Notes On the Principles of Pure And Applied Calculation And Applications of Mat
Notes On the Principles of Pure And Applied Calculation And Applications of Mat
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In Euclid it is proved, with the help of I. 4, by a reductio ad ab- surdum. This proof can hardly be regarded as any thing more than putting into formal evidence the impossibility of not perceiving immediately the equality of the two triangles when one is applied to the other.
I. 13 and 15. The equality of any two adjacent angles to two right angles, proved in the former of these propositions, is really a deduction, though of the simplest kind. But the equality of opposite angles when two strai...ght lines cross each other, is perceived immediately from the very conception of straight lines and angles, to which an appeal might at once have been made without intermediate reasoning. We have here an instance, like others that occur in the Elements of Euclid, of superfluity of reasoning.
I. 29. If parallel straight lines be defined as proposed in p. 62, the equality of the alternate angles follows from I. 15.
I. 32. The exterior angle of a triangle is proved to be equal to the two opposite interior angles, and the three interior angles are proved to be equal to two right angles, from the defi- nition of parallel straight lines and by I.
What to read after Notes On the Principles of Pure And Applied Calculation And Applications of Mat?
You can find similar books in the "Read Also" column, or choose other free books by Challis James to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
In Euclid it is proved, with the help of I. 4, by a reductio ad ab- surdum. This proof can hardly be regarded as any thing more than putting into formal evidence the impossibility of not perceiving immediately the equality of the two triangles when one is applied to the other.
I. 13 and 15. The equality of any two adjacent angles to two right angles, proved in the former of these propositions, is really a deduction, though of the simplest kind. But the equality of opposite angles when two strai...ght lines cross each other, is perceived immediately from the very conception of straight lines and angles, to which an appeal might at once have been made without intermediate reasoning. We have here an instance, like others that occur in the Elements of Euclid, of superfluity of reasoning.
I. 29. If parallel straight lines be defined as proposed in p. 62, the equality of the alternate angles follows from I. 15.
I. 32. The exterior angle of a triangle is proved to be equal to the two opposite interior angles, and the three interior angles are proved to be equal to two right angles, from the defi- nition of parallel straight lines and by I.
What to read after Notes On the Principles of Pure And Applied Calculation And Applications of Mat?
You can find similar books in the "Read Also" column, or choose other free books by Challis James to read onlineMoreLess
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