. Elements of geometry : containing books I to III. es, and AF, FG the other Ds, which make up the wholefigure ABCD, and which are .. called the a must complement AF=com lement V BD is a diagonal of CD A . CDJ5 respectively, then remaining ZZ7 AF= remaining ZZ7 /•>. ,\x. 3. Q. E. D. Ex. l. If through a point Q, within a parallelogramABCD-, two straight lines are drawn parallel to 1and rhe parallelograms OB, OD are equal ; the point 0 isin the diagonal JC. , AB(D is a parallelogram, AMN a straight linemeeting the Bides L, 7> (one of them being prodM, N. Shew tha
. Elements of geometry : containing books I to III. es, and AF, FG the other Ds, which make up the wholefigure ABCD, and which are .. called the a must complement AF=com lement V BD is a diagonal of CD A . CDJ5 respectively, then remaining ZZ7 AF= remaining ZZ7 /•>. ,\x. 3. Q. E. D. Ex. l. If through a point Q, within a parallelogramABCD-, two straight lines are drawn parallel to 1and rhe parallelograms OB, OD are equal ; the point 0 isin the diagonal JC. , AB(D is a parallelogram, AMN a straight linemeeting the Bides L, 7> (one of them being prodM, N. Shew that tliu triangle MBN is equal to tfa . 7o EUCLIDS [Book L Proposition XLTV. Problem. 7V> a given straight line t apply n pa eto, which shall In equal to a given triangle, and have oiequal to a given S A. • AB be the given t. line, G the risen a, D the .ivtU L . It it required to api ly to AB a EJ = A (7ami I of iU 18*=* L l>. Make a /Z7= aC, and having one oi itaangles= t J>, I. 42. and suppose it to be removed to such .. position that one ofthe sides containing this angle is in the same st. line with A />.and let the ZZ7 be denoted by BE1 ? Produce FO to //, draw A I! || to BG or /;/•, ami join V /•// n .-. sum tvro if. z s ; I. 20 .*. sum nf l s 1IKr. III!... -/iL, J^B will meel il produced towards .in meelThrough K draw A I or FI1, and produce HA, OB to fif, Then ///A A is a /~7. and //A is its diagonal ;and . I/. .U/. iouI //A, .. complement /•/. con plI\ I .*. CJBL= ;.. Book I.] PROPOSITION XLV. 71 Proposition XLV. Problem. To describe a parallelogram,, which shall be equal to arectilinear figure, and have one of its angles equal to aang
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