This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 Excerpt: ...the fame of whose learning has reached to our distant shores. May I see him? Philosopher. I am Euclid. Strang. Great and learned philosopher, the last of your propositions which has come to our knowledge in the far west is the fifth, in which you prove that the angles at the base of an isosceles triangle are equal, and ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 Excerpt: ...the fame of whose learning has reached to our distant shores. May I see him? Philosopher. I am Euclid. Strang. Great and learned philosopher, the last of your propositions which has come to our knowledge in the far west is the fifth, in which you prove that the angles at the base of an isosceles triangle are equal, and I cannot withhold from you my admiration of the lucid, direct, and convincing proof that you have given that this, your discovery, is true. May I ask if you have made any fresh discovery since that which has been made known to us? Euclid. I have. Strang. May I ask what is it? Euc. It is that if two angles of a triangle are equal, the sides opposite to those angles are also equal. Strang. And, revered philosopher, can you give a proof that this is true, as lucid, direct, and convincing as that which you gave that if the sides of a triangle are equal, the angles at the base of the triangle are also equal? Euc. I cannot. Strang. Then, 0 learned Euclid, great as is your reputation, I withhold my assent to the assertion you make. Taught by you, I refuse to give assent to that which has not been demonstrated. Euc. But though I cannot prove directly that the sides are equal, I can prove that it is false to say that they are unequal. Strang. Ah! How so? Euclid here draws the triangle given on page 84. Euc. If the sides B A, A C, are not equal, stranger, what must they be? Strang. They must be unequal. Euc. And if they are unequal, one of them must be what...? Strang. One of them must be greater than the other. Euc. And if one of them (say A B) is greater than the other, what may be cut off from the greater? Strang. A part may be cut off equal to the less. We were taught how to do so in your third proposition. Euc. And if that be done--if B D be cut o...
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