Heiho wa heiho nari (The ways of war form the ways of peace) - Tenshinsho Den Katori Shinto Ryu teaching.
Amateuristic martial arts are a sure way to serious injury - Shinmen Musashi no Kami Fujiwara no Genshin (Musashi Miyamoto)
Learn by being cut - Itto Ittosai
Let them cut your flesh, and you cut their bones. Let them cut your bones, and you cut their life - Tendo Ryu teaching.
Katsujinken (the sword that gifts life) - Yagyu Munenori
If you meet a Satsuma swordsman, do not concern yourself with Reiho - local saying.
From the moment you bow in for kata practice, you and your training partner are professional warriors whose only goal is to kill one another. You must have that mindset to properly execute or understand the kata - Shuzuku Shitama (Sosuishitsu Ryu)
"Heaven lies under the sword." - Samurai maxim
Hate to do this to you, Himura, but that's kinda missing the maxim itself (for the record, I've seen it attributed to Musashi). The full quote (in the form of a poem) is along the lines of "Underneath the upraised blade gapes Hell... Step in, however, and recieve Heaven as your reward". So Heaven isn't actually under the sword, Hell is. Heaven is gained by moving past Hell. Yeah, picky, but it's important.