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Un grand destin commence, un grand destin s'acheve
- A great destiny starts, a great destiny is completed. (French)
>From Attila, by Pierre Corneille ...
L' amour chez Attila n' est pas un bon suffrage ;
ce qu' on m' en donneroit me tiendroit lieu d' outrage,
et tout exprès ailleurs je porterois ma foi,
de peur qu' on n' eût par là trop de pouvoir sur moi.
Les femmes qu' on adore usurpent un empire
que jamais un mari n' ose ou ne peut dédire.
C' est au commun des rois à se plaire en leurs fers,
non à ceux dont le nom fait trembler l' univers.
Que chacun de leurs yeux aime à se faire esclave ;
moi, je ne veux les voir qu' en tyrans que je brave :
et par quelques attraits qu' ils captivent un coeur,
le mien en dépit d' eux est tout à ma grandeur.
Parlez donc seulement du choix le plus utile,
du courroux à dompter ou plus ou moins facile ;
et ne me dites point que de chaque côté
vous voyez comme lui peu d' inégalité.
En matière d' état ne fût-ce qu' un atome,
sa perte quelquefois importe d' un royaume ;
il n' est scrupule exact qu' il n' y faille garder,
et le moindre avantage a droit de décider.
Valamir.
Seigneur, dans le penchant que prennent les affaires,
les grands discours ici ne sont pas nécessaires :
il ne faut que des yeux ; et pour tout découvrir,
pour décider de tout, on n' a qu' à les ouvrir.
Un grand destin commence, un grand destin s' achève :
l' empire est prêt à choir, et la France s' élève ;
l' une peut avec elle affermir son appui,
et l' autre en trébuchant l' ensevelir sous lui.
Vos devins vous l' ont dit ; n' y mettez point d' obstacles,
vous qui n' avez jamais douté de leurs oracles :
soutenir un état chancelant et brisé,
c' est chercher par sa chute à se voir écrasé.
Appuyez donc la France, et laissez tomber Rome ;
aux grands ordres du ciel prêtez ceux d' un grand homme :
d' un si bel avenir avouez vos devins,
avancez les succès, et hâtez les destins.
Ardaric.
Oui, le ciel, par le choix de ces grands hyménées,
a mis entre vos mains le cours des destinées ;
mais s' il est glorieux, seigneur, de le hâter,
il l' est, et plus encor, de si bien l' arrêter,
que la France, en dépit d' un infaillible augure,
n' aille qu' à pas traînants vers sa grandeur future,
et que l' aigle, accablé par ce destin nouveau,
ne puisse trébucher que sur votre tombeau.
Seroit-il gloire égale à celle de suspendre
ce que ces deux états du ciel doivent attendre,
et de vous faire voir aux plus savants devins
arbitre des succès et maître des destins ?
J' ose vous dire plus. Tout ce qu' ils vous prédisent,
avec pleine clarté dans le ciel ils le lisent ;
mais vous assurent-ils que quelque astre jaloux
n' ait point mis plus d' un siècle entre l' effet et vous ?
Ces éclatants retours que font les destinées
sont assez rarement l' oeuvre de peu d' années ;
et ce qu' on vous prédit touchant ces deux états
peut être un avenir qui ne vous touche pas.
Cependant regardez ce qu' est encor l' empire :
il chancelle, il se brise, et chacun le déchire ;
de ses entrailles même il produit des tyrans ;
mais il peut encor plus que tous ses conquérants.
Le moindre souvenir des champs catalauniques
en peut mettre à vos yeux des preuves trop publiques :
Singibar, Gondebaut, Mérouée et Thierri,
là, sans Aétius, tous quatre auroient péri.
Les Romains firent seuls cette grande journée :
unissez-les à vous par un digne hyménée.
Puisque déjà sans eux vous pouvez presque tout,
il n' est rien dont par eux vous ne veniez à bout.
Quand de ces nouveaux rois ils vous auront fait maître,
vous verrez à loisir de qui vous voudrez l' être,
et résoudrez vous seul avec tranquillité
si vous leur souffrirez encor l' égalité.
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pig (pg)
n.
1.
a. Any of several mammals of the family Suidae, having short legs,
cloven hoofs, bristly hair, and a cartilaginous snout used for
digging, especially the domesticated hog, Sus scrofa, when young
or of comparatively small size.
b. The edible parts of one of these mammals.
