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. 1912 Excerpt: ...xy and y in the equation of the curve are zero. The equation is of the form ax2 + by2 + 2gx+c = 0. Now ab = 0, since the curve is a parabola, hence a = 0 or b = 0. We cannot have 1=0 unless the curve is a pair of straight lines parallel to the axis of y, hence a = 0. The equation is then of the form by2+2gx + c = 0. ...
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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. 1912 Excerpt: ...xy and y in the equation of the curve are zero. The equation is of the form ax2 + by2 + 2gx+c = 0. Now ab = 0, since the curve is a parabola, hence a = 0 or b = 0. We cannot have 1=0 unless the curve is a pair of straight lines parallel to the axis of y, hence a = 0. The equation is then of the form by2+2gx + c = 0. Now take the origin at (--c/2g, 0), i.e. on the curve; the constant of the equation then becomes zero. The equation of the parabola now takes the form y2 = 2g'x, or, as it is usually written, y2 = 4 ax. The axes of coordinates are the axis of the parabola and a tangent to the parabola at the point where its axis intersects it. In the following chapters we propose to discover the properties of the parabola, the ellipse, and the hyperbola from their equations in these simple forms. 9. Envelopes. In Chapter II we showed how to find the equation of the envelope of a straight line whose equation contains an arbitrary constant in the first or second degree. It will be convenient to extend this method to the equation of any curve which contains an arbitrary constant, or the constants of which are connected by given relations which leave one of them undetermined. If P, Q, 22 are three functions of the coordinates x and y, of the first or second degree, then 2P+kQ + R=0 (i) is an equation of the first or second degree, and represents some straight line or curve whatever value A may have. Two of these lines pass through any proposed point (x', y'), for if P', Q', if are the values of the functions P, Q, R when x', y' are substituted for x and y, we have the condition 2P' + $ + R' = 0 to determine A for loci of the type which pass through x', y'). These two lines will be tangents, straight or curved, from the point (x't y') to the curve enveloped by...
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New. Trade paperback (US). Glued binding. 552 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.
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
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Seller's Description:
New. Trade paperback (US). Glued binding. 552 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.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
