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I'd like to know how to analyze "是其于主也至忠矣" word for word.

公行之计，是其于主也至忠矣，

I would appreciate your help!

This is how I read this passage:

公行之計是其於主也至忠矣

[If] you/公 use (行) this (之; read it as 此) strategem (計), this (是) inevitably [shows] (其; read it as 乃 or 然) to (於) the lord (主) pause (也) great loyalty (至忠) ! (矣)

Using this strategem is a display of [your] loyalty/devotion towards the lord.

The verse is from 戰國策　卷二十八:

Though the OP asked one particular verse, and we must comprehend the related text (from page 80-82), in order to interpret it correctly.

或謂公仲曰．今有一舉而可以忠於主．便於國．利於身．願公之行之也

今天下散而事秦．則韓最輕矣．天下合而離秦．則韓最弱矣

合離之相．續則韓最先危矣．此君國長民之大患也．今公以韓先合於秦．天下隨之．是韓以天下事秦．秦之德韓也．厚矣．韓與天下朝．秦而獨厚取．德焉

公行之計．是其於主也．至忠矣

天下不合秦．秦令而不聽．秦必起兵以誅不服．秦久與天下結怨．構難而兵不決韓．息士民以待其釁

公行之計．是其於國也．大便也

昔者．周佼以西周善於秦而封於梗陽．周啟以東周善於秦而封於平原．今公以韓善秦．韓之重於兩周也．無計．而秦之爭機也．萬於周之時．今公以韓為天下先．合於秦．秦必以公為諸侯．以明示天下．

公行之計．是其於身大利也．願公之加務也

The context is:

Someone suggested (或謂) to mr 韓公仲 (公仲), said (曰) "there's now (今有) a strategy (一舉) that is loyal to the lord (忠於主), convenience to the nation (便於國), benefit to yourself (利於身), hope (願) your honourable (公) execute it (行之)

So "公行之計．是其於主也．至忠矣", I would interpret it as:

[If] your honourable (公) execute (行) this (之-->此) strategy (計), such execution is (是其), for the lord (於主), absolutely loyal (至忠).

Edited.

是其, reverse it to 其是, so

If] your honourable (公) execute (行) this (之-->此) strategy (計), such execution (其) is, (是) for the lord (於主), absolutely loyal (至忠).

也 and 矣 is, particle.

Have fun :)

公 - Sir (honorific)

行 - implement; carry out (v)

之 - possessive form: similar to ['s ] in English

计 - plan (direct object)

是 - affirm (v)

其 - it (pronoun)

于 - to

主 - master (indirect object)

也 - (= 也算) can be considered

至 - utmost

忠 - loyal

矣 - final particle (for emphasis)

公行之计，是其于主也至忠矣

The plan he came up with, suggest it to his master can be considered a showing of his utmost loyalty,

To analyse the quote, I would dive into the original text and read the article.

The part you quoted is from 或谓公仲 in 战国策，where 或 means someone. The article is documenting someone trying to lobby the lord of 韩国 to be the first one to show loyalty to 秦国。By that time, 秦国 is getting strong and starting to show the ambition of unifying the whole China. That someone is trying to persuade the lord of 韩国 that given 韩国 is relatively weak, showing loyalty to 秦国 is a wise choice and the earlier, the better.

The quote you have, is a small summary of the advantages, it means

（这样一来），您（the lord）所做的事情，就是向秦国表明，韩国对秦王是非常忠诚的

I will write the part of analyzing word by word mostly in Chinese as it is more accurate doing it this way

“公”指的是韩国国君

“行”的意思是“执行”

“之”是连接词，可以当做“的”

“计”的意思就是“计策”

“是”的意思是”就是“

“其”指的是某人所建议的这件事情

“于”的意思是“对于”

“主”指的是“秦王”

“也”是连接词，在古文中多当做“是”来讲

“至”就是“极度”的意思

“忠”就是“忠诚”的意思

“矣”表示陈述语气