 | George Salmon - Conic sections - 1852 - 338 pages
...-p; or the rectification and quadrature of the spiral of Archimedes depend on the same formulse as in the case of the parabola.* The following is...the theorem is obvious. The reader will find general formula? by Mr. Roberts connecting the element of the length of a curve with that of the locus of the... | |
 | Benjamin Williamson - Calculus of variations - 1880 - 398 pages
...corresponding normal divided by the old ordinale, then the locus of the extremity of the Ordinate so produced is a curve whose area is in a constant ratio to the length of the given curve. CHAPTER IX. VOLUMES AND SURFACES OF SOLIDS. 1 68. Solids. — The Prism and Cylinder. — The most... | |
 | Benjamin Williamson - Calculus of variations - 1884 - 424 pages
...corresponding normal divided by the old Ordinate, then the locus of the extremity of the ordmate so produced is a curve whose area is in a constant ratio to the length of the given curve. CHAPTER IX. VOLUMES AND SURFACES OF SOLIDS. 1 68. Solids. — The Prism and Cylinder. — The most... | |
 | Isaac Barrow - Geometry - 1916 - 246 pages
...corresponding normal divided by the old ordinate, then the locus of the extremity of the ordinate so produced is a curve whose area is in a constant ratio to the length of the given curve." Now this theorem is identical with the theorem of § 18 ; hence, remembering that the semi-cubical... | |
 | Isaac Barrow - Geometry - 1916 - 268 pages
...corresponding normal divided by the old ordinate, then the locus of the extremity of the ordinate so produced is a curve whose area is in a constant ratio to the length of the given curve." Now this theorem is identical with the theorem of § 18 ; hence, remembering that the semi-cubical... | |
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Archimedes depend on the same formulse as in the case of the parabola.* The following is a method by which rectification may in general be reduced to quadratures, and by which, in particular, Van Huraet rectified the semicubical parabola, the first curve... 