Definition of geometrical proportion. Meaning of geometrical proportion. Synonyms of geometrical proportion

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Definition of geometrical proportion

geometrical proportion
Proportion Pro*por"tion, n. [F., fr. L. proportio; pro before + portio part or share. See Portion.] 1. The relation or adaptation of one portion to another, or to the whole, as respect magnitude, quantity, or degree; comparative relation; ratio; as, the proportion of the parts of a building, or of the body. The image of Christ, made after his own proportion. --Ridley. Formed in the best proportions of her sex. --Sir W. Scott. Documents are authentic and facts are true precisely in proportion to the support which they afford to his theory. --Macaulay. 2. Harmonic relation between parts, or between different things of the same kind; symmetrical arrangement or adjustment; symmetry; as, to be out of proportion. ``Let us prophesy according to the proportion of faith.' --Rom. xii. 6. 3. The portion one receives when a whole is distributed by a rule or principle; equal or proper share; lot. Let the women . . . do the same things in their proportions and capacities. --Jer. Taylor. 4. A part considered comparatively; a share. 5. (Math.) (a) The equality or similarity of ratios, especially of geometrical ratios; or a relation among quantities such that the quotient of the first divided by the second is equal to that of the third divided by the fourth; -- called also geometrical proportion, in distinction from arithmetical proportion, or that in which the difference of the first and second is equal to the difference of the third and fourth. Note: Proportion in the mathematical sense differs from ratio. Ratio is the relation of two quantities of the same kind, as the ratio of 5 to 10, or the ratio of 8 to 16. Proportion is the sameness or likeness of two such relations. Thus, 5 to 10 as 8 to 16; that is, 5 bears the same relation to 10 as 8 does to 16. Hence, such numbers are said to be in proportion. Proportion is expressed by symbols thus: a:b::c:d, or a:b = c:d, or a/b = c/d. (b) The rule of three, in arithmetic, in which the three given terms, together with the one sought, are proportional. Continued proportion, Inverse proportion, etc. See under Continued, Inverse, etc. Harmonical, or Musical, proportion, a relation of three or four quantities, such that the first is to the last as the difference between the first two is to the difference between the last two; thus, 2, 3, 6, are in harmonical proportion; for 2 is to 6 as 1 to 3. Thus, 24, 16, 12, 9, are harmonical, for 24:9::8:3. In proportion, according as; to the degree that. ``In proportion as they are metaphysically true, they are morally and politically false.' --Burke.

Meaning of geometrical proportion from wikipedia

- U+007E ~ TILDE U+2237 ∷ PROPORTION U+223C ∼ TILDE OPERATOR (∼, ∼, ∼, ∼) U+223A ∺ GEOMETRIC PROPORTION (∺) Linear map Correlation...
- is known as geometrical proportion, not to be confused with arithmetical proportion and harmonic proportion. Fundamental rule of proportion. This rule...
- to ratios of geometrical quantities, and contributed to the development of analytic geometry. Omar Khayyam (1048–1131) found geometric solutions to cubic...
- In mathematics, the silver ratio is a geometrical proportion close to 70/29. Its exact value is 1 + √2, the positive solution of the equation x2 = 2x +...
- In mathematics, the supersilver ratio is a geometrical proportion close to 75/34. Its true value is the real solution of the equation x3 = 2x2 + 1. The...
- In mathematics, the plastic ratio is a geometrical proportion equal to 1.32471795724474602596... (sequence A060006 in the OEIS); it is the real solution...
- .. purely geometrical purposes ..." Livio 2002, pp. 7–8. Livio 2002, pp. 4–5. Livio 2002, p. 78. Hemenway, Priya (2005). Divine Proportion: Phi In Art...
- close relationship between numbers and geometrical forms. Early-Pythagorean philosophers proved simple geometrical theorems, including "the sum of the angles...
- In mathematics, the supergolden ratio is a geometrical proportion equal to 1.46557123187676802665... (sequence A092526 in the OEIS); it is the real solution...
- Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationship...