The Pursuit of Knowledge Under Difficulties, Vol. 2 of 2: Its Pleasures and Rewards (Classic Reprint) - Hardcover

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Excerpt from The Pursuit of Knowledge Under Difficulties, Vol. 2 of 2: Its Pleasures and Rewards

Might be facilitated. Now these operations, the reader, who may be ignorant of mathematics, will observe, always proceed by geometrical ratios or proportions. Thus, if certain lines he described m or about a triangle, one of these lines will bear the same geometrical proportion to another, as a cer tain side of the triangle does to a certain other side. Of the four particulars thus arranged, three must be known, and then the fourth will be found by multi plying together certain two of those known, and dividing the product by the other. This rule is de rived from the very nature of geometrical propor tion, but it is not necessary that we should stop to demonstrate here how it is deduced. It will be per ceived, however, that it must give occasion, in solv ing the problems of trigonometry, to a great deal of multiplying and dividing; operations which, as everybody knows, become very tedious whenever the numbers concerned are large and they are gen erally so_in astronomical calculations. Hence such calculations used to exact immense time and labour, and it became. Most important to discover, if possi ble, a way of shortening them. Napier, as we have said, applied himself assiduously to this object; and he was, probably, not the only person of that age whose attention it occupied. He was, however, undoubtedly the first who succeeded in it, which he did most completely by the admirable contri vance which we are now about to explain.

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