Radical axis of two circles

Radical Rad"i*cal (r[a^]d"[i^]*kal), a. [F., fr. L. radicalis having roots, fr. radix, -icis, a root. See {Radix}.] 1. Of or pertaining to the root; proceeding directly from the root. [1913 Webster]

2. Hence: Of or pertaining to the root or origin; reaching to the center, to the foundation, to the ultimate sources, to the principles, or the like; original; fundamental; thorough-going; unsparing; extreme; as, radical evils; radical reform; a radical party. [1913 Webster]

The most determined exertions of that authority, against them, only showed their radical independence. --Burke. [1913 Webster]

3. (Bot.) (a) Belonging to, or proceeding from, the root of a plant; as, radical tubers or hairs. (b) Proceeding from a rootlike stem, or one which does not rise above the ground; as, the radical leaves of the dandelion and the sidesaddle flower. [1913 Webster]

4. (Philol.) Relating, or belonging, to the root, or ultimate source of derivation; as, a radical verbal form. [1913 Webster]

5. (Math.) Of or pertaining to a radix or root; as, a radical quantity; a radical sign. See below. [1913 Webster]

{Radical axis of two circles}. (Geom.) See under {Axis}.

{Radical pitch}, the pitch or tone with which the utterance of a syllable begins. --Rush.

{Radical quantity} (Alg.), a quantity to which the radical sign is prefixed; specifically, a quantity which is not a perfect power of the degree indicated by the radical sign; a surd.

{Radical sign} (Math.), the sign [root] (originally the letter r, the initial of radix, root), placed before any quantity, denoting that its root is to be extracted; thus, [root]a, or [root](a + b). To indicate any other than the square root, a corresponding figure is placed over the sign; thus, [cuberoot]a, indicates the third or cube root of a.

{Radical stress} (Elocution), force of utterance falling on the initial part of a syllable or sound.

{Radical vessels} (Anat.), minute vessels which originate in the substance of the tissues. [1913 Webster]

Syn: Primitive; original; natural; underived; fundamental; entire.

Usage: {Radical}, {Entire}. These words are frequently employed as interchangeable in describing some marked alteration in the condition of things. There is, however, an obvious difference between them. A radical cure, reform, etc., is one which goes to the root of the thing in question; and it is entire, in the sense that, by affecting the root, it affects in an appropriate degree the entire body nourished by the root; but it may not be entire in the sense of making a change complete in its nature, as well as in its extent. Hence, we speak of a radical change; a radical improvement; radical differences of opinion; while an entire change, an entire improvement, an entire difference of opinion, might indicate more than was actually intended. A certain change may be both radical and entire, in every sense. [1913 Webster]