Greek Geometry From Thales to Euclid
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Antiphon's mistake, on account of his not having started from geo- metrical principles, as we shall see, cannot be disproved geometrically. That of Hippocrates, on the other hand, since he was deceived although he clung to geometrical principles, can be disproved geometrically. For we must analyse and examine those reasonings only which, pre- serving the acknowledged principles of the science, lead thus to further conclusions ; but there is no use in examining those in which these principles ar...e set aside.' * Antiphon, having drawn a circle, inscribed in it one of those polygons^^ that can be inscribed ; let it be a square. Then he bisected each side of this square, and AvTt9>uivrciX through the points of section drew straight lines at right angles to them, producing them to meet the circumference; these lines evidently bisect the corresponding segments of the circle. He then joined the new points of section to the ends of the sides of the square, so that four triangles were formed, and the whole inscribed figure became an octagon.
What to read after Greek Geometry From Thales to Euclid?
You can find similar books in the "Read Also" column, or choose other free books by Allman, George Johnston, 1824-1904 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Antiphon's mistake, on account of his not having started from geo- metrical principles, as we shall see, cannot be disproved geometrically. That of Hippocrates, on the other hand, since he was deceived although he clung to geometrical principles, can be disproved geometrically. For we must analyse and examine those reasonings only which, pre- serving the acknowledged principles of the science, lead thus to further conclusions ; but there is no use in examining those in which these principles ar...e set aside.' * Antiphon, having drawn a circle, inscribed in it one of those polygons^^ that can be inscribed ; let it be a square. Then he bisected each side of this square, and AvTt9>uivrciX through the points of section drew straight lines at right angles to them, producing them to meet the circumference; these lines evidently bisect the corresponding segments of the circle. He then joined the new points of section to the ends of the sides of the square, so that four triangles were formed, and the whole inscribed figure became an octagon.
What to read after Greek Geometry From Thales to Euclid?
You can find similar books in the "Read Also" column, or choose other free books by Allman, George Johnston, 1824-1904 to read onlineMoreLess
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