. Elements of geometry : containing books I to III. Then v 6A = OC, :.lOCA = lOAC\ La. sum ot l b 0( -1. OJO = twice z ( i £00 = sum of 1 s Or. I. 0 J .• ?. I. 32. • lBOC= twice z is, . £00 = twice l BAC 145 ///\ fBook tlX. Next, suppose 0 to be within (tig 1), or without (fig. 2) thelBAO. Fig. Join AO, and produce it to meet the Oc ? in , :is in the firs! L COB = twicer OL&D,and/ BOD= twice/ /M/>;.-., fig. 1, sum of - B />. BOD = twice sum of i s , thai is, l BOC = twin /..I. And, fig. 2, difference of zs ro/>, y;<//* = twice differenceo
. Elements of geometry : containing books I to III. Then v 6A = OC, :.lOCA = lOAC\ La. sum ot l b 0( -1. OJO = twice z ( i £00 = sum of 1 s Or. I. 0 J .• ?. I. 32. • lBOC= twice z is, . £00 = twice l BAC 145 ///\ fBook tlX. Next, suppose 0 to be within (tig 1), or without (fig. 2) thelBAO. Fig. Join AO, and produce it to meet the Oc ? in , :is in the firs! L COB = twicer OL&D,and/ BOD= twice/ /M/>;.-., fig. 1, sum of - B />. BOD = twice sum of i s , thai is, l BOC = twin /..I. And, fig. 2, difference of zs ro/>, y;<//* = twice differenceof zs CAD, BA D, that is, l BOC = twice /MC. Q. K. D Ex. From any point in a straight line, touching a circle,a Btraighl line is drawn through the centre, and is terminatedby the circumference; the angle between t^ese two straightlines is bisected by a Btraighl line, which intersects the Btraightline joining their extremities. Shew that the angle betweenthe lasl two Lines is half a right angle. Book III.] NOTE IT. l49 Note 2. On Flat and Reflex Angles. We have already explained (Note 3, liook I., p. 28) LowEuclids definition of an angle may be extended with advan-tage, so as to include the conception of an angle equal to tworight angles : and we now proceed to shew how the Definitiongiven in that Note may
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