Text-book of Euclid's elements for the use of schools : books I - VI and XI (1900)
Hall, H. S. (Henry Sinclair), 1848-1934, Stevens, F. H. (Frederick Haller), 1853-1933 · MacMillan : London · leaf 321
of thecircumscribed and nine-points circlesrespectively. (i) To prove that N is themiddle point of SO. It may be shewn that the perp. to XD from its middle point bisects SO ; Ex. 14, p. 106. Similarly the perp. to EY at its middle point bisects SO : that is, these perp8 intersect at the middle… … (ii) To prove that the radius of the nine-points circle is halfthe radius of the circumscribed circle. By the last Proposition, Xa is a diameter of the nine-points circle..*. the middle point of Xa is its centre:but the middle point of SO is also the centre of the nine-points circle. (Proved.)Hence…
Geometry · Mathematics
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