14069035 journal

## taggaの日記： 19世紀半ばの代数の教科書から1

86. Every multiplier is to be considered a number. We sometimes speak of multiplying bya a given weight or measure, a sum of money, &c. But this is abbreviated language. ... Buf if a part of the weight of a body be fixed upon as a unit, a quantity may be multiplied by a number equal to the number of these parts contained in the body. If a diamond is old by weight, a particular price may be agrred upon each grain [メートル法グレーン 1gr = 50mg]. A grain is here the unit; and it is evident that the value of the diamond, is equal to the given price repeated as many times, as there are grains in the whole weight. We say concisely, that the price is multiplied by the weight; meaning that it is multiplied by a number eual to the number of grains in the weight. In a similar manner, any quantity whatever may be supposed to be made up of parts, each being considered a unit, and any number of these may become a multiplier.

つまり、乗数が不名数でなければならないので、a \$/gr × b gr というのは、 a \$ × b の糖衣構文。

pp.383-384:

582. ... But how, it may be asked can geometrical quantities be multiplied into each other? One of the factors, in multiplication, is alwyas to be considered as a number. (Art. 86) ...

To explain this, it will be necessary to observe, that whenever one geogmetrical quantity is multiplied into another, some particular extent is to be considered the unit. It is immaterial what this extent is, provided it remains the same, in different parts of the same calculation. ...

585. ... The product of two lines is often spoken of, as being equal to a surface; adn the product of a line and a surface, as equal to a solid. ... But if a line has no breadh, how can the multiplication, that is the repetition, of a line produce a surface? ...

このあとの流れは、おおまかにはニュートンと同じだが、いきなり数にいかない。 とりあえず底辺と同じ流さで幅 1in の「棒」を作ってから、かけ算にしている。

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• #### 「糖衣構文」と直訳できる語句を期待していた(違(スコア:1)

by shibuya (17159) on 2019年12月14日 15時56分 (#3731621) 日記

個別の例示っぽい説明の上位概念を汲み取って現代風に整理すると
「syntax sugar を施されたこと」と同義なのだと理解しました。

// 糖衣構文という語彙、便利すぎる……

typodupeerror

192.168.0.1は、私が使っている IPアドレスですので勝手に使わないでください --- ある通りすがり