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Webster 1913 Edition

Progression

Pro-gres′sion

,
Noun.
[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.
Arithmetical progression
,
a progression in which the terms increase or decrease by equal differences, as the numbers [lbrace2]
2, 4, 6, 8, 10
10, 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 [lbrace2]
2, 4, 8, 16, 32, 64
64, 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, 1⁄6, 1⁄8, 1⁄10.

Webster 1828 Edition

Progression

PROGRES'SION

,
Noun.
[L. progressio, progredior.]
1.
The act of moving forward; a proceeding in a course; motion onwards.
2.
Intellectual advance; as the progression of thought.
3.
Course; passage.
4.
In mathematics, regular or proportional advance in increase or decrease of numbers; continued proportion, arithmetical or geometrical. Continued arithmetical proportion, is when the terms increase or decrease by equal differences. Thus,
2.
4. 6. 8. 10.
. 8. 6. 4. 2. by the difference 2.
Geometrical proportion or progression, is when the terms increase or decrease by equal ratios. Thus,
2.
4. 8. 16. 32. 64.
64.
32. 16. 8. 4. 2. by a continual multiplication or division by 2.

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