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Updated: June 16, 2025
Normals are treated, not in connexion with tangents, but as minimum or maximum straight lines drawn to the curves from different points or classes of points. Certain propositions of great difficulty enable us to deduce quite easily the Cartesian equations to the evolutes of the three conics. He was also a master of the theory of epicycles and eccentrics.
I overheard one of my urchins, clattering in front of me, shout to another: "I'm sure he's got the sack!" Turning round he perceived me, and grew as red as a turkey-cock. I laughed aloud. The boy's yell was a clarion announcement from the seventh heaven. I had got the sack! I should never teach him quadratic equations again.
The assistance of Mabel would not be of much value. The police? Before they could be got and the getting of them presented difficulties the burglars would have cleared away with their sacks of silver. Gerald stopped and thought hard; he held his head with both hands to do it. You know the way the same as you sometimes do for simple equations or the dates of the battles of the Civil War.
After a course of equations that flattened out my head like the Camargue, I was thrust into what are called surds, a sort of wood of errors, in which one spends hours in hewing one's way to get at nothing of the slightest profit to man or beast; finally, I believe my good tutor, now a bishop, got tired of me. I was stupefied by surds; and I entered the university.
It can integrate, too, innumerable equations of finite differences; and, in addition to these functions, it does its work cheaply and quickly; it corrects whatever errors are accidentally committed, and it prints all its calculations.”
So, racing against encroaching death, James Hudson Cavour turned to a new page in his diary, headed it, in firm, forceful letters, For Those Who Follow After, and inked in a clear and concise explanation of his work. It was all there, Alan thought exultantly: the diagrams, the specifications, the equations. It would be possible to build the ship from Cavour's notes.
He had managed to crawl back inside the cave, but, alone, with no one to tend him, he knew he had nothing to hope for. It was impossible for him to complete his ship. All his dreams were ended. His equations and his blueprints would die with him.
What would the American girl think of going through a history recitation in Russian, writing chemistry equations in French, or demonstrating a geometry proposition in Spanish? Some day Indian education may be conducted in its own vernaculars; to-day there are neither the necessary text-books, nor the vocabulary to express scientific thought.
The molecular weight of NaCl is 58.5 and that of KCl is 74.6. The atomic weight of chlorine is 35.5. Then Solving these equations for x shows the weight of NaCl to be 0.0625 gram. The weight of KCl is found by subtracting this from 0.15. The above is one of the most common types of indirect analyses. Others are more complex but they can be reduced to algebraic expressions and solved by their aid.
A rare copy of Sextus Empiricus, with the Greek and Latin side by side, lay open on an inclined desk at one end, and the table was strewn with papers, on which were roughly drawn a variety of mathematical figures, margined all around with odd-looking equations and algebraically-expressed formulæ.
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