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 . three sidesKF, FG, GK equal to t/te three given straight linesA, B, a 26 EUCLIDS ELEMENTS. PEOPOSITIOX 23. PROBLEM, At a given 2yomt in a given straight line^ to make arectilineal angle equal to a given rectilineal angle. Let AB he the given straight line, and A the givenpoint in it, and DOE the given rectilineal angle : it isrequired to make at the given point A, in the given straightline AB, an angle equal to the given r
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 . three sidesKF, FG, GK equal to t/te three given straight linesA, B, a 26 EUCLIDS ELEMENTS. PEOPOSITIOX 23. PROBLEM, At a given 2yomt in a given straight line^ to make arectilineal angle equal to a given rectilineal angle. Let AB he the given straight line, and A the givenpoint in it, and DOE the given rectilineal angle : it isrequired to make at the given point A, in the given straightline AB, an angle equal to the given rectilineal angleDCE. In CD, CE take anypoints D, E, and join the triangle AFG thesides of which shall be equalto the three straight lines CD, DE, EC; so that .-li^shall be equal to CD, AG to CE, and FG to DE. [I. angle FAG shall beequal to the angle DCE. Because FA, AG are equal to DC, CE, each to each,and the base FG equal to the base DE; [Construction. therefore the angle FAG is equal to the angle DCE. [I. 8. Wherefore at the given point A in the given straightline AB, the angle FAG has teen made equal to the givenrectilineal angle DCE. PROPOSITION 24. THEOREM. If two triangles have two sides of the one equal to ticosides of the other, each to each, but the angle contained hythe tico sides of one of them greater than the angle con-tained hy the two sides equal to them, of the other, the baseof that ichich has the greater angle shall he greater thanthe base of the oilier. Let ABC, DEF be two triangles, which have the twosides AB, AC, equal to the two sides DE, DF, each toeach, namelv, AB to DE, and AC to DF, but the anglt^^C greater than the angle EDF: the base BC shall be
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Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
