Hex

“ For the better understanding of this, I would observe that sensible intuitions are allied to general conceptions, by whose aid they may be reconstructed. Although, in reality, no sensible representation is offered to us, of any figure whatsoever, for example, a regular hexagon; the conception formed of the ideas, six, line, equality of angles, is all that we need to produce in our interior the sensible representation of the hexagon, and to construct it within us, if we require it. ”

“ The word, which is doubtlessly a compound, has not yet been satisfactorily explained; OHG. hag, AS. hœg, ‘hedge, wood,’ as the first component, seems indubitable. The second part has not been elucidated; some suppose that the prim. meaning of Hexe is ‘forest woman or demon’?. ”

“ But it took effort, all the same, to concentrate on herself instead of the work, the job, the employment agency. It took effort to sit down on a bench in the park, near the building where the case workers were, and plan out the next step.
A witch, certainly. The girl was a witch and she had put a hex on Mrs. Wladek, and that hex had to be removed.
How?
Mrs. Wladek thought first of the old woman in the store.
Certainly a gypsy woman would be able to take off a hex. Mrs. ”

“ Humphrey and Winifred and Rafe lived their lives out, and lay down to rest a century and a half since under the daisy-sprinkled English sod. Little Hexie died an aged woman, before any of us was born. ”

“ If the hexameter best helps the translator to the Homeric rapidity, what style may best help him to the Homeric plainness and directness? It is the merit of a metre appropriate to your subject, that it in some degree suggests and carries with itself a style appropriate to the subject; the elaborate and self-retarding style, which comes so naturally when your metre is the Miltonic blank verse, does not come naturally with the hexameter; is, indeed, alien to it. ”

“ But take the whole 255range of Greek epic poetry, take the later poets, the poets of the last ages of this poetry, many of them most indifferent, Coluthus, Tryphiodorus, Quintus of Smyrna, Nonnus. Never will you find in this instrument of the hexameter, even in their hands, the vices of the ballad-style in the weak moments of this last: everywhere the hexameter, a noble, a truly epical instrument, rather resists the weakness of its employer than lends itself to it. ”

“ Between the recognition of this rhythm as ideally the best, and the recommendation of it to the translator for instant practical use, there must come all that consideration of circumstances, all that pliancy in foregoing, under the pressure of certain difficulties, the absolute best, which I have said is so indispensable to the critic. The hexameter is, comparatively, still unfamiliar in England; many people have a great dislike to it. A certain degree of unfamiliarity, a certain degree of dislike, are obstacles with which it is not wise to contend. ”

“ Even to me, a Mathematician of no mean standing, and the Grandfather of two most hopeful and perfectly regular Hexagons, to find myself in the midst of a crowd of rotating Polygons of the higher classes, is occasionally very perplexing. And of course to a common Tradesman, or Serf, such a sight is almost as unintelligible as it would be to you, my Reader, were you suddenly transported into our country.
In such a crowd you could see on all sides of you nothing but a Line, apparently straight, but of which the parts would vary irregularly and perpetually in brightness or dimness. ”

“ And, finally, the middle lines of the trigrams, the second and fifth, that is, of the hexagrams, have a peculiar value and force. If we have a whole line (⚊) in the fifth place, and a divided line (⚋) in the second, or vice versâ, the correlation is complete. Let the subject of the fifth be the sovereign or a commander-in-chief, according to the name and meaning of the hexagram, then the subject of the second will be an able minister or a skilful officer, and the result of their mutual action will be most beneficial and successful. ”

“ My own opinion, as I have intimated, is, that the second account of the origin of the trigrams and hexagrams is the true one. However the idea of the whole and divided lines arose in the mind of the first framer, we must start from them; and then, manipulating them in the manner described, we arrive, very easily, at all the lineal figures, and might proceed to multiply them to billions. ”

