. Elements of geometry : containing books I to III. Let AB be the given st. line, and 0 a given pt. in is required to draw ft IB. Take any pt D in AC, and in CB make tE= Z>J5 describe an equilat. A ZAFA. Join FG i-V shall be j to J7J. I. 1 For in as DCF, ECF, v DC=CE,and CFis common, snr yi)=li:, .: iDCF= i I I.,, and .-. PCia l to AB, De£ 9. Q. E. i\ Cor. To draw a straight line at rigbl angles to a givenhi line 4Cfrom one extremity, C, take any point Din? I, prodn /., making CE=CD, and I as in the proposition. I. Shew that in the diagram of Prop. ix. .l/-\md ED• ich other at ri
. Elements of geometry : containing books I to III. Let AB be the given st. line, and 0 a given pt. in is required to draw ft IB. Take any pt D in AC, and in CB make tE= Z>J5 describe an equilat. A ZAFA. Join FG i-V shall be j to J7J. I. 1 For in as DCF, ECF, v DC=CE,and CFis common, snr yi)=li:, .: iDCF= i I I.,, and .-. PCia l to AB, De£ 9. Q. E. i\ Cor. To draw a straight line at rigbl angles to a givenhi line 4Cfrom one extremity, C, take any point Din? I, prodn /., making CE=CD, and I as in the proposition. I. Shew that in the diagram of Prop. ix. .l/-\md ED• ich other at right angles, and that ED is bi Ex, _ IfObe the point in which two lines, bisecting ABII ? i an equilateral triangle, at righl ai : shew thai 0 I. /? U equal Prop. xt. is a particular case of Prop, ix. Eook PKO: _M Proposition XII. T > draw a straight Itline of an unlimited length from a given point without Let AB be the given st. line of unlimited length) C thegiven pt. without it. It Ureq o draw from C a st. line j. to AB. Take any pt. D on the other side of .1 B. With centre ( and distance CD describe a • cutting Al ii, E and F. Bisect EF in 0, and join t of unlimited length,how might the construction fail ? Ex. 2. If in a triangle the perpendicular from the vertexon the base bisect the base, the triang Ex. 3. The lines drawn from the angular points of aaequilateral triangle to the middle points ide*are equal. 14 A I ( 7. t&S 1:1 A S. LBook I Miscellaneous Exercises on Props. I. to All. 1. Draw a ti- e for Prop. n. for the case when the givenpoint A is (a) below the line BC and to the right of it.(/3) below the line BC and to the left of it 2. Divide a given an
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