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.
In"fi*nite*ness, n. The state or quality of being infinite; infinity;
greatness; immensity. Jer. Taylor.
In`fin*i*tes"i*mal (?), a. [Cf. F. infinitésimal, fr. infinitésime
infinitely small, fr. L. infinitus. See Infinite, a.] Infinitely or
indefinitely small; less than any assignable quantity or value; very
small.
Infinitesimal calculus, the different and the integral calculus, when
developed according to the method used by Leibnitz, who regarded the
increments given to variables as infinitesimal.
In`fin*i*tes"i*mal, n. (Math.) An infinitely small quantity; that which
is less than any assignable quantity.
In`fin*i*tes"i*mal*ly, adv. By infinitesimals; in infinitely small
quantities; in an infinitesimal degree.
In*fin`i*ti"val (?), a. Pertaining to the infinite mood. "Infinitival
stems." Fitzed. Hall.
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.
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.
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.
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).
In*fin"i*tive, n. (Gram.) An infinitive form of the verb; a verb in the
infinitive mood; the infinitive mood.
In*fin"i*tive, adv. (Gram.) In the manner of an infinitive mood.
||In`fi*ni"to (?), a. [It.] (Mus.) Infinite; perpetual, as a canon
||whose end leads back to the beginning. See Infinite, a., 5.
||
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.
In*fin"i*tu`ple (?), a. [Cf. Quadruple.] Multiplied an infinite number
of times. [R.] Wollaston.
In*fin"i*ty (?), n.; pl. Infinities (#). [L. infinitas; pref. in- not
+ finis boundary, limit, end: cf. F. infinité. See Finite.]
1. Unlimited extent of time, space, or quantity; eternity;
boundlessness; immensity. Sir T. More.
There can not be more infinities than one; for one of them would
limit the other.
Sir W. Raleigh.
2. Unlimited capacity, energy, excellence, or knowledge; as, the
infinity of God and his perfections. Hooker.
3. Endless or indefinite number; great multitude; as an infinity of
beauties. Broome.
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4. (Math.) A quantity greater than any assignable quantity of the same
kind.
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.
In*firm" (n*frm"), a. [L. infirmus: cf. F. infirme. See In- not, and
Firm, a.] 1. Not firm or sound; weak; feeble; as, an infirm body; an
infirm constitution.
A poor, infirm, weak, and despised old man.
Shak.
2. Weak of mind or will; irresolute; vacillating. "An infirm judgment."
Burke.
Infirm of purpose!
Shak.