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. 1872 Excerpt: ...remaining in the one case will be equal to the magnitude remaining in the other. (Ax. III.) (The following demonstration is applicable to any one of the three figures given, which indicate the different positions which the parallelograms may occupy with relation to each other, with this exception, that in applying the ...
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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. 1872 Excerpt: ...remaining in the one case will be equal to the magnitude remaining in the other. (Ax. III.) (The following demonstration is applicable to any one of the three figures given, which indicate the different positions which the parallelograms may occupy with relation to each other, with this exception, that in applying the demonstration to the first figure, wherever the letter E occurs, the letter D must be substituted for it. The second and third figures had better be employed first in going through the proposition. The peculiarity of the first figure is that the points D and E coincide.) CDF CT EFOBDF Let A B D C, and A B F E be two parallelograms upon the same base, A B, and between the same parallels, A B and C F. It has to be shown that they are equal in area. To demonstrate this it is shown: 1st. That the As C A E and DBF are equal in area. 2nd. That the remainder left, when the A C A E is taken from the trapezium C A B F, is equal to the remainder left when the A B D F is taken away from the same figure. Since the straight lines C A and D B are parallel and the straight line C F intersects them, the exterior /_ F D B is equal to the interior and opposite on the same side of the intersecting line, namely, E C A. (Prop. XXIX.) Again, since the straight lines A E and B F are parallel, and the straight line C F intersects them, the exterior /_ C E A is equal to the interior and opposite Z on the same side of the intersecting line--namely, DFB. And because C A B D is a parallelogram, its opposite sides A C and B D are equal. Hence it appears that the two As C A E and DBF have two /s of the one (namely ACE and AE C) equal respectively to two /_s of the other (namely B D F and B F D), and a side of the one (viz. A C) equal to a side of the other similarly...
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Add this copy of The First and Second Books of Euclid Explained to to cart. $58.41, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2016 by Palala Press.
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