Hence, thought of as a line in a particular plane **yp, any tangent to Q has a unique image and moreover this image is the same for all planes through L.

Hence its image, C', meets any line of Af in Af points.

Hence it follows that the involution within the bundle must be a perspective De Jonquieres involution of order Af and the invariant locus must have a multiple line of multiplicity either Af or Af.

Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and ( following Newton's first law of motion ), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly — that is, in a straight line and at constant speed.

Hence, an entire line of program code could express the same idea a small number of characters that other programming languages might easily take 5 to 10 times as many characters to express.

In poetry, a monometer is a line of verse with just one metrical foot, exemplified by this portion of Robert Herrick's " Upon His Departure Hence ":

Hence a tumour cell line might show a different genetic fingerprint from that of the host tissue.

Hence, the total length increases by one third and thus the length at step n will be ( 4 / 3 )< sup > n </ sup > of the original triangle perimeter: the fractal dimension is log 4 / log 3 ≈ 1. 26, greater than the dimension of a line ( 1 ) but less than Peano's space-filling curve ( 2 ).

Hence, this line of argument goes, the objectively dominant effect would be the moral and economic damage due to the massive fear and panic such an incident would spur.

Hence the phrases " straight line " and " right line " were used to distinguish what are today called lines from " curved lines ".

Hence, the slope of this line yields, whereas its intercept is determined by.

Hence, they built the railway line though Lamy, instead.

Hence in Japan " The Transformers " did not debut under that brand till 1985, when the line was also rolled out to the majority of the rest of the world between Takara and Hasbro.

Hence, the outcome is either p < sub > i </ sub > or 1-p < sub > i </ sub >, as in the previous line.

Hence, when Holden decided to replace the successful full-size HZ Kingswood with a new model line, they designed the new car to be smaller and more fuel efficient.

Hence the line moved slowly, infantry and artillery firing on either side randomly.

Hence resources had been put into the Danevirke line and not into the flank positions, which stayed akin to battlefield fortifications rather than modern fortifications capable of withstanding a modern bombardment.

Hence defense along the Dannevirke line was, correctly, anticipated by the Danish high command to be a trap, in which its army would be surrounded and forced to give battle at hopeless odds.

Hence they cancel out each other to give minimum current in the main line.

Hence the line, ' I cry when angels deserve to die '.

Hence it was agreed internally to leave the more difficult locomotives until later, perhaps picking up the work when the volume of rolling stock and railway line abated.

Hence, e. g., a TCP segment is carried in one or more IP Layer packets, which are each carried in one or more Ethernet frames — though the mapping of TCP, IP, and Ethernet, to the layers of the OSI model is not exact.

Hence, if more than 50 per cent of an aesthetic subunit is lost ( damaged, defective, destroyed ) the surgeon replaces the entire aesthetic segment, usually with a regional tissue graft, harvested from either the face or the head, or with a tissue graft harvested from elsewhere on the patient ’ s body.

Hence a 7 segment plus decimal point package will only require nine pins ( though commercial products typically contain more pins, and / or spaces where pins would go, in order to match industry standard pinouts ).

Hence " Material Girl " was transferred as the closing song of the military segment of the show, and was re-arranged as an electric guitar version.

Hence, noting the simplicity achieved in Copernicus' formulation does not provide another reason for the acceptance of De Revolutionibus, another reason beyond its systematic superiority.

Hence, the lack of obvious racist graffiti does not necessarily mean that there actually is none.

Hence, in the 16th century, physic meant roughly what internal medicine does now.

Hence, depending on jurisdiction, a specialist physician ( internist ) often does not achieve recognition as a specialist until twelve or more years after commencing basic medical training — five to eight years at university to obtain a basic medical qualification, and up to another nine years to become a specialist.

Hence the PowerBook 100's design does not match those of the rest of the series, as it was actually designed after the 140 & 170 and further benefited from improvements learned during their development.

Hence, the Shakespeare quote above is semantically distributive, because there's not a man who ... is logically equivalent to every man does not ....

Hence the term supersessionism does not come from the Latin Church Fathers ' description of their own views but as the application of a modern term to older views.

Hence the ( impulse ) turbine is simpler, less expensive and does not need to be pressure-proof.

Hence, correlation does not imply causation ; in example, Gould said that the measures of the changes, over time, in " my age, the population of México, the price of Swiss cheese, my pet turtle ’ s weight, and the average distance between galaxies " have a high, positive correlation — yet that correlation does not indicate that Gould ’ s age increased because the Mexican population increased.

Hence it does not follow that a thing is not in motion in a given time, just because it is not in motion in any instant of that time.

Hence, from the Bayesian-Carnapian point of view, the observation of a non-raven does not tell us anything about the color of ravens, but it tells us about the prevalence of ravens, and supports " All ravens are black " by reducing our estimate of the number of ravens which might not be black.

Hence cutlery does not have quantized reference.

However, s < sub > 0 </ sub > does not appear anywhere in S. Hence, T cannot coincide with S.

Hence, a " steady-state " worldview based solely on Newton's laws and the conservation laws does not take entropy into account.

Hence relations can be defined by set theory, thus the theory of relations does not require any axioms or primitive notions distinct from those of set theory.

Hence, in this continual process of creative destruction, capitalism does not resolve its contradictions and crises, but merely " moves them around geographically ".

Hence, one can easily formulate the solution for finding shortest paths in a recursive manner, which is what the Bellman-Ford algorithm or the Floyd-Warshall algorithm does.

Hence equity does not stop at granting equitable relief, but goes on to render a full and complete collection of remedies.

Hence, if you play Rummikub, simply take all the tiles that anyone plays and you have the distinct advantage of being able to use those tiles, while everyone else does not.

Hence does capitalism remove from the worker the right to exercise control upon the value and the effects of his and her labour, which, in turn, robs the worker of the ability to either buy ( consume ) the goods and services, or to receive the full value from the sale of the product.

Hence, the idea that we can convert some NP-complete problems into Go problems does not help in explaining the present human superiority in Go.

Hence there is something — the referent of " Pegasus " — that does not exist.

Hence, an earned BAS degree does include having to take upper-division coursework as required in addition to traditional bachelor degree programs.