Nachala Evklida S Poi︠a︡snitelʹnym Vvedenīem I Tolkovanīi︠a︡mi. ..

Cover Nachala Evklida S Poi︠a︡snitelʹnym Vvedenīem I Tolkovanīi︠a︡mi. ..
Nachala Evklida S Poi︠a︡snitelʹnym Vvedenīem I Tolkovanīi︠a︡mi. ..
Euclid
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8). Но по УСЛ0В1Ю прямыя АВ и ВС соизмеримы, а АВ^ВВ, следовательно соизме- римы и пр ямыя ВВ и ВС. Но мы имеемъ (кн. 6, пред. 1): ВВ:ВО=:АВ:АС следовательно (кн. 10, пред. 10) плоп^ади АВ и АС соизмеримы. Но такъ какъ АВ есть рац1оцальная п.1|оп^адь, то (кн. 10, пред- 9) и площадь АС ращональна.
Предложенье 21. Ращональный прямоугольникъ АС, построенный на рац1ональной прямой АВ, 6^}адть иметь ращональную, по длине соизме- римую съ ней, высоту ВС (фиг. 325).
Доказат. Цостроимъ на прямой АВ ква
...дратъ АВ, этотъ квадратъ бу- детъ ращональный. Такъ какъ по услов1Ю прямоугольникъ АС ращональннй, то онъ соизмеримъ (кн.

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