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Ad infinitum
Ad infinitum Ad in`fi*ni"tum [L., to infinity.]
Without limit; endlessly.
Circle at infinity 4. (Math.) A quantity greater than any assignable quantity of
the same kind.
Note: Mathematically considered, infinity is always a limit
of a variable quantity, resulting from a particular
supposition made upon the varying element which enters
it. --Davies & Peck (Math. Dict.).
5. (Geom.) That part of a line, or of a plane, or of space,
which is infinitely distant. In modern geometry, parallel
lines or planes are sometimes treated as lines or planes
meeting at infinity.
Circle at infinity, an imaginary circle at infinity,
through which, in geometry of three dimensions, every
sphere is imagined to pass.
Circular points at infinity. See under Circular. Circular points at infinity 4. (Math.) A quantity greater than any assignable quantity of
the same kind.
Note: Mathematically considered, infinity is always a limit
of a variable quantity, resulting from a particular
supposition made upon the varying element which enters
it. --Davies & Peck (Math. Dict.).
5. (Geom.) That part of a line, or of a plane, or of space,
which is infinitely distant. In modern geometry, parallel
lines or planes are sometimes treated as lines or planes
meeting at infinity.
Circle at infinity, an imaginary circle at infinity,
through which, in geometry of three dimensions, every
sphere is imagined to pass.
Circular points at infinity. See under Circular. Circular points at infinityCircular Cir"cu*lar, a. [L. circularis, fr. circulus circle:
cf. F. circulaire. See Circle.]
1. In the form of, or bounded by, a circle; round.
2. repeating itself; ending in itself; reverting to the point
of beginning; hence, illogical; inconclusive; as, circular
reasoning.
3. Adhering to a fixed circle of legends; cyclic; hence,
mean; inferior. See Cyclic poets, under Cyclic.
Had Virgil been a circular poet, and closely adhered
to history, how could the Romans have had Dido?
--Dennis.
4. Addressed to a circle, or to a number of persons having a
common interest; circulated, or intended for circulation;
as, a circular letter.
A proclamation of Henry III., . . . doubtless
circular throughout England. --Hallam.
5. Perfect; complete. [Obs.]
A man so absolute and circular In all those
wished-for rarities that may take A virgin captive.
--Massinger.
Circular are, any portion of the circumference of a circle.
Circular cubics (Math.), curves of the third order which
are imagined to pass through the two circular points at
infinity.
Circular functions. (Math.) See under Function.
Circular instruments, mathematical instruments employed for
measuring angles, in which the graduation extends round
the whole circumference of a circle, or 360[deg].
Circular lines, straight lines pertaining to the circle, as
sines, tangents, secants, etc.
Circular note or letter.
(a) (Com.) See under Credit.
(b) (Diplomacy) A letter addressed in identical terms to a
number of persons.
Circular numbers (Arith.), those whose powers terminate in
the same digits as the roots themselves; as 5 and 6, whose
squares are 25 and 36. --Bailey. --Barlow.
Circular points at infinity (Geom.), two imaginary points
at infinite distance through which every circle in the
plane is, in the theory of curves, imagined to pass.
Circular polarization. (Min.) See under Polarization.
Circular or Globular sailing (Naut.), the method of
sailing by the arc of a great circle.
Circular saw. See under Saw. cleft infinitiveSplit infinitive Split infinitive (Gram.)
A simple infinitive with to, having a modifier between the
verb and the to; as in, to largely decrease. Called also
cleft infinitive. dative infinitiveGerund Ger"und, n. [L. gerundium, fr. gerere to bear, carry,
perform. See Gest a deed, Jest.] (Lat. Gram.)
1. A kind of verbal noun, having only the four oblique cases
of the singular number, and governing cases like a
participle.
2. (AS. Gram.) A verbal noun ending in -e, preceded by to and
usually denoting purpose or end; -- called also the
dative infinitive; as, ``Ic h[ae]bbe mete t[^o] etanne'
(I have meat to eat.) In Modern English the name has been
applied to verbal or participal nouns in -ing denoting a
transitive action; e. g., by throwing a stone. InfiniteInfinite In"fi*nite, a. [L. infinitus: cf. F. infini. See
In- not, and Finite.]
1. Unlimited or boundless, in time or space; as, infinite
duration or distance.
Whatever is finite, as finite, will admit of no
comparative relation with infinity; for whatever is
less than infinite is still infinitely distant from
infinity; and lower than infinite distance the
lowest or least can not sink. --H. Brooke.
2. Without limit in power, capacity, knowledge, or
excellence; boundless; immeasurably or inconceivably
great; perfect; as, the infinite wisdom and goodness of
God; -- opposed to finite.
Great is our Lord, and of great power; his
understanding is infinite. --Ps. cxlvii.
5.
O God, how infinite thou art! --I. Watts.
3. Indefinitely large or extensive; great; vast; immense;
gigantic; prodigious.
Infinite riches in a little room. --Marlowe.
Which infinite calamity shall cause To human life.
--Milton.
4. (Math.) Greater than any assignable quantity of the same
kind; -- said of certain quantities.
