 | Isaac Newton - Calculus - 1745 - 524 pages
...the fecond, tenth, fi Y y eleventh, eleventh, twelfth, and eighteenth, B. 12. El. in which he proves that Circles are to one another as the Squares of their Diameters; that a Cone is a third part of a Cylinder of the fame Bafe and Altitude ; that Cones and Cylinders... | |
 | Euclides - 1842 - 316 pages
...the circle. Now Euclid, in proving (Prop. 2. B. 12.) by means of polygons inscribed in the circles, that circles are to one another as the squares of their diameters, does not state expressly that the sides of the inscribed polygons are less than the least assignable... | |
 | Frances Power Cobbe - 1855 - 228 pages
...the consecutive deductions of the geometer is conscious of the necessary truth of the propositions, that circles are to one another as the squares of their diameters, and that spheres have to one another the triplicate ratio of that which their diameters have. If, then,... | |
 | Euclides - 1858 - 248 pages
...and to the making of a circle the double or the half of another circle, by Prop. 2, bk. xii. , ' ' that circles are to one another as the squares of their diameters. " 1°- To make a rectilineal figure AD KEF, similar to a given rectilineal figure ABLHC. Divide the... | |
 | Frances Power Cobbe - Ethics - 1859 - 308 pages
...the consecutive deductions of the geometer is conscious of the necessary truth of the propositions, that circles are to one another as the squares of their diameters, and that spheres have to one another the triplicate ratio of that which their diameters have. If, then,... | |
 | Euclides - 1863 - 74 pages
...angle ;" and to the making of a circle the double or the half of another circle, by Prop. 2, bk. xii., "that circles are to one another as the squares of their diameters.". 1Q. To make a rectil. figure ADKEF, similar to a given rectil. figure ABLHC. Divide the figure into... | |
 | James Gow - Mathematics - 1884 - 350 pages
...these further attempts. It appears that Hippocrates made some important additions to his proposition that circles are to one another as the squares of their diameters. He proved1 that similar segments of a circle are to one another as the squares of their chords (/3ao-«9)... | |
 | University of St. Andrews - 1902 - 740 pages
...Similar triangles are to one another in the duplicate ratio of their homologous sides. Show briefly now it is proved that circles are to one another as the squares on their radii. 5. Draw a perpendicular to a given plane from a given point without it. If two straight... | |
 | Alva Walker Stamper - Geometry - 1906 - 188 pages
...octagons, Xs and Y3 inscribed regular figures of sixteen sides, etc., the preceding process gives the proof that circles are to one another as the squares of their diameters. See De Morgan's article, Ceometry of the Greeks, in the Penny Encyclopedia, and Gow, pp. 171, 172.... | |
 | Alva Walker Stamper - Geometry - 1909 - 214 pages
...octagons, X, and Y3 inscribed regular figures of sixteen sides, etc., the preceding process gives the proof that circles are to one another as the squares of their diameters. See De Morgan's article, Geometry of the Greeks, in the Penny Encyclopedia, and Gow, pp. 171, 172.... | |
| |
... and so on. But only a mind which has traced the consecutive deductions of the geometer is conscious of the necessary truth of the propositions, that circles are to one another as the squares of their diameters, and that spheres have to one another... 
