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I am a bit confused with the following facts.

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Is the 月-like radical in 前{まえ} identical to 月?

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2 Answers 2

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As you yourself observe, 月 looks different on its own than as an element in 前, in which it represents a simplification of 舟. So no, they are not identical.

As an element in other characters, the element that looks like 月 variously represents other historical elements, including 肉, 舟, 丹, and 月 itself, among others. In some characters the derivation is still significant in how they're written—there are variants of 錆 where the lower-right 丹 was simplified to 円 instead of 月, for example. A lot of characters contain this element, so we can expect to see some variation in how it appears.

But we can try to find patterns. When does the left side curve? Here are my observations, based entirely on how I perceive the current forms of the characters, ignoring their history:

  1. 月 itself is written with a curve.

  2. In left-right characters where one side is written like 月, it is written with a curve:

    月肋肌肘肝肚肛朋股肢肪服肬肭肱胎胞胆肺朏胖脉胙胚胛胝脂脇胴
    朕胸脈脆胱胼胯豚脱脚脳朖脛脯脹腔腕勝腆腑腋脾腓腰腫腺腹腸腱
    腦腮腟腿腴腥膜膀膈膊膃膝膵膣滕膕膤臟膓膠膨膳膩膰縢臈臆謄膽
    朦膾膿臉膸臍臑臓臘騰臚朧臙・明胡朔朋期朗朝

  3. In certain characters descended from the above, it's also written with a curve:

    朋:萠崩堋棚弸繃鵬硼
    明:萌盟
    朝:廟潮嘲
    胡:湖楜瑚葫糊醐蝴餬
    朔:遡塑溯愬槊

    滕:藤籐
    縢:籘
    服:箙
    豚:遯
    肋:筋

  4. In certain other characters it's also written with a curve:

    望・覇霸・閒燗癇・羸瀛贏・朞

  5. The rest of the time, the left side of 月 is typically written straight:

    有肖肓侑肴肯肩育青冐郁宥胤削背胃前胥胄陏囿屑哨宵脅脊骨俞能
    消娟悁涓捐兪峭悄狷脩梢情清剪猜脣偸逍淆菁揃喩随硝愉堕婿惰散
    晴渭渝喟隋壻稍揄靖楕膏熊煎潸滑賄腎絹瑜蛸骭逾楡睛錆聾體髑髓
    魘龕静猾愈精態榾趙誚蜻膂瘉骰酳厭撒請膚徹罷撤翦瘠銷磆箭墮蝓
    蝟籠襲髏鶺鶻霄龍謂靜鞘諭骸輸覦骼隨踰橢鮪膺臀鍮瀞壓蹐膸臂癒
    擶鵑繖髀擺羂鮹寵瀧髄蘢鯖羆壟隴轍霰瓏

These are just my own observations. They aren't intended to be taken as absolute rules, and you may find variation in handwriting or in different fonts. For example, I've noticed that in some fonts on my computer, 潸 falls into category 4 instead of 5. But I think that overall the above is relatively accurate.

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In terms of historical development, no, the 月 in 前 wasn't originally the same character as 月 "moon". As you can see in the old Kangxi dictionary here (slightly left of the center of the page, towards the top), the old form of 前 was 止 on the top and 舟 on the bottom. The 止 on the top simplified into 䒑, and the 舟 on the bottom transmogrified into 刖. See also en.wiktionary.org/wiki/前#Translingual.

UPDATE: Looking again at the Kangxi entry, I realized that there were two old variants. The bottom part of modern 前 is based on the bottom part of the second variant of the old character, consisting of 舟 on the left and 刂 on the right. That 刂 piece is still there in 前, so the 月 portion of the modern 前 character is entirely derived from the 舟 part of the old character.

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