. Elements of geometry : containing books I to III. /t line into two parts, so thai the rect-*ngle contain / hy the whole and one of the parts shall be equalto the square on the other part. -?J?. Let AB be the given st. line. On AB descr. the sq. ADCH. Bisect AD in E and join EB. Produce DA to F, making EF=EB. On AF descr. the sq. AFGH. Then AB is dwub d in H so that rect. AB, BII=sq. on A If. Produce ill to v DA is bisected in E and produced to F,.*. rect. DF, FA together with sq. on AE=sq. on EF =sq. on iB, V EB=EF,=sum of sqq. on AB, from each the square on AE. Then rect. DF,
. Elements of geometry : containing books I to III. /t line into two parts, so thai the rect-*ngle contain / hy the whole and one of the parts shall be equalto the square on the other part. -?J?. Let AB be the given st. line. On AB descr. the sq. ADCH. Bisect AD in E and join EB. Produce DA to F, making EF=EB. On AF descr. the sq. AFGH. Then AB is dwub d in H so that rect. AB, BII=sq. on A If. Produce ill to v DA is bisected in E and produced to F,.*. rect. DF, FA together with sq. on AE=sq. on EF =sq. on iB, V EB=EF,=sum of sqq. on AB, from each the square on AE. Then rect. DF, FA=sc[. on AB. ? FG=FA. 10. II. 6. Ax. 3. Now i^T=rect. DF, FA, .: FK=AC. Take from each the common part AK. Then FH=IJ< ; that is, sq. on ^il=rect. AB, BH, v BC=AB. Thus AB is divided in H as was reqd. .. K. W. Ex. Shew that the squares on the whole line and one of theparts are equal to three times the square on the other part. 90 EUCLIDS ELEMENTS. tBook XL PnorosmoN XTI. Theorem:. In obtuse-angled triangles, if a perpendicular be drawn fromeither of the acute angles to the opposite side produced, the squareon the side subtending tin obtuse angle is greater th n
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