2. Informal. A person regarded as being piglike, greedy, or gross.
3.
a. A crude block of metal, chiefly iron or lead, poured from a
smelting furnace.
b. A mold in which such metal is cast.
c. Pig iron.
4. Offensive. Slang Used as a disparaging term for a police officer.
5. Slang. A member of the social or political establishment, especially
one holding sexist or racist views.
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hire·ling (hrlng)
n.
One who works solely for compensation, especially a person willing
to perform for a fee tasks considered menial or offensive.
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re·vi·sion·ism (r-vzh-nzm)
n.
1. Advocacy of the revision of an accepted, usually long-standing view,
theory, or doctrine, especially a revision of historical events
and movements.
2. A recurrent tendency within the Communist movement to revise Marxist
theory in such a way as to provide justification for a retreat from
the revolutionary to the reformist position.
adj. revisionist
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Pelagian \Pe*la"gi*an\,
1. [L. pelagius, Gr. ?, fr. ? the sea: cf. F. p['e]lagien.] Of or
pertaining to the sea; marine; pelagic; as, pelagian shells.
2. (Eccl. Hist.) A follower of Pelagius, a British monk, born in the later
part of the 4th century, who denied the doctrines of hereditary sin, of
the connection between sin and death, and of conversion through grace.
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First-order logic: predicate calculus
Second-order: logic with intensions
Third-order: logic with time and place in consideration
Borderline cases between logical and nonlogical constants are the following
(among others): (1) Higher order quantification, which means quantification
not over the individuals belonging to a given universe of discourse, as in
first-order logic, but also over sets of individuals and sets of n-tuples
of individuals. (Alternatively, the properties and relations that specify
these sets may be quantified over.) This gives rise to second-order logic.
The process can be repeated. Quantification over sets of such sets (or of
n-tuples of such sets or over properties and relations of such sets) as are
considered in second-order logic gives rise to third-order logic; and all
logics of finite order form together the (simple) theory of (finite) types.
(2) The membership relation, expressed by , can be grafted on to first-order
logic; it gives rise to set theory. (3) The concepts of (logical) necessity
and (logical) possibility can be added.
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phe·nom·e·non (f-nm-nn, -nn)
n., pl. phe·nom·e·na (-n.)
1. An occurrence, a circumstance, or a fact that is perceptible by
the senses.
2. pl. phe·nom·e·nons.
a. An unusual, significant, or unaccountable fact or
occurrence; a marvel.
b.A remarkable or outstanding person; a paragon. See
3. Philosophy.
a. That which appears real to the mind, regardless of whether its
underlying existence is proved or its nature understood.
b. In Kantian philosophy, the appearance of an object to the mind as
opposed to its existence in and of itself, independent of the mind.
4. Physics. An observable event.
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Edradour
Edradour is a unique, single Highland malt whisky, to be enjoyed in
recognition of those small, significant moments that make up the ebb
and flow of life.
Edradour is produced in Scotland's smallest distillery - and is hand made
today as it was over 150 years ago by just three men who are devoted to the
time-honoured methods of whisky making. Indeed equipment used at the
distillery has remained unchanged since the day the distillery opened and is
only just capable of producing commercial quantities. Only 12 casks of
whisky
are produced a week, making Edradour single malt a rare pleasure for
a fortunate few.
If you manage to find it, you will be one of the few people lucky enough
to experience its charm - golden in the glass, smooth and creamy with a
nutty,
honeyed finish.
Enjoy Life's small victories with Edradour.
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an·ti·freeze (nt-frz)
n.
A substance, often a liquid such as ethylene glycol or alcohol, mixed
with another liquid to lower its freezing point.
...sweet tasting but toxic when consumed
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Stempelglanz
a term used in german coin grading
equivalent grading (USA) =
MS70 (circulated) = Stempelglanz
MS70 toned = entspricht Stempelglanz bei Ni- und Silbermünzen
perfect toned unc = similar MS70 toned
perfect brillant unc = similar MS70
MS65 (circulated) = fast Stempelglanz
MS60..MS63 (circulated) = unzirkuliert
AU = fast unzirkuliert (vz+)
fair (FR)= Zwischenerhaltung ge+
about good = Zwischenerhaltung etwas besser als fair (ge+)
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12/10/1041
death of Byzantine Emperor MICHAEL IV
at the monastery of the Holy Anargyroi.
from THE CHRONOGRAPHIA, Book IV:
The emperor, before the decease of his body, sought another more spiritual,
change. He disdained the imperial rank which he was in so short a time to
relinquish, mastered all his natural impulses and turned to God.**61 In
order
that he might not be interrupted while thus changing has like and making
his confession to the Deity, he set out from his palace and retired to the
monastery he had built, or rather, he was conveyed thither by his bearers.
