Let Fall (垂) from the Xingyi Eight Characters Secret (形意八字訣)

垂

有三垂，即
一。氣垂則氣降丹田，身穩如山。
二。兩肩下垂，則臂長而活，肩催肘前。
三。兩肘下垂，則兩肱自圓，能固兩脅。
是謂之三垂。

李存義

"Let Fall. The three things that one must let fall:
a) When the qi is suspended, the qi descends to the dantian, and the body is stable as a mountain.
b) When both shoulders hang down, the arms are long and lively, and the shoulders push the elbows to the front.
c) When both elbows hang down, then both arms are naturally round, and can solidify the ribs.
These are the three things that one must let fall."
From the book Xingyi Connected Fist (形意連環拳), by Lǐ Cúnyì (李存義), and from Xingyi Mother Fists (形意母拳) by Jiāng Róngqiáo (薑容樵) based on the translations by Joseph Crandall

Embrace (抱) from the Xingyi Eight Characters Secret (形意八字訣)

抱

有三抱，即
一。丹田要抱，氣不外散，擊敵必準。
二。心氣要抱，遇敵有主，臨變不變。
三。兩脅要抱，出入不亂，遇敵無險。
是謂之三抱。

李存義

"Embrace. The three things that must embrace are:
a) The dantian must be embraced, the qi is not let out. Stricking the opponent needs precision.
b) The emotions must be embraced. When meeting the opponent, have self-control. Don't change when facing change.
c) Both ribs must be embraced. Then leaving and entering is not confused and meeting the opponent is not dangerous
These are the three things that must be embraced."
From the book Xingyi Connected Fist (形意連環拳), by Lǐ Cúnyì (李存義), and from Xingyi Mother Fists (形意母拳) by Jiāng Róngqiáo (薑容樵) based on the translations by Joseph Crandall

Agile (敏) from the Xingyi Eight Characters Secret (形意八字訣)

敏

有三敏，即
一。心要敏，如怒狸攫鼠，則能隨機應變。
二。眼要敏，如饑鷹之捉兔，能預視察機宜。
三。手要敏，如捕羊之餓虎，能先發制人。
是謂之三敏。

李存義

"Agile. The three things that must be agile are:
a) The heart must be agile like an angry cat catching a mouse. Then you will be able to change according to the situation.
b) The eyes must be agile, like a hungry eagle catching a rabbit. The you will be able to examine in advance what to do.
c) The hands must be agile, like a hungry tiger snatching a goat. Then they can issue first to control the opponent
These are the three things that must be agile."

From the book Xingyi Connected Fist (形意連環拳), by Lǐ Cúnyì (李存義), and from Xingyi Mother Fists (形意母拳) by Jiāng Róngqiáo (薑容樵) based on the translations by Joseph Crandall

Round (圓) from the Xingyi Eight Characters Secret (形意八字訣)

圓

有三圓，即
一。脊背要圓，其力催身，則尾閭中正，精神貫頂。
二。前胸要圓，兩肘力全，心窩微收，呼吸通順。
三。虎口要圓，勇猛外宣，則手有裹抱力。
是謂之三圓。

李存義

"Round. The three things that must be round are:
a) The back should be round. Its strenght breaks the opponent's body, and the sacrum will be centered and upright.The spirit of vitality will permeate to the top of the head,
b) The chest must be round. Then both elbow will be completely strong, the heart cavity slightly contracts, breathing is unhindered and smooth.
c) The tiger's mouth must be round. Then bravery and fierceness will be proclaimed. Then the hands will be able to embrace.
These are the three things that must be round."

From the book Xingyi Connected Fist (形意連環拳), by Lǐ Cúnyì (李存義), and from Xingyi Mother Fists (形意母拳) by Jiāng Róngqiáo (薑容樵) based on the translations by Joseph Crandall

Cover (扣) from the Xingyi Eight Characters Secret (形意八字訣)

扣

有三扣，即
一。兩肩要扣，則前胸空闊，氣力到肘。
二。手背足背要扣，則氣力到手，跟步力厚。
三。牙齒要扣，則筋骨緊縮。
是謂之三扣。

李存義

"Cover. The three things that must be like covers are:
a) Both shoulders should be like covers. The chest is empty and broad. The qi strength arrives in the elbows.
b) If the backs of the hands and feet are like covers, then the qi strenght will arrive in the hands and the post steps will be strong and deep.
c) The teeth must be like covers. Then the tendons and bones will tighten and contract.
These are the three things that muse be like covers."

From the book Xingyi Connected Fist (形意連環拳), by Lǐ Cúnyì (李存義), and from Xingyi Mother Fists (形意母拳) by Jiāng Róngqiáo (薑容樵) based on the translations by Joseph Crandall

Push Up From Below (頂) from the Xingyi Eight Characters Secret (形意八字訣)

頂

有三頂，即
一。頭向上頂，有衝天之雄，頭為週身之主，
上頂則後三關易通，臂氣因之上達泥丸以養性。
二。手掌外頂，有推山之功，則氣貫周身，力達四肢。
三。舌上頂，有吼獅吞象之容，
能導上升之腎氣，下行歸丹田以固命。
是謂之三頂。

