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1
Redefining Geometrical Exactness: Descartes' Transformation ...
the circle can be squared, and many other things can be performed, very
pleasing to know.8 As the title indicated, Clavius claimed no less than having
found the gen- The quadratrix uinely geometrical constructions of all regular
polygons, and ...
2
Annals of Philosophy, Or, Magazine of Chemistry, Mineralogy, ...
If, therefore, we find a fourth proportional to the base of that quadratrix, its side,
and the radical of the given circle, it will be equal to the quadrantal arch of that
circle ; and the rectangle under twice this line and the radius will be equal to the
area ...
3
A philosophical and mathematical dictionary: containing an ...
QUADRATRIX, or Quadratix, in Geometry, is a mechanical line, by means of
which, right lines are found equal to the circumference of circles, or other curves,
and of the parts of the same. Or, more accurately, the quadratrix of a curve, is a ...
4
A geometrical treatise of conic sections: In four books. To ...
In the following solu- ' tions the possibility of describing the quadratrix is
necessarily supposed. PROP. IV. PR OB. I. From a given retl'1lineal angle to cut
off any part required, by means of the quadratrix. Fig. 13. Let k c e be a given
rectilineal ...
5
The Historical Roots of Elementary Mathematics
The set of all these points is the quadratrix. For example, when the rotating line
segment reaches position AF such that mLBAF = 45°, or half the rotation from AB
to AD, the sliding line segment will reach position GH, where G is the midpoint of
...
Lucas N. H. Bunt, Phillip S. Jones, Jack D. Bedient,
2012
6
Pappus of Alexandria: Book 4 of the Collection: Edited With ...
29: Analytical Determination of the Quadratrix from the Archimedean Spiral #34 It
can, however, also be made the subject of analysis2 by means of a spiral
described in the plane, in a similar way. B Z C E H I K L D A For: Assume that the
ratio ...
squaring the circle. It is proved by Archimedes that the rectangle under the radius
and semi-perimeter of a circle is equal to its area. But the radius of a circle is to its
quadrant as the base of the quadratrix is to its side. If, therefore, we find a ...
8
The Annals of Philosophy
But the radius of a circle is to its quadrant as the base of the quadratrix is to its
side. if, therefore, we find a fourth proportional to the base 01' that quadratrix, its
side,- and the radical of the given circle, it will-be equal to the quadrantal arch of
...
9
A Treatise of Fluxions: Or, an Introduction to Mathematical ...
And if we rightly confider the new Equation exprefllng the Nature of the Curve
AMH, it will appear, that the Vertex of the Quadratrix (or the Curve) AHD does not
always co-incide with the Vertex of the Curvilineal Figure AD4Z? which is to be ...
10
A geometrical treatise of conic sections. To which is added, ...
tions the possibility of describing the quadratrix is necesfarily supposed. PROP.
IV. PROB. L From a given reflilineal angle to cut off any part required, by means
of the quadratrix. Fig. i$. Let k c e be a given rectilineal angle ; it is required to cut
...