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Updated: June 7, 2025
Its length is exactly equal to 3/4 of the diameter of the sphere, as can be found and demonstrated by means of these waves, nearly in the same way as the mensuration of the preceding curve; though it may also be demonstrated in other ways, which I omit as outside the subject.
Squeers' famous advertisement of Dotheboys Hall, announced that the programme of the Academy would include "reading, taught as an art and upon the most approved principles of elocution, writing, arithmetic, euclid, algebra, mensuration, trigonometry, book-keeping, geography, grammar, spelling and dictation, composition, logic and debate, French, Latin, shorthand, history, music, and general lectures on astronomy, natural philosophy, geology, and other subjects."
So completely, indeed, have these organic dimensions served as the substrata of all mensuration, that it is only by means of them that we can form any estimate of some of the ancient distances. For example, the length of a degree on the Earth's surface, as determined by the Arabian astronomers shortly after the death of Haroun-al-Raschid, was fifty-six of their miles.
If a man wishes to build a house, does it fetter him to know square measure, cubic contents, geometry, mensuration, and mechanical laws? Yet when he builds his house, he builds it in his own individual way; he stamps it with his own personality and ideas. While building it, perchance, he discovers some new relation or geometric law.
Our sensations will undoubtedly be in proportion to such circumstances, or our joy to the appreciation or mensuration of the evil which has been removed. To value the blessing of the abolition as we ought, or to appreciate the joy and gratitude which we ought to feel concerning it, we must enter a little into the circumstances of the trade.
What could she do but come close so close that a minute arc of her skirt touched his foot and asked him how he was getting on with his sketches, and set herself to learn the principles of practical mensuration as applied to irregular buildings? Then she must ascend the pulpit to re-imagine for the hundredth time how it would seem to be a preacher. Presently she leant over the front of the pulpit.
Penn, on the contrary, insisted on finding the fortieth degree by mensuration from the capes of Virginia, the true situation of which had been already ascertained.
He used to reckon his sacks by chalk strokes all in a row like garden-palings, measure his ricks by stretching with his arms, weigh his trusses by a lift, judge his hay by a chaw, and settle the price with a curse. But now this accomplished young man does it all by ciphering and mensuration.
It ends with information as to house-rent, letters of credit and exchange, tables of interest, games of chance, mensuration, and weights and measures. In an appendix Cardan examines critically the work of Fra Luca Pacioli da Borgo, an earlier writer on the subject, and points out numerous errors in the same.
So clearly is this recognized, that the development of large scale business has led to the evolution of new methods of accountancy, designed to make detailed mensuration possible. We have most of us heard of them vaguely under such names as "comparative costings," but too few of us appreciate their full significance.
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