“ My Pentagonal Sons were men of character and standing, and physicians of no mean reputation, but not great in mathematics, and, in that respect, unfit for my purpose. But it occurred to me that a young and docile Hexagon, with a mathematical turn, would be a most suitable pupil. Why therefore not make my first experiment with my little precocious Grandson, whose casual remarks on the meaning of 33 had met with the approval of the Sphere? ”

“ Six planes of symmetry of two kinds intersect in the hexad axis. The hexad axis is uniterminal and all the forms are open forms. The general form {hikl} consists of twelve faces at one end of the crystal, and is a dihexagonal pyramid. ”

“ Such a minor change I have attempted by occasionally shifting, in the first foot of the hexameter, the accent from the first syllable to the second. In the current English hexameter, it is on the first. Mr Spedding, who proposes radically to subvert the constitution of this hexameter, seems not to understand that anyone can propose to modify it partially; he can comprehend revolution in this metre, but not reform. ”

“ But thus humbly useful to the future translator I still hope my hexameters may prove; and he it is, above all, whom one has to regard. The general public carries away little from discussions of this kind, except some vague notion that one advocates English hexameters, or that one has attacked Mr. Newman. On the mind of an adversary one never makes the faintest impression. ”

“ The fifty-ninth hexagram, called Hwân ䷺, is formed by the trigrams Khân ☵, representing water, and Sun ☴, representing wind, and it is said on it:— (The symbol of) water and (that of wind) above it form Hwân. The ancient kings, in accordance with this, presented offerings to God, and established the ancestral temple.' The union of the two trigrams suggested to king Wăn the idea of dissipation in the alienation of men from the Supreme Power, and of the minds of parents from their children; a condition which the wisdom of the ancient kings saw could best be met by the influences of religion. ”

“ The hexagram includes the cases where one follows others, and where others follow him; and the auspice of great progress and success is due to this flexibility and applicability of it. But in both cases the following must be guided by a reference to what is proper and correct. ”

“ It curdles my blood to think that some obscure person in America, who has latterly been indulging in dactyllic and spondaic metre, has dared to name himself [102] partly in imitation of the sobriquét by which we designated our friend.
Recollecting poor Pellucid’s warm admiration of the hexameter then, I have made strict search among his papers, on the chance of finding some classical Latin or Greek poem of his composition, but without success. At one time a ray of hope darted through me, as I came upon a paper carefully folded, and docketted, “Notions for a Fight between Hector and Achilles;” ”

“ If two pairs of opposite sides of a cyclic hexagon be respectively parallel to each other, the remaining pair of sides are also parallel.
6. If two circles intersect in the points A, B, and any two lines ACD, BFE, be drawn through A and B, cutting one of the circles in the points C, E, and the other in the points D, F, the line CE is parallel to DF.
7. ”

“ Comparing the Latin Hexameter and English heroic rhyme, the former has obviously the advantage in the following particulars. It is greatly preferable as to arrangement, by the latitude it admits in placing the long and short syllables. Secondly, the length of an Hexameter line hath a majestic air: ours, by its shortness, is indeed more brisk and lively, but much less fitted for the sublime. And, thirdly, the long high-sound{442}ing words that Hexameter admits, add greatly to its majesty. ”

“ Spedding objects to the English hexameter that it imperfectly represents the movement of the ancient hexameter, I answer: We must work with the tools we have. The received English type, in its general outlines, is, for England, the necessary given type of this metre; it is by rendering the metrical beat of its pattern, not by rendering the accentual beat of it, that the English language has adapted the Greek hexameter. To render the metrical beat of its pattern is something ”

“ For example, three dactylic stanzas, in each of which a pentameter couplet is followed by a hexameter line, and this again by a heptameter, are introduced by Prof. Hart thus: "The Dactylic Tetrameter, Pentameter, and Hexameter, with the additional or hypermeter syllable, are all found combined in the following extraordinary specimen of versification. * * * This is the only specimen of Dactylic hexameter or even pentameter verse that the author recollects to have seen." ”

