see Francis Bacon's work
Novum Organum 1620

Defining logics as a rightful organon, as-Sazavari sees its aims and tasks ...

... claim rightful co-ownership of it. WHAT IS LOGIC? Aristotle (384-321 BC): Greek Philosopher who codified the first text in logic known today as the Organon. He ...
www.geocities.com/philodept/diwatao/logic.htm

www.stanford.edu/dept/relstud/faculty/pdf/Hermenei.pdf
File Format: PDF/Adobe Acrobat - View as Text
... of logic to its rightful place within ontology, the science of beingness... Be that as it may, the five treatises of the Organon appear to fall ...

www.dcs.kcl.ac.uk/staff/jane/Woods-Aristotle.pdf
... Aristotle's logical writings are the several monographs collected under the title Organon, which means "tool" or "in- strument". Logic then would be a ...

About Sabzavari:
Autobiography and Silence:
... in metaphysics and philosophy, studying such works with Mulla Ibrahim Hakim-i Sabzavari.
This man, a disciple of the eminent philosopher Mulla Hadi Sabzavari ...
www2.h-net.msu.edu/~bahai/diglib/articles/A-E/cole/rais.htm

One brief idea: You perhaps know Bertold Brecht? He wrote his basic theoretical work, called "Kleines Organon fur das Theater" (1948) (A small Organon for the theatre), which thus describes the system of rules and laws for theatre art.
Second person who should be mentioned and whose use of this word deeply influenced wide range of philosophers is the great Englihsman: Бэкон Ф. Соч., М., 1972, т.1, с.883-92 ("Новый Органон"); т.2, с.487-525 ("Новая Атлантида"). Sorry, I cannot give more exact Englihs reference:(
What is more funny, in new program of philosophy course in universities we also can find the same source but wit rather different treatment:
Философия Нового времени. Социокультурные предпосылки ее возникновения. Просвещение и наука.
Ф.Бэкон как творец теории “идолов”. Эмпиризм и индуктивный метод. Отношение к знанию и науке. “Новый Органон” как контраверза Аристотелю.
Р.Декарт - основоположник рационализма. Роль сомнения. Правила познавательного метода. Критерий определенности. Дуализм как философская позиция.
“Рассуждения о методе”.....

+>
www.philosophy.ru/edu/ref/gubin/04.html

+>Aristotelian works: ...По темам сочинения делятся на четыре основные группы. Во-первых, это труды по логике, обычно собирательно именуемые О р г а н о н . Сюда входят Категории; Об истолковании; Первая аналитика и Вторая аналитика; Топика

further...Поэтому весьма возможно, что позднейшее понятие о логике как
« о р у д и и » (греч. « о р г а н о н »), хотя сам Аристотель ее так не называл, соответствует его собственным представлениям...

See also the page where the Christian aspect of the use of this word is discussed
anthropologia.spbu.ru/ru/texts/schleier/akadem.html

Hope you also can see that the words "lawful", "regulatory" and so might give more idea about the ZAKONNY meaning:).

Yours,
Tagir.

I agree with organon. The term was indeed conceived in Greek and it is still used in its original form today.
As far as zakony is concerned, I would use legitimate rather than legal or rightful.
I hope this was of some help.
Katarina

organon is OK, but if you don't want to use that word, you can say a system of laws, an organic system of laws, etc.
Hope this helps!
:>))

Or: an appropriately established/assumed or accepted code of rules/organon
I would suggest that "zakonny" here implies "substantiated" rather than smth pertaining to legislation.
Sincerely, GI