Inside this place of meditation, kneeling on the floor of the church, he
prayed
to God that he might appear a well-pleasing sacrifice and be received pure
after his consecration. Thus he conciliated the Almighty and won His favour.
Then he put himself in the hands of the priests, asking them to sacrifice a
willing victim -- auspicious omen -- and they, grouped round him on either
side, chanted the opening prayers of the Sacrifice to the Lord. They took
off
him the imperial robe and the purple, and they garbed him in the Holy Mantle
of Christ. Then they took from his head the diadem and put on the Helmet
of [81] Salvation,**62 armed his chest and back with the Cross, and bravely
girding him against the spirits of evil, let him go. So much for his zeal
and
determination.
In the thought that he was now changed to a higher life, he rejoiced and
was exceeding glad. He had become swift-footed, as it were, and nimble
for the spiritual journey. His own household, on the other hand, and
especially
the elder brother, were covered in a cloud of despair, so much so that
they were unable to restrain their sympathetic laments. Not even the empress
controlled her emotion. When she heard from someone about his tonsure,
she dared to leave the women's quarters, overcoming every natural
disinclination,
and went on foot to see him. But Michael, whether through shame at
he evils he had brought upon her, or because in his attention to God he had
forgotten her, refused her permission to enter his presence.
She returned to the palace, and he, when the hour of prayer summoned and it
was time for him to attend for the usual hymns, gently rose from his
couch. When he was about to put on his shoes and found that the footwear he
had formerly had was still unchanged, (because the customary leather
sandals of the monks had not been prepared for him) he was angry at this
lack of prevision and went barefoot to church, supported on either side. His
respiration was laboured already and he was beginning to breathe his last,
so he again went to his couch and lay down. For a little while he was
silent,
for he had lost the power of speech and his breathing was difficult. Then
he gave up his soul to God. In the course of his reign, Michael had done and
planned many things; in few had he met with failure. For my own part, when
I examine his deeds and compare successes with failures, I find that the
former were more numerous and it does not appear to me that this man failed
to attain the higher life. In fact, I am convinced that he did obtain a
better lot.
So he died, in the moment of great victory, after a reign of seven years,
and
on the very day when he received the tonsure.**63 Yet there was no
magnificent
funeral or burial-place for him when his life on earth was done, for he was
buried in the church itself, on the left side as you enter, beside
the holy altar.
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histamenon nomisma
"established coin" or full-weight coin
DEBASEMENT OF THE GOLD NOMISMA, 867-1092
Michael IV (1034-1041) 90.5%
DEBASEMENT. Macedonian emperors alloyed the nomisma with silver to meet
costs of the Bulgarian Wars against Tsar Symeon (894-897; 912-924) and the
of reconquest Western Bulgaria in 977-1005. During his Syrian campaigns,
Nicephorus II revived minting a light weight nomisma of 22 carats (3.95
grs.)
called the NOMISMA TETARTERON. Although one-twelfth lighter than the full
nomisma (nomisma histamenon or "established coin"), the tetarteron was
issued
in official payments as the equivalent of a full weight nomisma. In 1005
Basil II restored the nomisma's purity and suspended minting the tetarteron,
and at his death he had amassed a reserve of 14,400,000 nomismata. His
profligate heirs revived the tetarteron and debased the nomisma until it
was an ELECTRUM alloy of gold and silver by 1056. After the defeat at
Manzikert in 1071, prices soared and successive debasements reduced the
nomisma to a miserable bronze coin alloyed with gold and silver. In 1092
ALEXIUS I recoined these miserable descendants of Constantine's solidus
in a great currency reform.
