The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . contain an angleBDC greater than theangle 5^ a Produce BD to meet AC ^i E. Because two sides of a triangle are greater than thethird side, the two sides BA, AEoi the triangle ABE aregreater than the side BE. [I. 20. To each of these add ECTherefore BA, AC are greater than BE, ; the two sides CE, ED of the triangle CED aregreater than the third side CD. [I. 20. To each of these add CE, EB are greater than CD,
The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . contain an angleBDC greater than theangle 5^ a Produce BD to meet AC ^i E. Because two sides of a triangle are greater than thethird side, the two sides BA, AEoi the triangle ABE aregreater than the side BE. [I. 20. To each of these add ECTherefore BA, AC are greater than BE, ; the two sides CE, ED of the triangle CED aregreater than the third side CD. [I. 20. To each of these add CE, EB are greater than CD, it has been shewn that BA, AC are greater than BE, EC; much more then are BA, ^(7 greater than BD, DC. Again, because the exterior angle of any triangle isgreater than the interior opposite angle, the exteriorangle BDC of the triangle CDE is greater than the angleCED. [I. 16. For the same reason, the exterior angle CEB of the tri-angle ABE is greater than the angle it has been shewn that the angle BDC is greater thanthe angle CEB; much more then is the angle BDC greater than the angleBAC Wherefore, iffr(ym, the ends &c. ). BOOK I. 22. 25. PROPOSITION 22. PROBLEM. To make a triangle of which the sides shall he equal tothree gicen straight lines, hut any two whatever of thesemust he greater than the third. Let A, B, Che the three given straight lines, of whichany two whatever are greater than the third; namely,A and B greater than C; A and C gieater than B; andB and C greater than A : it is required to make a triangleof which tlie sides shall be equal to A, B, C, each to each. Take a straight lineDE terminated at thepoint Z>, but unlimitedtowards B, and makeDF equal to A, FG ?qual to B, and GH qual to C. [I. 3. -rora the centre F,X the distance FD,escribe the circleDKL. \_Poit. 3. irom the centre G, at the distance GH, describe the circleIILK, cutting the former circle at KF, KG. The triangle KFG shall have its sides• iaal to the three straight lines
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Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
