Elementary plane geometry : inductive and deductive / by Alfred Baker . Give reasons. CHAPTER XIII. Relation Between Seg-ments of Intersecting:Chords. 1. AEB and CED are any twochords in a circle, intersectingat E. In the second figure CEB andAED are any two lines drawnperpendicular to each other, andand on these we lay off thefollowing distances mth thedividers: AE = AE of circleEB = EB CE=CE ^ ED = ED Complete the rectangles CEDFand AEBG, and let FD and GB meet in H. Then produce the lines FC, HE and GA,and note how nearly they come to passing throughthe same point (at K). Go over the measur
Elementary plane geometry : inductive and deductive / by Alfred Baker . Give reasons. CHAPTER XIII. Relation Between Seg-ments of Intersecting:Chords. 1. AEB and CED are any twochords in a circle, intersectingat E. In the second figure CEB andAED are any two lines drawnperpendicular to each other, andand on these we lay off thefollowing distances mth thedividers: AE = AE of circleEB = EB CE=CE ^ ED = ED Complete the rectangles CEDFand AEBG, and let FD and GB meet in H. Then produce the lines FC, HE and GA,and note how nearly they come to passing throughthe same point (at K). Go over the measurements andconstruction with extreme care, getting rid of all inac-curacies. Do these lines (FC, HE, GA) all pass throughthe same point? If they do, how do the areas CEDF,AEBG compare in size (Ch. VIIL, 6), and therefore therectangles , , contained by the segmentsof the chords ? Measure the number of millimetres in each, of thelines AE, EB, CE, ED in the circle, and examinewhether the product of AE and EB is approximatelyequal to the product of CE and ED. 94. Segments of Chokds of Circles. 95 Describe other circles, draw two chords in each, andrepeat in the case of each circle the construction ofthe second figure. Repeat also the measurements andmultiplications. The result of our observations may be stated asfollows: If two chords of a circle cut one an-other within the circle, the rectangle containedby the segments of the one is equal to therectangle contained by the segments of theother. 2. Draw accurately the tangent EC;draw also the secant EAB. In the second figure CEA, BEC areany two lines drawn at right angles toeach other, and on these we lay off thefolloAving distances with the dividers: EA = EA of circleEB = EB - EC, EC = EC - Complete the rectangle EBGA and thesquare ECFC, and let FC, GA meetin H. Then produce the lines FC,HE and GB, and note how nearly theycome to passing through the samepoint (at K). Go over the measure-ments and construction with extremeca
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