301. Fractions, how expressed.

Fractions are expressed, as with us, by ordinal numbers, either accompanied by some word meaning »part,” as in the proverbial phrase kalāṃ nārhati ṣoḍaśīm (see f. i. Panc. II, 61, M. 2, 86), Ragh. 2, 66 upabhoktuṃ ṣaṣṭāṃśamurvyāḥ (to enjoy the sixth part of the earth), or put alone, when substantives of the neuter gender M. 8, 398 tato viṃśaṃ nṛpo haret (the king must take the twentieth part of it).

Moreover, they may be denoted also by compounds made up of a cardinal number + such a word as bhāga, aṃśa etc. M. 8, 140 aśītibhāgaṃ gṛhṇīyāt (be may take ¹⁄₈₀); ibid. 304 dharmaṣaḍbhāgaḥ (a sixth part of the virtue); Kumâras. 5, 57 tribhāgaśeṣāsu niśāsu (when but a third part of the night is left); Varâh. Brh. 53, 25 pañcāśaḥ = ⅕ (*1).

Very common are ardham = ½ and pādaḥ = ¼. They are substantives and accordingly coustrued with a genitive, but often also compounded. Note such turns as Bhoj. 48 sapādaśataṃ gajendrāḥ (125 tall elephants, lit. a hundred + a fourth of it), R. 2, 39, 36 ardhasaptaśatāḥ pramadāḥ = half seven-hundred women, that is 350. Râj. 1, 286 tatsūnusriṃśataṃ sārdhāṃ varṣāṇām anvaśānmahīm (— reigned 45 years —). Such numbers as 1½, 2½ etc. are signified by the compounds ardhadvitīya, ardhatṛtīya etc., that are adjectives and bahuvrîhis, literally meaning »the second, third etc. being [but] half” (*2). M. 4, 95 yuktaś chāndāṃsy adhīyīta māsān vipro ‘rdhapañcamān (for 4½ month a brahman must study the vedic texts). »One and a half” is also adhyardham [literally = »with a half more”], as adhyardhaśatam = 150.

Rem. How the interest of money is denoted, may appear from this passage of Manu (8, 142): dvikaṃ trikaṃ catuṣkaṃ ca pañcakaṃ ca śataṃ samam / māsasya vṛddhiṃ gṛhṇīyād varṇānām anupūrvaśaḥ (he may take 2, 3, 4 and 5⁰⁄₀ a month according to the caste).

(*1)
This mode of designating fractions is however not free from ambiguousness, as tribhāga may denote also »three parts.” See Mallin. on Kumâras. 5, 57. Nor are compounds, beginning with ardha- always exempt from it. So f. i. ardhaśatam may be = half a hundred that is 50, or = a hundred + half of it, that is 150. R. 2, 34, 13 ardhasaptaśatāḥ is explained in the Petr. Dict., as being 750, but Gorresio is right in accepting it = 350.

(*2)
On this subject see the disputation of Patañjali I, p. 426 who, as is often the case, rather obscures than illustrates the subject which he treats.

301. 倍数の表現法

倍数（fraction）は、英語がそうであるように序数で表される。大別して2つの方法がある：
1. 部分（part）を意味するいくつかの語を付す
kalāṃ nārhati ṣoḍaśīm（ことわざ。Panc. II, 61, M. 2, 86）
Ragh. 2, 66 upabhoktuṃ ṣaṣṭāṃśamurvyāḥ (to enjoy the sixth part of the earth)

2. 実名詞のn.であればそれを単独で置く
M. 8, 398 tato viṃśaṃ nṛpo haret (the king must take the twentieth part of it)

加えて、倍数は、基数詞にbhāgaやaṃśa等の語を付加した複合語によっても表しうる（*1）。
M. 8, 140 aśītibhāgaṃ gṛhṇīyāt (be may take 1/80)
ibid. 304 dharmaṣaḍbhāgaḥ (a sixth part of the virtue)
Kumâras. 5, 57 tribhāgaśeṣāsu niśāsu (when but a third part of the night is left)
Varâh. Brh. 53, 25 pañcāṃśaḥ = ⅕

非常に一般的なのはardham（=½）とpādaḥ（=¼）である。これらは実名詞であり、よってgen.が文法的に結びつくが、しばしば複合語にもなる。以下のような表現に注意せよ：
Bhoj. 48 sapādaśataṃ gajendrāḥ (125 tall elephants, lit. a hundred + a fourth of it)
R. 2, 39, 36 ardhasaptaśatāḥ pramadāḥ = half seven-hundred women, = 350
Râj. 1, 286 tat sūnusriṃśataṃ sārdhāṃ varṣāṇām anvaśānmahīm (— reigned 45 years —)

1½や2½のような数は、ardhadvitīyaやardhatṛtīyaなどの複合語によって表される。これは形容詞かつbahuvrīhiで、文字通りの意味は「第2、第3…は半分だけ」（*2）。
M. 4, 95 yuktaś chāndāṃsy adhīyīta māsān vipro ‘rdhapañcamān (for 4½ month a brahman must study the vedic texts)

任意の数とその半分は、adhyardhaśatam（＝150）のようにadhyardham（…と半分以上）によっても表される。

【補足】
借金の利息の表し方は以下に見て取られる：
Manu 8, 142 dvikaṃ trikaṃ catuṣkaṃ ca pañcakaṃ ca śataṃ samam / māsasya vṛddhiṃ gṛhṇīyād varṇānām anupūrvaśaḥ (he may take 2, 3, 4 and 5⁰⁄₀ a month according to the caste)

（*1）
ただし、tribhāgaは「3つの部分」を表す場合もあるため、分数を指示するこの仕方は〔どちらを意味するのかという点で〕曖昧さから逃れられない。Kumâras. 5, 57へのMallināthaの注釈を参照せよ。また、ardha-で始まる複合語は、常に〔分数であるから、分数か部分の数を表すのか分からない、という曖昧さを〕免れる。よって、例えばardhaśatamは「100の半分」＝50、あるいは「100＋その半分」＝150である。R. 2, 34, 13 ardhasaptaśatāḥは、Sanskrit Wörterbuchには750と説明されるが、350と解するGorresioが正しい。

（*2）
この主題に関しては、Patañjali I, p. 426の論を参照せよ。もっとも、しばしばそうであるように、彼は扱う主題を明確にするよりもむしろ曖昧にしているのであるが。