Arithmetical progression, a progression in which the terms increase or decrease by equal differences, as the numbers &lbrace22, 4, 6, 8, 1010, 8, 6, 4, 2&rbrace2 by the difference 2.

Geometrical progression, a progression in which the terms increase or decrease by equal ratios, as the numbers &lbrace22, 4, 8, 16, 32, 6464, 32, 16, 8, 4, 2&rbrace2 by a continual multiplication or division by 2.

Harmonic progression, a progression in which the terms are the reciprocals of quantities in arithmetical progression, as ½, ¼, &frac16, &frac18, &frac1x10.

Progressional
(Pro*gres"sion*al) a. Of or pertaining to progression; tending to, or capable of, progress.

Progressionist
(Pro*gres"sion*ist), n.

1. One who holds to a belief in the progression of society toward perfection.

of any kind; as, the progress of a negotiation; the progress of art. (d) In knowledge; in proficiency; as, the progress of a child at school. (e) Toward ideal completeness or perfection in respect of quality or condition; — applied to individuals, communities, or the race; as, social, moral, religious, or political progress.

2. A journey of state; a circuit; especially, one made by a sovereign through parts of his own dominions.

The king being returned from his progresse.
Evelyn.

Progress
(Pro*gress") (?; formerly pronounced like Progress, n.), v. i. [imp. & p. p. Progressed ; p. pr. & vb. n. Progressing.]

1. To make progress; to move forward in space; to continue onward in course; to proceed; to advance; to go on; as, railroads are progressing. "As his recovery progressed." Thackeray.

Let me wipe off this honorable dew,
That silverly doth progress on thy checks.
Shak.

They progress in that style in proportion as their pieces are treated with contempt.
Washington.

The war had progressed for some time.
Marshall.

2. To make improvement; to advance. Bayard.

If man progresses, art must progress too.
Caird.

Progress
(Prog"ress) (?; see Progress, v. i.), v. t. To make progress in; to pass through. [Obs.] Milton.

Progression
(Pro*gres"sion) n. [L. progressio: cf. F. progression.]

1. The act of moving forward; a proceeding in a course; motion onward.

2. Course; passage; lapse or process of time.

I hope, in a short progression, you will be wholly immerged in the delices and joys of religion.
Evelyn.

3. (Math.) Regular or proportional advance in increase or decrease of numbers; continued proportion, arithmetical, geometrical, or harmonic.

4. (Mus.) A regular succession of tones or chords; the movement of the parts in harmony; the order of the modulations in a piece from key to key.

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