“ The hexameter of the ancients may be considered as consisting of fifteen syllables, so melodiously disposed, that, as every one knows who has examined the poetical authors, very pleasing and sonorous lyrick measures are formed from the fragments of the heroick. ”

“ This ἔκφρασις, consisting of 416 hexameters, forms the second book of the Palatine Anthology. The writer’s chief models are Homer and Nonnus, whom he follows closely in the structure of his hexameters. Opinions are divided as to the merits of the work. ”

“ Taken in every point of view, [94] is one of the most curious and singular in the New Testament. It has been well observed, that the first words make a regular Greek hexameter verse, supposed to be quoted from some Greek poet not now extant; and the last clause of the verse, with a very little change, makes another hexameter: - Πασα δοσις αγαθη, και παν δωρημα τελειον, Εστ' απο των φωτων Πατρος καταβαινον ανωθεν. ”

“ The above hexameters are perfectly regular, both in being purely dactylic, and in having the regular cæsura, namely the end of a word at the beginning of the third dactyl, as—
We from the land that we love
We go as exiles away.
But these hexameters admit of irregularities in the same manner as the common English measures of which we have spoken. We may have dissyllable feet instead of trissyllable in any place in the line; thus in the fourth—
Tityrus, you in the shade of a chestnut idly reclining. ”

“ The little Hexagon meditated on this awhile and then said to me: "But you have been teaching me to raise numbers to the third power; I suppose 33 must mean something in Geometry; what does it mean? " "Nothing at all," replied I, "not at least in Geometry; for Geometry has only Two Dimensions." And then I began to show the boy how a Point by moving through a length of three inches makes a Line of three inches, which may be represented by 3 ”

“ The hexagon may further degenerate into a triangle, giving the theorem (Fig. 24) The lines joining the vertices to the points of contact of the opposite sides of a triangle circumscribed about a conic all meet in a point. ”

“ The attempt to fashion the Great Extreme as a circle must be pronounced a failure.
But when we start from the two lines as bases, the formation of all the diagrams by a repetition of the process indicated above is easy. The addition to each of the trigrams of each of the two fundamental lines produces 16 figures of four lines; dealt with in the same way, these produce 32 figures of five lines; and a similar operation with these produces the 64 hexagrams, each of which forms the subject of an essay in the text of the Yî. ”

“ Line 5 is strong, and in its correct place, with 2 as its proper correlate; thus producing the auspicious symbolism.
The issue of the hexagram is seen in line 6; which represents the ideal of following, directed by the most sincere adherence to what is right. This influence not only extends to men, but also to spiritual beings. ”

“ Each of the thirty-six edges may be straight or crooked or curved; the pairs of opposite edges, whether of the quadrilaterals or hexagons, need not be equal and parallel; neither the four corners of each quadrilateral nor the six corners of each hexagon need be in one plane. ”

“ The `sexa-' prefix is Latin but incorrect in this context, and `hexa-' is Greek. The word `octal' is similarly incorrect; a correct form would be `octaval' (to go with decimal) , or `octonary' (to go with binary) . If anyone ever implements a base-3 computer, computer scientists will be faced with the unprecedented dilemma of a choice between two *correct* forms; both `ternary' and `trinary' have a claim to this throne.
:hexit: /hek'sit/ n. A hexadecimal digit (0—9, and A—F or a—f) . Used by people who claim that there are only *ten* digits, dammit ”

“ It will be seen, from this example, that the syllables, Ut, Re, Mi, Fa, Sol, La, [3] were originally sung to the notes C, D, E, F, G, A; that is to say, to the six sounds of the Natural Hexachord: and that the Semitone fell between the third and fourth syllables, Mi and Fa, and these only. [See Hexachord.] But, when applied to the Hard Hexachord, these same six syllables represented the notes G, A, B, C, D, E ”