Davies, Charles, 1798-1876 · New York and Chicago, A. S. Barnes and company · leaf 42
BOOK II. 41 Of the Circle, THEOREM I. A diameter is greater than any other chord.Let AD be any chord. Draw the radii CA, CD to its extremities.We shall then have A C-\- CD greaterthan AD (Book I. Th. X*). But AAC+CD is equal to the diameterAB: hence, the diameter AB iscreator than AD. … THEOREM [I. If from the centre of a circle a line be drawn to the middle ofa chord, I. It will be perpendicu \ar to the chord; II. And it will bisect the arc of the chord.Let C be the centre of a circle, and AB any chord. Draw CD throughD, the middle point of the chord, andproduce it to E: then…
Geometry · Plane trigonometry
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