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§ 5. Ƚɭɤ ɡɚԙɵ ɠԥɧɟ ɤԛɲɬɟɪ ԥɫɟɪɿɧɿԙ ɬԥɭɟɥɫɿɡɞɿɝɿ
Ɍԥɠɿɪɢɛɟɥɟɪ ɦɟɧ ɤԧɩɬɟɝɟɧ ɡɟɪɬɬɟɭɥɟɪ, ɛɟɥɝɿɥɿ ɛɿɪ ɞɟԙɝɟɣɞɟ ɨɪɵɧ

ɚɭɵɫɬɵɪɭ ɦɟɧ ԥɪɟɤɟɬ ɟɬɭɲɿ ɤԛɲɬɿԙ ɚɪɚɫɵɧɞɚ ɩɪɨɩɨɪɰɢɨɧɚɥɞɵԕ
ɡɚԙɞɵɥɵԕɬɵԙ ɛɚɪɵɧ ɤԧɪɫɟɬɟɞɿ. Ȼԝɥ ɡɚԙɞɵɥɵԕɬɵ 1660 ɠɵɥɵ ɚԑɵɥɲɵɧ
ԑɚɥɵɦɵ Ɋ. Ƚɭɤ: «ut tensio sik vis – ԝɡɚɪɭ ԕɚɧɞɚɣ ɛɨɥɫɚ, ɤԛɲ ɫɨɧɞɚɣ» ɞɟɩ
ɥɚɬɵɧ ɬɿɥɿɧɞɟ ɬԝɠɵɪɵɦɞɚԑɚɧ ɟɞɿ. Ƚɭɤɬɵԙ ɛԝɥ ɟԙɛɟɝɿ ɬɟɤ 1676 ɠɵɥɵ ԑɚɧɚ
ɠɚɪɵԕ ɤԧɪɝɟɧɞɿ.

Ʉɟɡ ɤɟɥɝɟɧ Ⱥ ɧԛɤɬɟɫɿɧɿԙ ɯ ɛɚԑɵɬɵɧɞɚԑɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭɵɧ Ƚɭɤ ɡɚԙɵ
ɛɨɣɵɧɲɚ,

GA Cx ˜ P (1.6)

ɞɟɩ ɠɚɡɭԑɚ ɛɨɥɚɞɵ.
Ȼԝɥ ɠɟɪɞɟ Ɋ ɨɪɵɧ ɚɭɵɫɬɵɪɭɞɵ ɬɭԑɵɡɚɬɵɧ ɤԛɲ ɬɟ, ɚɥ ɋɯ – ɤԛɲ ɩɟɧ ɨɪɵɧ
ɚɭɵɫɬɵɪɭɞɵԙ ɚɪɚɫɵɧɞɚԑɵ ɩɪɨɩɨɪɰɢɨɧɚɥɞɵԕ ɤɨɷɮɮɢɰɢɟɧɬ. Ȼԝɥ
ɤɨɷɮɮɢɰɢɟɧɬ (ɋɯ) ɬɟɤ ԕɚɧɚ ɦɚɬɟɪɢɚɥɞɚɪɞɵԙ ɮɢɡɢɤɚɥɵԕ ԕɚɫɢɟɬɬɟɪɿɧɟ
ɛɚԑɵɧɵɲɬɵ ɟɦɟɫ, ɨɥ ԕɚɪɚɥɵɩ ɨɬɵɪԑɚɧ Ⱥ ɧԛɤɬɟɫɿ ɦɟɧ Ɋ ɤԛɲɿ ԥɪɟɤɟɬ ɟɬɿɩ
ɬԝɪԑɚɧ ɧԛɤɬɟɧɿԙ ɚɪɚԕɚɲɵԕɬɵԑɵɧɚ, ɬɿɩɬɿ, ɠԛɣɟɧɿԙ ɝɟɨɦɟɬɪɢɹɥɵԕ ɟɪɟɤɲɟɥɿɝɿɧɟ
ɛɚɣɥɚɧɵɫɬɵ ɟɤɟɧɿɧɟ ɤԛɦԥɧ ɠɨԕ. Ɇɿɧɟ, ɫɨɧɞɵԕɬɚɧ (1.6) ԕɚɬɵɧɚɫɵɧ ɠԛɣɟɥɟɪ
ԛɲɿɧ Ƚɭɤ ɡɚԙɵ ɞɟɩ ԕɚɪɚɭԑɚ ɛɨɥɚɞɵ. ɋɨɧɵɦɟɧ ԕɚɬɚɪ ɠɨԑɚɪɵɞɚ

