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. 1875 Excerpt: ...of these numbers is a fourth proportional to the three others A, B, C. If two mean numbers C, B are equal, the equality _ =_ becomes: _ =-, and the fourth term D takes the B D B D name of third proportional to the two numbers A, B. In this case the mean number B is the mean proportional between the numbers A and D. It ...
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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. 1875 Excerpt: ...of these numbers is a fourth proportional to the three others A, B, C. If two mean numbers C, B are equal, the equality _ =_ becomes: _ =-, and the fourth term D takes the B D B D name of third proportional to the two numbers A, B. In this case the mean number B is the mean proportional between the numbers A and D. It results from the preceding equality that B2 = A X D. Therefore the mean proportional B between the numbers A and D is equal to the square root of the product of those numbers. 60. Two straight lines drawn between the sides of an angle, or of the angle vertically opposite, are anti-paral Reciprocally.--If through point B, taken on one of the sides of angle BAC, two straight lines BC, BE be drawn in the interior of the angle, such that AB2 = AC. A E, these two straight lines are anti-parallel in relation to that angle. THEOREM XIX. If from the summit A of the right angle of a right-angled triangle ABC, the perpendicular AT) be dropped on the hypothenuse, 1st, each side of the rigid angle is a mean proportional between the hypothenuse and its projection on the hypothenuse; 2nd, the perpendicular AT) is a mean proportional between the two segments BD and CD of the ypothenuse. For, first, the straight lines A C, A D are anti-parallels in relation to angle B, because they form a right angle, one with side B A, the other with side B C. This gives: B A3 = BC.BD. The relation C Aa = B C. C D could be proved in like manner. 2. The straight lines A C and A D being anti-parallels in relation to angle B, the angles BAD and C are equal. Therefore, if the triangle A D B be applied to triangle A D B', by turning it over A D the angle B'AD will be equal to C, and the two straight lines AB' and AC will be anti-parallel in relation to angle ADC. This will give A...
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Add this copy of Euclid Simplified, Compiled From the Most Important to cart. $46.69, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2010 by Nabu Press.
