the ISA DMA controller to the card itself, it failed for a number of DOS games that either were not fully compatible with this CPU mode or needed so much free conventional memory that they could not be loaded with the driver occupying part of this memory.

Since the true vocal folds adduct during the swallow, a finite period of apnea ( swallowing apnea ) must necessarily take place with each swallow.

Since the length of an engine is roughly proportional to the number of cylinders in one bank ( plus the width of one connecting rod in a " V " engine ), the straight-six is necessarily longer than alternative layouts such as L4, V6, or V8.

Since considerations of the physical details of actions are necessarily bound up with a person's subjective preferences, and could have been brought about without the action of a rational will, Kant concluded that the expected consequences of an act are themselves morally neutral, and therefore irrelevant to moral deliberation.

Since Placentalia therefore includes all living eutherians, the nonplacental eutherians are necessarily extinct ; the picture to the right shows a fossil of one such animal, Eomaia.

Note: Since ISO 3166-2 is only occasionally updated, this table does not necessarily reflect the latest subdivision changes.

Since Laos is of no more purely military value to Moscow itself than it is to Washington, this approach might be expected to head off Mr. Khrushchev for the moment.

Since the Santo Spirito hospital had taken only men, he had had no experience in the study of female anatomy ; ;

Since there are almost no schools in the country offering graduate work in interior design this rule cannot at present be observed.

Since Af are linearly independent functions and the exponential function has no zeros, these R functions Af, form a basis for the space of solutions.

Since the complex of singular lines is of order K and since there is no complex of invariant lines, it follows from the formula Af that the order of the involution is Af.

A final class of exceptional lines is identifiable from the following considerations: Since no two generators of Af can intersect, it follows that their image curves can have no free intersections.

Since the details of the elections were settled the change of government had no direct effect on the technical aspects of the elections, and may have been more important as an indication of royal displeasure with the U.N.F.P.

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

Since there is no binding authority in the Communion, these international bodies are a vehicle for consultation and persuasion.

Since phonemes are abstractions of speech sounds, not the sounds themselves, they have no direct phonetic transcription.

Since then the " Common Strategy " policy in the USA and the rest of the world has no longer been used.

Since it was an analog standard, it is very susceptible to static and noise and has no protection from eavesdropping using a scanner.

Since many AI problems have no formalisation yet, conventional complexity theory does not allow the definition of AI-completeness.

Since the Admiralty no longer exists as a department, these are now used as an " office bank " by the British government:

This subextension is called a separable closure of K. Since a separable extension of a separable extension is again separable, there are no finite separable extensions of K < sup > sep </ sup >, of degree > 1.

Since the runner would now have been at second anyway, the passed ball no longer has any impact on the earned / unearned calculation.

" Since no one in the raiding party is carrying any change, nor do they realize that there is nothing stopping them from simply riding around the tollbooth, Taggart sends someone back to town to " get a shitload of dimes ".

Since that time, no consensus had yet been reached, and Disraeli was criticised for mixing up details over the different " schedules " of income.

Since in a majority of constellations the brightest star is designated Alpha ( α ), many people wrongly assume that Bayer meant to put the stars exclusively in order of their brightness, but in his day there was no way to measure stellar brightness precisely.

Since you're asking me, I'll say no, I don't think he is ...

Since there is no heir to inherit Elimelech's land, levirate custom required a close relative ( usually the dead man's brother ) to marry the widow of the deceased in order to continue his family line ( Deuteronomy 25: 5 – 10 ).

Since the House of Lords no longer had the power to block the bill, the Unionist's Ulster Volunteers led by Sir Edward Carson, launched a campaign of opposition that included the threat of armed resistance in Ulster and the threat of mutiny by army officers in Ireland in 1914 ( see Curragh Incident ).