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Updated: May 29, 2025
By means of these general laws, the measurement of all lines, angles, and spaces whatsoever might be accomplished by measuring a single straight line and a sufficient number of angles; which is the plan actually pursued in the trigonometrical survey of a country; and fortunate it is that this is practicable, the exact measurement of long straight lines being always difficult, and often impossible, but that of angles very easy.
The simpler changes of formation were so simple that complication could not be got into them; but, that happy stage past, we went on to evolutions of huge masses of ships in three columns, in which the changes of dispositions, from one order to another, became subjects of trigonometrical demonstration, quite as troublesome as Euclid.
Macaulay, while a student at Cambridge, wrote to his mother: "Oh, for words to express my abomination of mathematics ... 'Discipline' of the mind! Say rather starvation, confinement, torture, annihilation!... I feel myself becoming a personification of Algebra, a living trigonometrical canon, a walking table of logarithms.
If the height of this volcano is 1905 toises, as the last trigonometrical measure of Borda indicates, its summit ought to be visible at a distance of 43 leagues, supposing the eye on a level with the ocean, and a refraction equal to 0.079 of distance.
"All right but I'll bet it's slower than the rise of a toy balloon." Seaton threw down the papers and picked up his slide-rule, a twenty-inch trigonometrical duplex. "You'll concede that it is allowable to neglect the radial component of the orbital velocity of the earth for a first approximation, won't you or shall I figure that in too?" "You may ignore that factor." "All right let's see.
Oh that I were to pore over Thomas Aquinas, and to adjust the relation of Entity with the two Predicaments, so that I were exempted from this miserable study! "Discipline" of the mind! Say rather starvation, confinement, torture, annihilation! But it must be. I feel myself becoming a personification of Algebra, a living trigonometrical canon, a walking table of Logarithms.
A change of some kind had taken place during his absence. The nightwatchman, Hager, had been heard praying in his attic for the boys. A boy, in great trouble with a trigonometrical problem which would not come right, had solved the difficulty by linking work with prayer. The boys in the "First Room" i.e., the elder boys made an agreement to speak with one another openly before the Holy Communion.
They became staunch admirers of the system, while other meteorological savants participated in the trials for the express purpose of ascertaining just what the ship could do. As a result of elaborate trigonometrical calculations it was ascertained that the airship attained an independent speed of 30 feet per second, which exceeded anything previously achieved.
Properly speaking, there is no mystery about men, but only a great dulness and lethargy in our perceptions of them. The secret of the universe is no more a secret than is the answer to a school-boy's problem. A mathematician will draw you a triangle and a circle, and show you the trigonometrical science latent therein. But a profounder mathematician would do as much with the equation man!
Captain Servadac knew the country well; he had at one time been engaged upon a trigonometrical survey of the district, and consequently had an accurate knowledge of its topography. His idea now was to draw up a report of his investigations: to whom that report should be delivered was a problem he had yet to solve.
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