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 line segment AB does not have to intersect line segment CD to be considered perpendicular lines, because if the line segments are extended out to infinity, they would still form congruent adjacent angles.

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 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 the prime issue, as I see it, is whether a democratic or free society can master technology for the benefit of mankind, or whether technology will rule and develop its own society compatible with its own needs as a force of nature.

Hence these words of David: In the morning I put to death all the wicked of the land, that I might cut off all the workers of iniquity from the city of the Lord.

Hence I can see no reason to doubt that natural selection might be most effective in giving the proper colour to each kind of grouse, and in keeping that colour, when once acquired, true and constant.

Hence, mutual recognition of rational individuals turns out to be a condition necessary for the individual ' I ' in general.

Hence, Fighter Wing 1 was JG 1, its first Gruppe ( group ) was I ./ JG 1, using a Roman numeral for the Gruppe number only, and its first Staffel ( squadron ) was 1 ./ JG 1.

Hence luen kirjan means " I will read the book ".

" Hence, I believe there is only one name that can be given to this car, a name I shall give to it on this very evening.

Hence, they ordered the Spartan king, Cleombrotus I, to march to war from Phocis.

Hence John too may have been the son of Marozia and Alberic I.

Hence the kings buried at Naghsh-e Rustam are probably Darius the Great, Xerxes I, Artaxerxes I and Darius II.

Hence, he used " we " as " God and I ...," or so the legend goes.

Hence the term " I think, therefore I am ".

Hence the Emperor's famous wry comment: " The Empress is a Legitimist, Morny is an Orleanist, Prince Napoleon is a Republican, and I myself am a Socialist.

Hence I have very little doubt, that if the whole genus of humble-bees became extinct or very rare in England, the heartsease and red clover would become very rare, or wholly disappear.

Hence the name: he said, " I intend it to be really a mirror of feminine life as well on its grave as on its lighter sides .... to be entertaining without being frivolous, and serious without being dull ".

Hence it is surmised that the Gupta era began on the occasion of the coronation of Chandragupta I.

Hence, the use of the term " giggle factor " and the saying, " I wouldn't want to be found dead next to a psychic.

Hence I have little information to offer in the matter.

Hence, I understand that I can err without God's having given me a special ability to do so.

Hence, I is finitely generated by finitely many invariants of G ( because if we are given any – possibly infinite – subset S that generates a finitely generated ideal I, then I is already generated by some finite subset of S ).