The bronze follis retained its standard and purchasing power for two
centuries
(c. 830-1030). Finds from excavated sites suggest that during this period
production of folles was greatly expanded and use of coins in daily
transactions
rose to levels of the sixth century. JOHN I (969-976) altered the design of
the
follis by replacing the imperial image with the portrait of Christ
Pantocrator
and the reverse inscription of "Jesus Christos King of Kings." The so-called
ANONYMOUS FOLLES suffered steady debasement after 1028 as successive
emperors
overstruck many older coins of their predecessors. Romanus III (1028-34)
thus
overstruck worn folles of Class A2 (minted by Basil II) as folles of Class
B,
and then Michael IV (1034-41) overstruck those of Class A3 as folles of
Class C. Such hasty recycling of old coins led to rapid deterioration of
weight standards and engraving.
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Byzantine Coins & Their Values: Coins Listed 2250
By Bendall, Simon; O'Hara, Michael; Sear, David R.
Published by Sanford J. Durst
(August 1987)
ISBN: 0713477407
Number of pages: 526
Binding: Library binding
Subjects: Coins, Byzantine Coins & Medals
http://shop.barnesandnoble.com/bookSearch/isbnInquiry.asp?sourceid=00002283862295844708&ISBN=0713477407&bfdate=02-02-2001+17:00:52
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vide ut supra (Latin)
- "see as above"
- "see the preceding statement"
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à la - also a la (ä lä, ä l, l).
prep.
In the style or manner of: ex. a poem à la Ogden Nash.
[French short for à la mode de, in the manner of.]
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Cauchy:
Augustin-Louis Cauchy
A famous French mathemetician, with significant work in differential
equations.
Several mathematical methods bear his name.
Paris was a difficult place to live in when Augustin-Louis Cauchy was a
young
child due to the political events surrounding the French Revolution. When he
was four years old his father, fearing for his life in Paris, moved his
family
to Arcueil. There things were hard and he wrote in a letter:
We never have more than a half pound of bread - and sometimes not
even that. This we supplement with the little supply of hard crackers
and rice that we are allotted.
They soon returned to Paris and Cauchy's father was active in the education
of
young Augustin-Louis. Laplace and Lagrange were visitors at the Cauchy
family
home and Lagrange in particular seems to have taken an interest in young
Cauchy's mathematical education. Lagrange advised Cauchy's father that his
son should obtain a good grounding in languages before starting a serious
study of mathematics. In 1802 Augustin-Louis entered the Ecole Centrale du
Panthéon where he spent two years studying classical languages.
In addition to his heavy workload Cauchy undertook mathematical researches
and he proved in 1811 that the angles of a convex polyhedron are determined
by its faces. He submitted his first paper on this topic then, encouraged by
Legendre and Malus, he submitted a further paper on polygons and polyhedra
in 1812. Cauchy felt that he had to return to Paris if he was to make an
impression with mathematical research. In September of 1812 he returned to
Paris after becoming ill. It appears that the illness was not a physical one
and was probably of a psychological nature resulting in severe depression.
Back in Paris Cauchy investigated symmetric functions and submitted a memoir
on this topic in November 1812. This was published in the Journal of the
Ecole Polytechnique in 1815. However he was supposed to return to Cherbourg
in February 1813 when he had recovered his health and this did not fit with
his mathematical ambitions. His request to de Prony for an associate
professorship at the Ecole des Ponts et Chaussées was turned down but he
was allowed to continue as an engineer on the Ourcq Canal project rather
than return to Cherbourg. Pierre Girard was clearly pleased with his
previous work on this project and supported the move.
In 1817 when Biot left Paris for an expedition to the Shetland Islands in
Scotland Cauchy filled his post at the Collège de France. There he lectured
on methods of integration which he had discovered, but not published,
earlier.
Cauchy was the first to make a rigorous study of the conditions for
convergence
of infinite series in addition to his rigorous definition of an integral.
His
text Cours d'analyse in 1821 was designed for students at Ecole
Polytechnique
and was concerned with developing the basic theorems of the calculus as
rigorously as possible. He began a study of the calculus of residues in 1826
in Sur un nouveau genre de calcul analogue au calcul infinétesimal while in
1829 in Leçons sur le Calcul Différential he defined for the first time a
complex function of a complex variable.
Cauchy did not have particularly good relations with other scientists.
His staunchly Catholic views had him involved on the side of the Jesuits
against the Académie des Sciences. He would bring religion into his
scientific work as for example he did on giving a report on the theory of
light in 1824 when he attacked the author for his view that Newton had not
believed that people had souls.