5. (Mus.) Capable of endless repetition; -- said of certain
forms of the canon, called also perpetual fugues, so
constructed that their ends lead to their beginnings, and
the performance may be incessantly repeated. --Moore
(Encyc. of Music).
Syn: Boundless; immeasurable; illimitable; interminable;
limitless; unlimited; endless; eternal. Infinitely
Infinitely In"fi*nite*ly, adv.
1. Without bounds or limits; beyond or below assignable
limits; as, an infinitely large or infinitely small
quantity.
2. Very; exceedingly; vastly; highly; extremely. ``Infinitely
pleased.' --Dryden.
Infiniteness
Infiniteness In"fi*nite*ness, n.
The state or quality of being infinite; infinity; greatness;
immensity. --Jer. Taylor.
Infinitesimal
Infinitesimal In`fin*i*tes"i*mal, n. (Math.)
An infinitely small quantity; that which is less than any
assignable quantity.
Infinitesimally
Infinitesimally In`fin*i*tes"i*mal*ly, adv.
By infinitesimals; in infinitely small quantities; in an
infinitesimal degree.
Infinitival
Infinitival In*fin`i*ti"val, a.
Pertaining to the infinite mood. ``Infinitival stems.'
--Fitzed. Hall.
InfinitiveInfinitive In*fin"i*tive, n. [L. infinitivus: cf. F.
infinitif. See Infinite.]
Unlimited; not bounded or restricted; undefined.
Infinitive mood (Gram.), that form of the verb which merely
names the action, and performs the office of a verbal
noun. Some grammarians make two forms in English: (a)
The simple form, as, speak, go, hear, before which to is
commonly placed, as, to speak; to go; to hear. (b) The
form of the imperfect participle, called the infinitive in
-ing; as, going is as easy as standing.
Note: With the auxiliary verbs may, can, must, might, could,
would, and should, the simple infinitive is expressed
without to; as, you may speak; they must hear, etc. The
infinitive usually omits to with the verbs let, dare,
do, bid, make, see, hear, need, etc.; as, let me go;
you dare not tell; make him work; hear him talk, etc.
Note: In Anglo-Saxon, the simple infinitive was not preceded
by to (the sign of modern simple infinitive), but it
had a dative form (sometimes called the gerundial
infinitive) which was preceded by to, and was chiefly
employed in expressing purpose. See Gerund, 2.
Note: The gerundial ending (-anne) not only took the same
form as the simple infinitive (-an), but it was
confounded with the present participle in -ende, or
-inde (later -inge). Infinitive
Infinitive In*fin"i*tive, n. (Gram.)
An infinitive form of the verb; a verb in the infinitive
mood; the infinitive mood.
Infinitive
Infinitive In*fin"i*tive, adv. (Gram.)
In the manner of an infinitive mood.
Infinitive moodInfinitive In*fin"i*tive, n. [L. infinitivus: cf. F.
infinitif. See Infinite.]
Unlimited; not bounded or restricted; undefined.
Infinitive mood (Gram.), that form of the verb which merely
names the action, and performs the office of a verbal
noun. Some grammarians make two forms in English: (a)
The simple form, as, speak, go, hear, before which to is
commonly placed, as, to speak; to go; to hear. (b) The
form of the imperfect participle, called the infinitive in
-ing; as, going is as easy as standing.
Note: With the auxiliary verbs may, can, must, might, could,
would, and should, the simple infinitive is expressed
without to; as, you may speak; they must hear, etc. The
infinitive usually omits to with the verbs let, dare,
do, bid, make, see, hear, need, etc.; as, let me go;
you dare not tell; make him work; hear him talk, etc.
Note: In Anglo-Saxon, the simple infinitive was not preceded
by to (the sign of modern simple infinitive), but it
had a dative form (sometimes called the gerundial
infinitive) which was preceded by to, and was chiefly
employed in expressing purpose. See Gerund, 2.
Note: The gerundial ending (-anne) not only took the same
form as the simple infinitive (-an), but it was
confounded with the present participle in -ende, or
-inde (later -inge). InfinitoInfinito In`fi*ni"to, a. [It.] (Mus.)
Infinite; perpetual, as a canon whose end leads back to the
beginning. See Infinite, a., 5. Infinitude
Infinitude In*fin"i*tude, n.
1. The quality or state of being infinite, or without limits;
infiniteness.
2. Infinite extent; unlimited space; immensity; infinity. ``I
am who fill infinitude.' --Milton.
As pleasing to the fancy, as speculations of
eternity or infinitude are to the understanding.
--Addison.
3. Boundless number; countless multitude. ``An infinitude of
distinctions.' --Addison.
InfinitupleInfinituple In*fin"i*tu`ple, a. [Cf. Quadruple.]
Multipied an infinite number of times. [R.] --Wollaston. Split infinitiveSplit infinitive Split infinitive (Gram.)
A simple infinitive with to, having a modifier between the
verb and the to; as in, to largely decrease. Called also
cleft infinitive.
Meaning of INFINIT from wikipedia
