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Topic: Subtangent

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	subtangent (Site not responding. Last check: 2007-10-22)
		In geometry, the subtangent is the projection of the tangent upon the axis of abscissas (i.e., the x-axis).
		In polar coordinates, the tangent to a curve can be specifically defined as a line segment, tangential to the curve, which extends from the given point P on the curve to a point T, such that line TO is perpendicular to line OP, where O is the origin.
		Then "tangent" specifically also means the length of PT, and the subtangent is the line TO, or -- interchangeably -- the length of line TO.
	www.yourencyclopedia.net /subtangent.html (275 words)

	VisualCalc
		The slope of the tangent is the height divided by the length of the subtangent.
		The slope of a curve is its height divided by the length of the subtangent.
		One endpoint of the translated subtangent is at C. When point P moves along a tractrix, t is constant and C moves along a circle.
	www.cco.caltech.edu /~mamikon/VisualCalc.html (5469 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Barrow was the first to formalize a relationship between the area problem and the tangent problem.
		Newton and Leibniz introduced the ideas of the derivative (instead of the subtangent calculations) which makes calculus the flexible and powerful tool it is today.
		Fermat used the awkward subtangent instead of the yet undiscovered slope of a line.
	www.pitt.edu /~jwt01/HistOfMath/15.ppt (1708 words)

	Science of Logic - Quantum (Site not responding. Last check: 2007-10-22)
		The subtangent, now, is made to be the side of a triangle whose other sides are the ordinate and the tangent connected to it.
		Now since in a quadratic equation with two equal roots the coefficient of the term containing the unknown in the first power is twice the single root, we obtain an equation which yields the required determinations.
		This procedure must be regarded as the brilliant device of a genuinely analytical mind, in comparison with which the dogmatically assumed proportionality of the subtangent and the ordinate with the postulated infinitely small, so-called increments, of the abscissa and ordinate drops into the background.
	www.marxists.org /reference/archive/hegel/works/hl/hl274.htm (5138 words)

	Calculus for Biology Chapter 14 -- True or False (Site not responding. Last check: 2007-10-22)
		The problem of finding tangent lines was one of the driving forces behind the development of the differential calculus.
		The subtangent is defined as the line segment between the point where the tangent line intersects the y-axis and the point (0, y).
		Fermat's procedure consists of finding the tangent line by considering the secant line through (x, y) and a nearby point.
	cwx.prenhall.com /bookbind/pubbooks/neuhauser/chapter14/truefalse1/deluxe-content.html (103 words)

	Fermat, Pierre de
		His argument concerning the speed of light was found later to be in agreement with the wave theory of the 17th-century Dutch scientist Huygens, and was verified experimentally in 1869 by Fizeau.
		In addition to the law of refraction, Fermat obtained the subtangent to the ellipse, cycloid, cissoid, conchoid, and quadratrix by making the ordinates of the curve and a straight line the same for two points whose abscissae were x and x - e.
		There is nothing to indicate that he was aware that the process was general, and it is likely that he never separated it his method from the context of the particular problems he was considering (Coolidge, page 458).
	www.math.rutgers.edu /courses/436/436-s00/Papers2000/pellegrino.html (3192 words)

	israeli.ca - Subtangent (Site not responding. Last check: 2007-10-22)
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		We couldn't find any results for Subtangent in Books.
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	www.israeli.ca /Subtangent/reference/fullview/wikipedia/472551 (154 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		The first problem of this kind was posed by Florimond De Beaune and solved by Descartes without using differential calculus.
		The issue was to find a curve whose subtangent had a constant value.
		In modern terms one could say that, recalling the fact that the subtangent of a curve
	www2.math.unifi.it /~archimede/archimede_inglese/mostra_calcolo/guida/node16.html (1447 words)

	Leibniz segments in a dynamic setting (Site not responding. Last check: 2007-10-22)
		Insert the measure of the length QN of the subnormal and the length QT of the subtangent in the sketch and drag S along the directix d.
		The subnormal QN has constant length and the midpoint of the subtangent QT is the vertex of the parabola.
		Use part c of Problem 1 to prove the theorem that you conjectured in part b.
	students.ed.uiuc.edu /kjudd/eport/leibnizsegments.htm (333 words)

	db_description
		Longitude for the subtangent point of the 150 km apparent tangent altitude ray
		Latitude for the subtangent point of the 3 km apparent tangent altitude ray
		Longitude for the subtangent point of the 3 km apparent tangent altitude ray
	www.oma.be /BIRA-IASB/Scientific/Topics/Lower/Satellite/MSDOL/db_description.html (996 words)

	The Analyst: a Discourse addressed to an Infidel Mathematician (Site not responding. Last check: 2007-10-22)
		Let AB be a curve, the abscissa AP = x, the ordinate PB = y, the difference of the abscissa PM = dx, the difference of the ordinate RN = dy.
		dy + z: whence the true expression for the subtangent should have been There was therefore an error of defect in making dy the divisor; which error was equal to z, i.e.
		But this is a plain mistake; for it is evident that as a secant cannot be a tangent, so a subsecant cannot be a subtangent.
	www.blackmask.com /books23c/analystberk.htm (10866 words)

	fermat
		B) Use the equation from part A) with the function
		Let PT be the desired tangent at point P on a curve.
		The length of the line segment TQ is called the subtangent.
	isolatium.uhh.hawaii.edu /m205L/lab6/fermat/Fermat.htm (346 words)

	No Title
		Hence to find extrema Fermat would equate the two, divide by E, then set E to zero.
		Therefore if c is the subtangent to f(x) at (a,b)
		Now y'=y/t, where t is the subtangent and thus
	www.math.tamu.edu /~don.allen/history/precalc/precalc.html (1970 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Subtangent Altitudes (0, 10, 20,..., 70) (km) real(kind=4),dimension(8) :: Tan_Alt !
		Subtangent Latitudes @ Tan_Alt (deg) real(kind=4),dimension(8) :: Tan_Lat !
		Subtangent Longitudes @ Tan_Alt (deg) real(kind=4),dimension(8) :: Tan_Lon !Interpolated Met Vectors !
	eosweb.larc.nasa.gov /PRODOCS/sage2/read_software/specinfo.f90 (305 words)

	The Analyst: a Discourse addressed to an Infidel Mathematician (Site not responding. Last check: 2007-10-22)
		But herein there is an error arising from the aforementioned false supposition, whence the value of PT comes out greater than the Truth: for in reality it is not the Triangle RNB but RLB which is similar to PBT, and therefore (instead of RN) RL should have been the first term of the Proportion, i.
		There was therefore an error of defect in making dy the divisor: which error was equal to z, i.
		And supposing NO to be infinitely diminished, the subsecant NM will in that case coincide with the subtangent NL, and v as an Infinitesimal may be rejected, whence it follows that
	www.maths.tcd.ie /pub/HistMath/People/Berkeley/Analyst/Analyst.html (12001 words)

	Definition of subtangent - Merriam-Webster Online Dictionary
		subtangent is one of more than 1,000,000 entries available at Merriam-WebsterUnabridged.com.
		For More Information on "subtangent" go to Britannica.com
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	www.m-w.com /dictionary/subtangent (82 words)

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