He did important work on differential equations and applications to
mathematical physics. He also wrote on mathematical astronomy, mainly
because
of his candidacy for positions at the Bureau des Longitudes. The 4-volume
text Exercises d'analyse et de physique mathematique published between 1840
and 1847 proved extremely important.
Numerous terms in mathematics bear Cauchy's name:- the Cauchy integral
theorem, in the theory of complex functions, the Cauchy-Kovalevskaya
existence
theorem for the solution of partial differential equations, the
Cauchy-Riemann
equations and Cauchy sequences. He produced 789 mathematics papers, an
incredible achievement. This achievement is summed up in [4] as follows:-
... such an enormous scientific creativity is nothing less than
staggering, for it presents research on all the then-known areas of
mathematics ... in spite of its vastness and rich multifaceted
character,
Cauchy's scientific works possess a definite unifying theme, a secret
wholeness. ... Cauchy's creative genius found broad expression not only
in his work on the foundations of real and complex analysis, areas to
which his name is inextricably linked, but also in many other fields.
Specifically, in this connection, we should mention his major
contributions to the development of mathematical physics and to
theoretical mechanics... we mention ... his two theories of elasticity
and his investigations on the theory of light, research which required
that he develop whole new mathematical techniques such as Fourier
transforms, diagonalisation of matrices, and the calculus of residues.
His collected works, Oeuvres complètes d'Augustin Cauchy (1882-1970), were
published in 27 volumes.
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cybernetic seal
????
an electronic sig, address ??
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limit ordinal
An ordinal is a set of which every element is both a subset and an ordinal.
The empty set is, thus, trivially an ordinal. Every element of an ordinal
is said to be less than it: `m in n' is also written `m < n' - and this
implies that m is a subset of n, so anything < m is also < n, so < is
transitive.
On relations (in general) we define a mapping, successor, which takes any
relation, r, to its union with the set {r}. This differs from r unless
`r in r'. Note that successor(r) subsumes r and, consequently, anything that
r subsumes. When r is a set, so is its successor: and things it subsumes are
known as its subsets. If an ordinal is the successor of anything, then that
thing is a member (and subset) of our ordinal and, consequently, an ordinal
(but note that empty, among others, is not the successor of anything).
The successor, N, of any ordinal is the successor of a set, hence a set: it
subsumes its predecessor, which is one of its members, an all N's other
members
are subsumed by this subset of N, hence by N; and all N's members are
ordinals,
so the successor of any ordinal is an ordinal.
An ordinal which is its own union (such as empty), or equivalently not the
successor of anything, is described as a limit ordinal.
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quadratically factoring
everyone has done this in math class. in case you've forgotten how:
example from math forum...
2 6y - 2
_____ + ____________
y - 1 y^2 + 2y - 3
2a^2 - a 6
___________ _ ____________
2a^2 + a - 3 2a^2 + a - 3
answer...
To factor a polynomial there are basically three steps:
1. Identify and factor out common factors of all the coefficients.
2. Identify and factor out variables appearing in all the terms.
3. Factor the remaining piece, if possible.
The first step would be successful on 6*y-2, since both coefficients
have a factor of 2: 6*y - 2 = 2*(3*y-1).
The second step would be successful on 2*a^2 - a, since the variable
"a" appears in both terms: 2*a^2 - a = a*(2*a-1).
When the remaining piece has degree 1 (the variable appears only to
the first power, not to any higher power), you are done. When the
remaining piece has degree 2 or higher, it may factor into pieces of
lower degree.
There are quite a large array of different ways to try to factor that
kind of polynomial. I will only describe the one for factoring
quadratic (or degree 2) polynomials.
You want to factor a quadratic polynomial of the form
a*x^2 + b*x + c,
where a, b, and c are some expressions not involving x, often whole
number constants.
Multiply together a*c. Try to find a way of factoring that product
into two numbers r and s, whose sum is b. Thus,
r*s = a*c
and
r + s = b.
Remember that r and s may be positive or negative! If satisfying these
equations is impossible, then the polynomial cannot be factored.
Example: 20*x^2 + x - 12.
a*c = 20*(-12) = -240.
Can you factor -240 into two numbers whose sum is b = +1?
Yes, 16 and -15 will do fine.
