What does 夫鷄 (부계) mean?

In its translation of the following article from the Annals of King Sejong, the National Institute of Korean History translated 夫鷄 (부계) as "대저 닭은," which translates as "generally speaking, the chicken," but I think 夫鷄 should be translated here as "male (夫) chicken (鷄)" based not only on the context of which it is used in this article but also on how it was used in another article I have read.

Also, the article mentions 明水 (명수), which literally means "bright (明) water (水)." The "bright water" was supposedly collected from the dew that formed on mirrors while they reflected the image of the moon.

Anyway, the following article is talking about ritual wine and water cups referred to as the "rooster cup" (鷄彛 - 계이) and the "phoenix cup" (鳥彛 - 조이). The drawings of the cups below are also from the Annals of King Sejong.

禮(예)書(서)云(운) 鷄(계)彝(이)鳥(조)彝(이), 謂(위)刻(각)而(이)畫(획)之(지), 爲(위)鷄(계)鳳(봉)之(지)形(형). 春(춘)祀(사)夏(하)禴(약)祼(관)用(용)鷄(계)彝(이)鳥(조)彝(이). 夫(부)鷄(계), 東(동)方(방)之(지)物(물), 仁(인)也(야); 鳥(조), 南(남)方(방)之(지)物(물), 禮(예)也(야), 此(차)先(선)王(왕)所(소)以(이)用(용)祀(사)禴(약)也(야). 春(춘)則(즉)鷄(계)彝(이)盛(성)明(명)水(수), 鳥(조)彝(이)盛(성)鬱(울)鬯(창), 夏(하)則(즉)鳥(계)彝(이)盛(성)明(명)水(수), 鷄(계)彝(이)盛(성)鬱(울)鬯(창). 斝(가)黃(황)之(지)相(상)爲(위)用(용), 亦(역)若(약)此(차)。

계이(鷄彝)

《예서(禮書)》에 이르기를,

"계이(鷄彝)와 조이(鳥彝)는 술잔에 새겨 그림을 그려서 닭과 봉(鳳)의 형상을 만든다. 봄 제사[春祀]와 여름 제사[夏禴]의 관향(祼享)에 계이와 조이를 사용한다. 대저 닭은 동방(東方)의 생물(生物)이니 인(仁)이요, 새[鳥]는 남방(南方)의 생물(生物)이니 예(禮)이다. 이것이 선왕께서 봄 제사와 여름 제사에 사용하는 까닭이다. 봄에는 계이(鷄彝)에 명수(明水)를 채우고, 조이(鳥彝)에 울창(鬱鬯)을 채우며, 여름에는 조이에 명수(明水)를 채우고, 계이(鷄彝)에 울창(鬱鬯)을 채운다. 가이(斝彝)와 황이(黃彝)의 서로 사용됨도 역시 이와 같다."

고 하였다.

The Book of Rites (禮書) says (云) the gye-i (鷄彝) [and] jo-i (鳥彝) are named for (謂) the cravings (刻) and (而) drawings (劃) on them (之), [which] are (爲) in the shapes of roosters[or] phoenixes (鷄鳳之形). [At] the spring and summer memorial services (春社夏禴), in the wine-pouring ceremony (祼), [they] use (用) the gye-i (鷄彝) [and] jo-i (鳥彝). The Rooster (夫鷄) is the creature of the east (東方之物) [and] is benevolence (仁也). The phoenix (鳥) is the creature of the south (南方之物) [and] is propriety (禮也). These (此) [were] the former kings’ (先王) reasons (所以) [for] using (用) [them at] the memorials (祀禴也). In the spring (春則), the gye-i (鷄彝) is filled with (盛) bright water (明水), [and] the jo-i (鳥彝) is filled with (盛) ulchang liquor (鬱鬯). In the summer (夏則), the jo-i (鳥彝) is filled with (盛) bright water (明水), [and] the gye-i (鷄彝) is filled with (盛) ulchang liquor (鬱鬯). The ga-i [cup] (斝彝) [and] hwang-i [cup] (黃彝) are mutually used (相爲用) also (亦) like (若) this (此).

Source: http://sillok.history.go.kr/id/wda_20002008_013