BIBLIOGRAPHY

History

  • [2025-04-24 Thu 23:25]

KEYWORDS

Quantity ์–‘

  • Quantity - Link ์–‘ - ๋งํฌ

See also: ๋˜ํ•œ ๋ณด๊ธฐ:

  • discreteness ๋ถˆ์—ฐ์†์„ฑ

Topics ์ฃผ์ œ

1. The nature and existence of quantity: its relation to matter, substance, and body; the transcendental categories of quantity - ์–‘์˜ ๋ณธ์งˆ๊ณผ ์กด์žฌ: ๊ทธ๊ฒƒ์˜ ๋ฌผ์งˆ, ์‹ค์ฒด, ์‹ ์ฒด์™€์˜ ๊ด€๊ณ„; ์–‘์˜ ์„ ํ—˜์  ๋ฒ”์ฃผ๋“ค

a. The relation between quantity and quality: reducibility of quality to quantity - ์–‘๊ณผ ์งˆ์˜ ๊ด€๊ณ„: ์งˆ์˜ ์–‘์œผ๋กœ์˜ ํ™˜์› ๊ฐ€๋Šฅ์„ฑ

b. The relation of quantities: equality and proportion - ์–‘๋“ค์˜ ๊ด€๊ณ„: ๋™๋“ฑ์„ฑ๊ณผ ๋น„๋ก€์„ฑ

2. The kinds of quantity: continuous and discontinuous - ์–‘์˜ ์ข…๋ฅ˜: ์—ฐ์†์  ๋ฐ ๋ถˆ์—ฐ์†์ 

3. The magnitudes of geometry: the relations of dimensionality - ์ง€์˜ค๋ฉ”ํŠธ๋ฆฌ์˜ ํฌ๊ธฐ: ์ฐจ์›์˜ ๊ด€๊ณ„

a. Straight lines: their length and their relations; angles, perpendiculars, parallels - ์ง์„ : ๊ทธ ๊ธธ์ด์™€ ๊ด€๊ณ„; ๊ฐ๋„, ์ˆ˜์ง์„ , ํ‰ํ–‰์„ 

b. Curved lines: their kinds, number, and degree - ๊ณก์„ : ์ข…๋ฅ˜, ์ˆ˜, ๊ทธ๋ฆฌ๊ณ  ์ •๋„

1) Circles ์›
2) Ellipses ํƒ€์›
3) Parabolas ํฌ๋ฌผ์„ 
4) Hyperbolas ์Œ๊ณก์„ 

c. The relations of straight and curved lines: tangents, secants, asymptotes - ์ง์„ ๊ณผ ๊ณก์„ ์˜ ๊ด€๊ณ„: ์ ‘์„ , ํ• ์„ , ์ ๊ทผ์„ 

d. Surfaces ํ‘œ๋ฉด

1) The measurement and transformation of areas - ์˜์—ญ์˜ ์ธก์ • ๋ฐ ๋ณ€ํ™˜
2) The relations of surfaces to lines and solids - ๋ฉด๊ณผ ์„  ๋ฐ ์ž…์ฒด์˜ ๊ด€๊ณ„

e. Solids: regular and irregular - ์ž…์ฒด: ์ •๊ทœ ๋ฐ ๋ถ€์ •๊ทœ

1) The determination of volume - ๋ถ€ํ”ผ์˜ ๊ฒฐ์ •
2) The relations of solids: inscribed and circumscribed spheres; solids of revolution - ์ž…์ฒด์˜ ๊ด€๊ณ„: ๋‚ด์ ‘ ๋ฐ ์™ธ์ ‘ ๊ตฌ; ํšŒ์ „์ฒด ์ž…์ฒด

4. Discrete quantities: number and numbering - ์ด์‚ฐ๋Ÿ‰: ์ˆ˜์™€ ๋ฒˆํ˜ธ ๋งค๊ธฐ๊ธฐ

a. The kinds of numbers: odd-even, square- triangular, prime-composite - ์ˆซ์ž์˜ ์ข…๋ฅ˜: ํ™€์ˆ˜-์ง์ˆ˜, ์ œ๊ณฑ์ˆ˜-์‚ผ๊ฐ์ˆ˜, ์†Œ์ˆ˜-ํ•ฉ์„ฑ์ˆ˜

b. The relations of numbers to one another: multiples and fractions - ์ˆซ์ž์™€ ์ˆซ์ž์˜ ๊ด€๊ณ„: ๋ฐฐ์ˆ˜์™€ ๋ถ„์ˆ˜

c. The number series as a continuum - ์—ฐ์†์ฒด๋กœ์„œ์˜ ์ˆ˜์—ด

5. Physical quantities ๋ฌผ๋ฆฌ๋Ÿ‰

a. Space: the matrix of figures and distances - ๊ณต๊ฐ„: ๋„ํ˜•๊ณผ ๊ฑฐ๋ฆฌ์˜ ํ–‰๋ ฌ

b. Time: the number of motion - ์‹œ๊ฐ„: ์šด๋™์˜ ์ˆ˜

c. The quantity of motion: momentum, velocity, acceleration - ์šด๋™๋Ÿ‰: ์šด๋™๋Ÿ‰, ์†๋„, ๊ฐ€์†๋„

d. Mass: its relation to weight - ์งˆ๋Ÿ‰: ๋ฌด๊ฒŒ์™€์˜ ๊ด€๊ณ„

e. Force: its measure and the measure of its effect - ํž˜: ๊ทธ ์ธก์ •๊ณผ ๊ทธ ํšจ๊ณผ์˜ ์ธก์ •

6. The measurements of quantities: the relation of magnitudes and multitudes; the units of measurement - ์ˆ˜๋Ÿ‰ ์ธก์ •: ํฌ๊ธฐ์™€ ๋‹ค์ค‘์˜ ๊ด€๊ณ„, ์ธก์ • ๋‹จ์œ„

a. Commensurable and incommensurable magnitudes - ์ƒ์‘ํ•˜๋Š” ๊ทœ๋ชจ์™€ ์ƒ์‘ํ•  ์ˆ˜ ์—†๋Š” ๊ทœ๋ชจ

b. Mathematical procedures in measurement: superposition, congruence; ratio and proportion; parameters and coordinates - ์ธก์ •์—์„œ์˜ ์ˆ˜ํ•™์  ์ ˆ์ฐจ: ์ค‘์ฒฉ, ํ•ฉ๋™; ๋น„์œจ๊ณผ ๋น„๋ก€; ๋งค๊ฐœ๋ณ€์ˆ˜์™€ ์ขŒํ‘œ

c. Physical procedures in measurement: experiment and observation; clocks, rules, balances - ์ธก์ •์—์„œ์˜ ๋ฌผ๋ฆฌ์  ์ ˆ์ฐจ: ์‹คํ—˜๊ณผ ๊ด€์ฐฐ; ์‹œ๊ณ„, ์ž, ์ €์šธ

7. Infinite quantity: the actual infinite and the potentially infinite quantity; the mathe- matical and physical infinite of the great and the small - ๋ฌดํ•œํ•œ ์–‘: ์‹ค์ œ ๋ฌดํ•œ๊ณผ ์ž ์žฌ์  ๋ฌดํ•œํ•œ ์–‘; ํฌ๊ณ  ์ž‘์€ ๊ฒƒ๋“ค์˜ ์ˆ˜ํ•™์  ๋ฐ ๋ฌผ๋ฆฌ์  ๋ฌดํ•œ