李存義

"Push up from below. The three things that must push up from below are:
a) The «rear skull bone» is pushed upwards with the bravery to rush to heaven. The head is the master of the whole body. If it is pushed up, the it is easy to pass through the rear three gates.  The kidney qi is able of extende upward through the Niwan and nourish the disposition.
b) If the palm of the hand is pushed outward, it has the skill of pushing mountains. The qi permeates the whole body and strength is extended to the four limbs.
c) If the tongue is pushed up, we have the air of a roar lion swallowing an elephant, and can lead the kidney qi upward, and then down again to return to the datian. Use it to solidify your life.
These are the three things that must push up from below"

From the book Xingyi Connected Fist (形意連環拳), by Lǐ Cúnyì (李存義), and from Xingyi Mother Fists (形意母拳) by Jiāng Róngqiáo (薑容樵) based on the translations by Joseph Crandall

Xingyi Eight Characters Secret (形意八字訣) by Jiāng Róngqiáo (薑容樵)

The corpus of available texts in Xíngyìquán (形意拳) is not as vast as a more popular art like Tàijíquán (太極拳). Certain texts can be found in different "founding books", like some of the chapters in the "Xingyi Connected Fist (形意連環拳)" by Lǐ Cúnyì (李存義) that are present also in the books by Jiāng Róngqiáo (薑容樵). At the end of the day, as the translator Joseph Crandall points out in his preface to "Xingyi Connected Fist (形意連環拳)", it is difficult to assert the original author. Evidence advanced by Joseph Crandall in the preface point though to Jiāng Róngqiáo (薑容樵), which I accept here in the posts.
The fact that these small number of texts are presented over and over again demonstrates the importance attached to it by practicioners, and they therefore become the canon of the art.

形意八字訣

四梢而外，又有八字訣即頂、
扣、圓、敏、抱、垂、曲、挺、是也。
樁法拳式站定時，此八字須具備焉，
所以蓄力養氣，使敵我者無所措使。
而八字者，又各有三種焉，分述之如下

李存義

"Besides the Four Extremities there are also the Eight Characters. These are:

Push up from Below
Cover
Round
Agile
Embrace
Let Fall
Bend
Stretch

These Eight Characters must be present and complete. Use them to store up strength, nourish the qi, and make the enemy yours. All of these are published here. They are also manifested in the Five Elements Fists. The Eight Characters are divided into triads and are delineated below."

From the book Xingyi Connected Fist (形意連環拳), by Lǐ Cúnyì (李存義), and from Xingyi Mother Fists (形意母拳) by Jiāng Róngqiáo (薑容樵) based on the translations by Joseph Crandall

Tai Chi Secrets by Yang Jwing Ming (楊俊敏)

This collection of original Tàijíquán (太極拳) texts, translations and commentaries is probably the most complete to date. Master Yang Jwing Ming (楊俊敏) covers a lot of material on the three books: Tai Chi Secrets of the Yang Style (太極拳楊氏先哲秘要), Tai Chi Secrets of the Wu Style (太極拳吳氏先哲秘要) and Tai Chi Secrets of the Wu & Li Styles (太極拳武李氏先哲秘要). There is material for a life of study and the books complement quite well the other handbooks proposed by the prolific Master Yang Jwing Ming (楊俊敏).
Some of the material is also present on the Lost Tai Chi Classics from the Late Ch'ing Dinasty, by Douglas Wyle. But the approach is different, as the "Lost Tai Chi Classics" cover it from the scholar point of view, here the texts are presented from the practicioner point of view.

Lost T'ai Chi Classics from the Late Ch'ing Dinasty by Douglas Wile

A necessary source for anyone that wants to have access to the source texts, this book is in the bibliography of all other books I read on the subject.
Beyond presenting a number of key texts both in Chinese and in translation, the author Douglas Wile presents a wide panorama of the social, cultural and political motivations for the emergence of Tai Chi Chuan as a martial art. He also discusses the origins and history of the texts, in a balanced and scholar way.
By reading these book, it is possible to have access to the sources without falling in mystifications or idealisations that would take the praticant off-path.

Tǎqiáo (塔橋), Dā Quèqiáo (搭鵲橋) or touching the palate with the tip of the tongue

塔
橋

One of the first things that is asked when starting the first lesson in Internal Martial Arts is to put the tip of the tongue behind the gum, touching the palate. According to Master Jou Tsung Hwa (周宗樺) in the Tao of Meditation, this is called Tǎqiáo (塔橋), or literally the tower (塔) bridge (橋). Through my practice, I heard different explanations for doing it:
- From a Martial Arts point of view, creating this habit, one avoids the risk os biting one's own tongue.
- From an energy point of view, this ensures the connection between the Governing Vessel (督脈) and the Conception Vessel (任脈).
- The last explanation is that it ensures that the students don't have the opportunity for chatting and therefore have to concentrate on the lesson.

搭
鵲
橋

Another name for the same position can be found in the book "Special Taoist Taiji Stick & Ruler Qigong" (道家太極棒尺氣功) by Wáng Fèngmíng (王鳳鳴), based on Féng Zhìqiáng (馮志強) teachings. The position is called there "Building the Magpie Bridge" (搭鵲橋), a reference to the Princess (織女) and the Cowherd (牛郎) legend.
In that legend the Magpie Bridge (鵲橋) is built on the Night of Sevens or Qī​xī​jié (七夕节) to allow the two lovers (a divine princess and a human cowherd) turned constellations to meet.