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 . her equal to two right FG is in the same straight line with GL. [I. 14. And because^i^is parallel to HG, and HG to ML,[ is parallel to ML ; [I. 30. and KM, FL are parallels ; {Construction. therefore IZFLMi^ a parallelogram. [Definition. And because the triangle ABD is equal to the parallelo-gram HF, [ the triangle BBC to the parallelogram GM; [ whole rectilineal figure ABCD is
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 . her equal to two right FG is in the same straight line with GL. [I. 14. And because^i^is parallel to HG, and HG to ML,[ is parallel to ML ; [I. 30. and KM, FL are parallels ; {Construction. therefore IZFLMi^ a parallelogram. [Definition. And because the triangle ABD is equal to the parallelo-gram HF, [ the triangle BBC to the parallelogram GM; [ whole rectilineal figure ABCD is equal to the wholeparallelogram KFLM. [A xiom , the parallelogram KFLM haa heen de-scribed equal to the given rectilineal figure ABCD, andhaving the angle FKM equal to the given angle E. From this it is manifest, how to a givenstraight line, to apply a parallelogram, which shall have anangle equal to a given rectilineal angle, and shall be equalto a given rectilineal figure: namely, by applying to thegiven straight line a parallelogram equal to the first tri-angle ABD, and having an angle equal to the given angle ;and so on. [I. BOOK I. 4G. 49 PROPOSITION 46. describe a square on a given straight line. Let AB be the given straight line: it is required todescribe a square on AB. From the point A draw ACat right angles to AB; [I. 11. and make AD equal ioAB; [ D draw DE parallel toAB; and through B draw BE[.arallel to ^Z>. [ A DEB shall be a square. For A DEB is by constructiona parallelogram; therefore AB m equal to DE,and ^Z> to BE. [I. 34. JBuc yli5 is equal to ^Z>. [Construction. Therefore the four straight lines BA, AD, DE, EB areequal to one another, and the parallelogram A DEB isequilateral. {Axiom 1. Likewise all its angles are riglit since the straight line AD meets the parallels AB,DE, the angles BAD, ADE are together cqu;xl to tworight angles ; [T. 29. but BAD is a right angle ; [Constructio
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