How do we use these numbers? They are the r and s which fit into
(a*x + r)*(a*x + s)/a = (a^2*x^2 + a*[r+s]*x + r*s)/a,
= a*x^2 + (r+s)*x + (a*c)/a,
= a*x^2 + b*x + c.
In the example, then,
20*x^2 + x - 12 = (20*x + 16)*(20*x - 15)/20,
= (5*x + 4)*(4*x - 3).
In the last step we canceled factors in common between the denominator
and each factor in the numerator, which were a 4 from the first factor
and a 5 from the second.
Understood?
Now you try this on your denominators y^2 + 2*y - 3 and 2*a^2 + a - 3.
In the first one, a*c = -3 and b = 2, so you want to find r and s with
r*s = -3 and r + s = 2. In the second one, you want to find r and s
with r*s = -6 and r + s = 1.
......you can also solve quadratic equations by factoring.
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Venienti occurrite morbo. (Persius, Satires, III, 64)
- Meet the misfortune as it comes.
- Go out and meet the approaching disease.
- Take the oncoming distress head on.
- Attend to the first symptoms of disease.
... or something of the like.
saepe oculos, memini, tangebam paruus oliuo,
grandia si nollem morituri uerba Catonis 45
discere non sano multum laudanda magistro,
quae pater adductis sudans audiret amicis.
iure; etenim id summum, quid dexter senio ferret,
scire erat in uoto, damnosa canicula quantum
raderet, angustae collo non fallier orcae, 50
neu quis callidior buxum torquere flagello.
haut tibi inexpertum curuos deprendere mores
quaeque docet sapiens bracatis inlita Medis
porticus, insomnis quibus et detonsa iuuentus
inuigilat siliquis et grandi pasta polenta; 55
et tibi quae Samios diduxit littera ramos
surgentem dextro monstrauit limite callem.
stertis adhuc laxumque caput conpage soluta
oscitat hesternum dissutis undique malis.
est aliquid quo tendis et in quod derigis arcum? 60
an passim sequeris coruos testaque lutoque,
securus quo pes ferat, atque ex tempore uiuis?
elleborum frustra, cum iam cutis aegra tumebit,
poscentis uideas; uenienti occurrite morbo,
et quid opus Cratero magnos promittere montis? 65
discite et, o miseri, causas cognoscite rerum:
quid sumus et quidnam uicturi gignimur, ordo
quis datus, aut metae qua mollis flexus et unde,
quis modus argento, quid fas optare, quid asper
utile nummus habet, patriae carisque propinquis 70
quantum elargiri deceat, quem te deus esse
iussit et humana qua parte locatus es in re.
disce nec inuideas quod multa fidelia putet
in locuplete penu, defensis pinguibus Vmbris,
et piper et pernae, Marsi monumenta clientis, 75
maenaque quod prima nondum defecerit orca.
Still snoring? Head and neck joint all gone slack,
Cheeks unstitched, yawning off yesterday's.....?
Tell me! Have you any aim in life,
Or is it enough to live for the moment now,
Following footsteps where the footstep leads,
Slinging rocks or mud at croaking fleeting crows?
Medicine can't do much when the skin is swollen and green,
Why pay the doctors thousands? Catch and check the disease.
For God's sake get the basic issues clear - - -
What are we humans, what's the aim of Life,
The shape of it, where is the hairpin turn
Best to be taken, and when? What's the right use of gold,
Of hope and prayer, what barb's on the dollar bill?
What would you give to country, family, friends?
What sort of a man did God wish you to be,
Playing what sort of role?...
Don't skew off, hear!
Just because you have cupboards of foodstuff rotting silently,
Reward for a rich case won in Umbria, and hams
Gift of a Marsian client, and wine sauce herring jars
Hardly yet opened...
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a·pex (pks)
n., pl. a·pex·es or a·pi·ces (p-sz, p-).
1. The highest point; the vertex: the apex of a triangle; the apex of
a hill.
2. The point of culmination. See Synonyms at summit.
3. The usually pointed end of an object; the tip: the apex of a leaf.
4. The point on the celestial sphere toward which the sun and solar
system
appear to be moving relative to the fixed stars [syn: solar apex, apex
of the sun's way] [ant: antapex]
In mathematics apex frequently refers to an angle (i.e. apex of a triangle,
or the apex of a cone, the point of a cone) or as a high or low point on
a graph of a function (i.e. the tops of the "humps" in a cosine graph, or
the base of a parabola)
The word is used to mean the same thing in auto racing, but the definition
is
more visually clear. In racing, the apex is the "high point" in a turn...
the
point in the curve where you are now pulling out of the corner instead of
turning into the corner.
