The Great Path Has No Gate in Chinese / Japanese...

安樂の法門 represents that the Dharma Gate or the Door to Enlightenment leads to peace and happiness.

The Dharma Gate is the method of attaining or actualizing peace and happiness in Zen and other Buddhist traditions.

黑旗門 is often romanized as “Hek Ki Boen” in Cantonese, this is the title for a certain branch school of Wing Chun or Eng Chun martial arts.

大道無門 is a Buddhist proverb that means “The Great Way has no entrance,” “The Great Way is gateless,” or “The Great Path lacks a gate.”

This can be translated in many other ways.

This concept was authored within a long sacred text by 無門慧開 (known as Wúmén Huìkāi in Chinese or Mumon Ekai in Japanese). He was a Chinese Chan Master (in Japanese, a Zen Master) who lived between 1183 and 1260 AD. His most famous work was a 48-koan collection titled “The Gateless Barrier” or “The Gateless Gate” (無門關 Wú Mén Guān in Chinese, or 無門関 Mu Mon Kan in Japanese). This calligraphy title is a notable line from this collection.

I like this reference to the source of this proverb: The Gateless Gate 無門關

This is the Dharma Gate, The Gate to Enlightenment, or Dharmaparyāya.

The doctrines, or wisdom of Buddha is regarded as the door to enlightenment.

門 is the Chinese, Japanese Kanji, and old Korean Hanja for gate, door, gateway, doorway, opening, entrance, valve, or switch.

Most commonly, this is simply a gate or door.

門 is also a Chinese surname that romanizes as Men.

In Japanese, this can be surnames romanizing as Yuki, Mon, To, or Kado.

In the Buddhist context, beyond meaning a door or gate, this can be a counter for a Buddhist sect, teaching, or school (we might say “slice” of bread, this would be a “gate” of teaching). In this way, it kind of refers to one of several doors that lead to salvation or nirvana.

In modern Japanese, 門主 is the title of a head priest of a temple or monastery.

This can also refer to the spiritual leader of the sect and/or direct descendant of its founder.
In the past, this could refer to the founder of a Buddhist sect.

The literal meaning of 門主 is gatekeeper or keeper of the gate.

In the Chinese Buddhist dictionary, this entry comes up as the controller of a gate or sect. However, this term is not commonly used in Chinese.

無門関 is the specifically Japanese title for “The Gateless Barrier.” This has both direct meaning and is the title of a 13th-century collection of koans, compiled by Zen Master Mumon (actually a Chinese Chan Master known as Wumen in China).

The original title is 無門關, but the last Kanji was simplified to 関 in modern Japan.

無門關 is the ancient title for “The Gateless Barrier.” This has both direct meaning and is the title of a 13th-century collection of koans, compiled by a Chinese Chan Master known as Wumen in China (known in Japan as Zen Master Mumon).

While this is the original title, you may see this written as 無門関 in Japan, where the last character, 關, was simplified to 関 after 1945.