ɬԝɠɵɪɵɦɞɚɥԑɚɧ ɨɪɵɧ ɚɭɵɫɬɵɪɭ ɦɟɧ ɤԛɲ ɚɪɚɫɵɧɞɚԑɵ ɫɵɡɵԕɬɵԕ ԕɚɬɵɧɚɫɬɵԙ
ɤԛɲɿ ɛɿɪɬɿɧɞɟɩ ԧɫɤɟɧɞɟ ɞɟ, ɚɡɚɣԑɚɧ ɤɟɡɞɟ ɞɟ ɡɚԙɞɵ ɟɤɟɧɿɧ ɚɣɬԕɚɧ ɠԧɧ.
Ɇԝɧɵԙ ԧɡɿ ɦɚɬɟɪɢɚɥɞɚɪɞɵԙ ɫɟɪɩɿɦɞɿɥɿɤ ԕɚɫɢɟɬɿɧ ɫɢɩɚɬɬɚɣɞɵ.
Ʉԛɲ ɩɟɧ ɨɪɵɧ ɚɭɵɫɬɵɪɭ ԧɡɚɪɚ ɩɪɨɩɨɪɰɢɨɧɚɥɞɵ ɛɨɥɚɬɵɧ ɠԛɣɟɥɟɪɝɟ,
ɤԛɲɬɟɪ ԥɪɟɤɟɬɿɧɿԙ ɬԥɭɟɥɫɿɡɞɿɝɿ ɩɪɢɧɰɢɩɿɧ (ɫɭɩɟɪɩɨɡɢɰɢɹ ɩɪɢɧɰɢɩɿɧ)
ԕɨɥɞɚɧɭԑɚ ɛɨɥɚɞɵ. Ȼԝɥ ɩɪɢɧɰɢɩ ɛɨɣɵɧɲɚ, ɫɵɪɬԕɵ ɤԛɲɬɟɪɞɿԙ ԥɪɟɤɟɬɿɧɟɧ
ɫɟɪɩɿɦɞɿ ɦɚɬɟɪɢɚɥɞɚɪɞɚ ɩɚɣɞɚ ɛɨɥɚɬɵɧ ɿɲɤɿ ɤԛɲɬɟɪ ɦɟɧ ɨɪɵɧ ɚɭɵɫɬɵɪɭɥɚɪ,
ɫɨɥ ɫɵɪɬԕɵ ɤԛɲɬɟɪɞɿԙ ɞɟɧɟɝɟ ɬԛɫɭ ɬԥɪɬɿɛɿɧɟ, ɹԑɧɢ ԕɚɣ ɤԛɲɬɿԙ ԕɚɣ ɤԛɲɬɟɧ
ɤɟɣɿɧ ɬԛɫɭɿɧɟ ɛɚɣɥɚɧɵɫɬɵ ɟɦɟɫ.
Ɇɵɫɚɥɵ, ɤɟɡ ɤɟɥɝɟɧ ɛɿɪ ɠԛɣɟɝɟ Ɋ1 ɤԛɲɿ ɬԛɫɿɩ ɬԝɪɫɵɧ. Ɉɫɵ ɤԛɲɬɿԙ

ԥɪɟɤɟɬɿɧɟɧ Ⱥ ɧԛɤɬɟɫɿɧɿԙ ɯ ɛɚԑɵɬɵɧɞɚԑɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭɵ ɠɨԑɚɪɵɞɚ
ɤɟɬɿɪɿɥɝɟɧ ɮɨɪɦɭɥɚ (6) ɛɨɣɵɧɲɚ ɬԧɦɟɧɞɟɝɿɲɟ ɬɚɛɵɥɚɞɵ:

G A1 C x1 ˜ P1 . (1.7)

ȿɧɞɿ Ɋ1 ɤԛɲɿɧ ɚɥɵɩ ɬɚɫɬɚɩ, ɫɨɥ ɠԛɣɟɧɿԙ ɛɚɫԕɚ ɛɿɪ ɧԛɤɬɟɫɿɧɟ Ɋ2 ɤԛɲɿɧ
ɬԛɫɿɪɟɣɿɤ. Ȼԝɥ ɤɟɡɞɟ Ⱥ ɧԛɤɬɟɫɿɧɿԙ ɨɪɵɧ ɚɭɵɫɬɵɪɭɵ ɛɵɥɚɣɲɚ ɬɚɛɵɥɚɞɵ:

G A2 C x2 ˜ P2 (1.8)

Ɋ1 ɠԥɧɟ Ɋ2 ɤԛɲɬɟɪɿ ɠԛɣɟɧɿԙ ԥɪ ɧԛɤɬɟɫɿɧɟ ɬԛɫɤɟɧɞɿɤɬɟɧ ɋɯ1 ɦɟɧ ɋɯ2 ԧɡɚɪɚ
ɬɟԙ ɛɨɥɦɚɭɵ ɚɣɬɩɚɣ-ɚԕ ɬԛɫɿɧɿɤɬɿ.
ȿɧɞɿ ɨɫɵ ɟɤɿ ɤԛɲ ( Ɋ1, Ɋ2 ) ɠԛɣɟɝɟ ɛɿɪ ɭɚԕɵɬɬɚ ԥɪɟɤɟɬ ɟɬɫɿɧ. Ɉɥ ԛɲɿɧ,
ɚɥɞɵɦɟɧ Ɋ1 ɤԛɲɿɧ ɬԛɫɿɪɟɦɿɡ ɞɟ, ɨɧɚɧ ɤɟɣɿɧ Ɋ2 ɤԛɲɿɧ ɬԛɫɿɪɟɦɿɡ. Ɉɥ ɤɟɡɞɟ ɨɪɵɧ
ɚɭɵɫɬɵɪɭ ɛɵɥɚɣɲɚ ɬɚɛɵɥɚɞɵ:

G A1 C x1 ˜ P1 + C / x2 ˜ P2 . (1.9)

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