## A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |

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Page 8

Hence the A ' DEA , DEC are

Hence the A ' DEA , DEC are

**identically equal**( 1. 4 ] . .. DAC = L DCA , and hence DCB = DBC . 6 . Let ABC be the rt . On BC describe an equilat . ABDC ; bisect 2 DBC by BE ; then · ABC is trisected by BD , BE . Page 15

AR AOB , AOC are equal in all respects ( I. 8 ] . 8. In AS BAD , DAE , 2 BAD = L DAE , LBDA = L ADE , and AD is common . . : . BD = DE [ 1. 26 ] . 9. By hypothesis AB = AD , BC = CD , AC is common ; .. As ABC , ADC are

AR AOB , AOC are equal in all respects ( I. 8 ] . 8. In AS BAD , DAE , 2 BAD = L DAE , LBDA = L ADE , and AD is common . . : . BD = DE [ 1. 26 ] . 9. By hypothesis AB = AD , BC = CD , AC is common ; .. As ABC , ADC are

**identically equal**... Page 16

Let the median AD bisect BC ; produce AD to E making DE equal to AD , join EC . Then AS ABD , EDC are

Let the median AD bisect BC ; produce AD to E making DE equal to AD , join EC . Then AS ABD , EDC are

**identically equal**( 1. 4 ] and AB = CE . Now AC + CE > AE ( 1. 2C ] . That is , AB + AC > 2AD . 9. This follows at once from Ex . 8 ... Page 17

26 ] . 6. The two A $ formed are

26 ] . 6. The two A $ formed are

**identically equal**( 1. 29 , 1. 26 ) . 7. Let o be pt . equidist . from the parts , and let POQ , XOY be drawn to cut them . Draw LOM perp . to the parls ; then A $ LOP , MOQ are**identically equal**( 1. Page 18

Through P draw PQ part . to AC meeting AB in Q ; on QB make QX equal to AQ ; join XP and produce it to meet AC in Y. Then QP drawn from middle pt . of Ax par- . to AY bisects XY [ Ex . 1 ] ... Then AS ABE , CDF are

Through P draw PQ part . to AC meeting AB in Q ; on QB make QX equal to AQ ; join XP and produce it to meet AC in Y. Then QP drawn from middle pt . of Ax par- . to AY bisects XY [ Ex . 1 ] ... Then AS ABE , CDF are

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A Key to the Exercises and Examples Contained in a Text-Book of Euclid's ... H S 1848-1934 Hall No preview available - 2018 |

A Key to the Exercises and Examples Contained in a Text-Book of Euclid's ... H. S. Hall No preview available - 2017 |

### Common terms and phrases

ABCD angles Assistant base bisector bisects BOOK Cambridge centre chord circle College common constant containing describe diam diameter distance draw drawn Edited ELEMENTARY ENGLISH equal EXAMPLES Exercises external Fcap Fellow figure fixed four given given st greater GREEK half Hence HISTORY identically equal Illustrated inscribed intersect Introduction JOHN Join LATIN Let ABC locus Master Mathematics meet middle point Notes parl parm passes perp plane preparation Press produced Prof Professor proved radius ratio rect respectively revised School segment shewn sides similar Similarly solutions Take tangent touch Translated triangle twice University vols

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