The term apex is also commonly used in astronomy; both for relative
positions/
relative motion and when calculating positions/motion between bodies.
i.e.
Lagrange Point
French mathematician and astronomer Joseph Louis Lagrange showed that three
bodies can lie at the apexes of an equilateral triangle which rotates in its
plane. If one of the bodies is sufficiently massive compared with the other
two, then the triangular configuration is apparently stable. Such bodies are
sometimes referred to as Trojans. The leading apex of the triangle is known
as the leading Lagrange point or L4; the trailing apex is the trailing
Lagrange point or L5.
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internal metric
- "inside measurement", a statistic or measurment determined internally from
the data available.
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"Only drowning men could see him"
Suzanne by Lenoard Cohen, "Songs of Leonard Cohen" (1968) Track 1, 3:47
Suzanne takes you down to her place near the river
You can hear the boats go by
You can spend the night beside her
And you know that she's half crazy
But that's why you want to be there
And she feeds you tea and oranges
That come all the way from China
And just when you mean to tell her
That you have no love to give her
Then she gets you on her wavelength
And she lets the river answer
That you've always been her lover
And you want to travel with her
And you want to travel blind
And you know that she will trust you
For you've touched her perfect body with your mind.
And Jesus was a sailor
When he walked upon the water
And he spent a long time watching
From his lonely wooden tower
And when he knew for certain
Only drowning men could see him
He said "All men will be sailors then
Until the sea shall free them"
But he himself was broken
Long before the sky would open
Forsaken, almost human
He sank beneath your wisdom like a stone
And you want to travel with him
And you want to travel blind
And you think maybe you'll trust him
For he's touched your perfect body with his mind.
Now Suzanne takes your hand
And she leads you to the river
She is wearing rags and feathers
From Salvation Army counters
And the sun pours down like honey
On our lady of the harbour
And she shows you where to look
Among the garbage and the flowers
There are heroes in the seaweed
There are children in the morning
They are leaning out for love
And they will lean that way forever
While Suzanne holds the mirror
And you want to travel with her
And you want to travel blind
And you know that you can trust her
For she's touched your perfect body with her mind.
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Coimbra
a city in Portugal; also the university
Old city, with a life that began in Aeminium, when the Roman occupied the
Iberian Peninsula, Coimbra is many centuries of history, culture and
tradition.
History in its documents, authentic monuments to the art of distant times;
culture in its old university (founded in 1290); tradition in the its
students'
life, very present in its song, the Fate of Coimbra.
In spite of the number of its inhabitants being about one hundred thousand,
it occupies an area very superior to the common of the European cities with
identical population, thanks to the green zones and of the vulgar type
of residence.
Its urban perimeter is divided in two different zones: the Alta,
corresponding
partly to the primitive medieval town, occupying the hill of the University;
the Baixa, located on the suburb of the medium age and the zone of expansion
of the centuries immediately subsequent, also including the margin of the
river Mondego, Sofia's street and the with her surroudings.
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Arbella
In 1630 John Winthrop organized a fleet of 11 ships to carry immigrants
from England to America. Departing in two groups in April and May, they
arrived at various dates in June and July. These ships were:
The Ambrose
The Arbella (Flagship)
The Charles
The Hopewell
The Jewel
The Mayflower (NOT the ship with the "pilgrims" in it)
The Success
The Talbot
The Trial
The Whale
The William & Francis
On April 8, 1630 The Arbella departed Yarmouth, Isle of Wight, and arrived
at Salem, Massachusetts, June 13 and following days.
also, in Moby Dick: (Chapter 14, "Nantucket")
Sailing east from New England, the Pequod inherits and reverses the mission
of the Arbella, the ship that brought John Winthrop and his fellow colonists
to Massachusetts Bay in 1630. Ahab's ritual in this chapter as a demonic
inversion of Puritan communion.
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Nantucket
an island 30 miles at sea, off the coast of Cape Cod, Massachusetts, USA
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Quiquagesima
Quiquagesima Sunday; a special day on the Liturgical Calendar of
the Ecclesia Gnostica.
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binary
- two, of base two, etc.
