Tracts on Mathematical and Philosophical Subjects: Comprising Among Numerous Important Articles, the Theory of Bridges, with Several Plans of Recent Improvement
Tracts on Mathematical and Philosophical Subjects: Comprising Among Numerous Important Articles, the Theory of Bridges, with Several Plans of Recent Improvement
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. 1812 Excerpt: ...true aestimatios, or positive roots, but no fictitious or negative ones; and for this reason, that the odd powers of minus being minus, and the even powers plus, the two terms x3 + bx would be negative, and equal to a positife sum TOl. H. P ax + c, which is absurd: and further, that the case x3 + ax--b x = c has three ...
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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. 1812 Excerpt: ...true aestimatios, or positive roots, but no fictitious or negative ones; and for this reason, that the odd powers of minus being minus, and the even powers plus, the two terms x3 + bx would be negative, and equal to a positife sum TOl. H. P ax + c, which is absurd: and further, that the case x3 + ax--b x = c has three roots, one plus and two minus, which are the same, with the signs changed, as the roots of the case x + bx + c = ax. He also shows the relation of the coefficients when the equation has only one real root, in a variety of cases: but that the case x3 + c = ax + bx has always one negative root, and either two positive roots, or none at all; the number of roots failing by pairs, or the impossible roots, as we now call them, -being always in pairs. Of all these circumstances Cardan gives a great many particular examples in numeral coefficients, and subjoins geometrical demonstrations of the properties here enumerated; such as, that the two corresponding or reciprocal cases have the same root or roots, but with different signs or affections; and how many true or positive roots each case has. Upon the whole, it appears from this short chapter, that Cardan had discovered most of the principal properties of the roots of equations, and could point out the number and nature of the roots, partly from the signs of the terms, and partly from the magnitude and relations of the coefficients. He shows in effect, that when the case has all its roots, or when none are impossible, the number of its positive roots is the same as the number of changes in the signs of the terms, when they are all brought to one side: that the coefficient of the 2d term is equal to the sum of all the roots positive and negative collected together, and consequently that when the 2d te..
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Fine. Sewn binding. Cloth over boards. 404 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Tracts on Mathematical and Philosophical Subjects: to cart. $75.07, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2016 by Palala Press.
Add this copy of Tracts On Mathematical and Philosophical Subjects: to cart. $105.86, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2016 by Palala Press.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Sewn binding. Cloth over boards. 404 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Tracts on Mathematical and Philosophical Subjects: to cart. $105.87, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2016 by Palala Press.