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con·gru·ence (knggr-ns, kn-gr-)
n., pl. con·gru·enc·es.
1. Agreement, harmony, conformity, or correspondence: “What an
extraordinary congruence of genius and era” (Rita Rack).
2. Mathematics.
a. The state of being congruent.
b. A statement that two quantities are congruent.
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Chemnitz:
Martin Chemnitz
A Lutheran theologian in the 16th century whos works include Examination of
the Council of Trent; Enchiridion; The Lords Supper; and The Two Natures
of Christ. Chemnitz was considered a man immense learning, orthodoxy and
piety. He rose to a position of great influence and is, to this day,
considered to be second in the Lutheran Church only to Martin Luther
himself. It was Chemnitz (along with other Gnesio-Lutherans like
Jacob Andrae, Nicholas Selnecker, David Chytraeus, Andrew Musculus and
Christopher Koerner) who gave the Lutheran Church "The Formula of Concord",
and with it the completed "Book of Concord" of 1580. The publication of
these documents had the effect of galvanizing and uniting Lutherans under
the banner of Lutheran orthodoxy.
see next entry...
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Si Martinus non fuisset, Martinus vix stetisset.
- If the second Martin (Chemnitz) had not come, the first
Martin (Luther) would not have stood.
Refers to the influence of Martin Chemnitz on the Lutheran church.
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zabra
- an Israeli-born Jew
- also, Aba Zabra, a monk who lived in the days of the negus zara yakob
(15th century) to whom the book teezaza sanbat (precepts of the sabbath)
is attributed. A Falashas work, Falashas are the only Jews in the world
with a monastic tradition... The cave where Abba Zabra lived became the
largest Falasha monastary. Last century, 200 monks were said to be living
there.
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atzaura
?????????
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Consuetudo loci observanda est.
- The custom of the place shall be attended to.
- The custom of the place is to be observed.
During the golden years of Rome, the use of slaves in everyday life
was very commonplace. They were, in essence, servants without wages,
though it was expected that they be kept fed and in good health. This is
important to note, as the Roman concept of slavery was not the same as
the Anglo-American practice of chattel slavery. Slaves were typically the
spoils of the Romans' military victories. Slaves were brought in from
the far reaches of the Empire, bringing different languages, cultures
and religious beliefs with them. Consequently, it is quite possible that
the slaves, although subjugated, did have some influence on Roman culture.
The important thing to realize about Roman slavery is that it was not
without the opportunity for advancement. A slave who had worked hard
for his master, saved his master's life, or been virtuous in various
other ways could be granted his freedom through the act of manumission.
This granted him status as a libertus, or freed-man. While he was not a
Roman citizen, he did have considerably more rights and opportunities
(the emperor's right hand man was traditionally a freed-man). He could
operate his own business if he chose, or work (and be paid) for the
Empire, or even be supported by a patron. He did not have all the
rights of a Roman citizen ("civis Romanus sum"), but still was accorded
more respect under the law. In fact, it was possible, though infrequent,
that a liberatus could, with the blessing of the emperor,
become a Roman citizen.
Once the slave had gained a basic control of the language, he would be
able to communicate with his master; perhaps if he was particularly
good with Latin, he might work for his master as a scribe. The next step
in the education of a slave involved acquainting him with the culture
and customs of Roman life ("consuetudo loci observanda est"). This would
involve the further development of the slave's conversational skills,
another large milestone in the development of a free mind. These
conversational skills would allow the slave to be able to operate a
business or work for the Empire, not to mention making him
considerably more adept at manipulating his master.
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Letters of Marque
LETTERS OF MARQUE were official licences issued on behalf of the head of
government in time of war to private citizens which gave them limited legal
protection to act as PRIVATEERS. That is, to use their own ships, at their
own expense, to make war on the merchant shipping of countries with which
their own county was at war, and to profit from the sale of any ships and
cargoes they could capture. Without this protection they would simply be
treated as pirates if captured.
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Rive Gauche
Paris, the "left bank" of the Siene, famous for the Latin quarter, art
districts, bohemian streets and "old Paris".
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"keleuson me elthein pros se epi ta hudata" (Matthew, 14, 28)
- command me to come to you over the waters
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1.276779674019
one of the known, primitive, irreducible integer polynomials with degree at
most 72 having Mahler measure larger than 1 but less than 1.3
???????
maybe a key or something