## 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 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 . For 4 DBC = two - thirds

of a rt .

Hence the A ' DEA , DEC are

**identically equal**( 1. 4 ] . .. DAC = L DCA , andhence 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 . For 4 DBC = two - thirds

of a rt .

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**( 1. Page 16

The exceptional case is when o is at the intersection of the diagonals . 8. Let the

median AD bisect BC ; produce AD to E making DE equal to AD , join EC . Then

AS ABD , EDC are

The exceptional case is when o is at the intersection of the diagonals . 8. 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. Page 17

Let POQ be terminated by the parls . at P , Q , and bisected at O ; through o draw

XOY perp . to the parls .; then As XOP , YOQ are

two A $ formed are

Let POQ be terminated by the parls . at P , Q , and bisected at O ; through o draw

XOY perp . to the parls .; then As XOP , YOQ are

**identically equal**( 1. 26 ] . 6. Thetwo A $ formed are

**identically equal**( 1. 29 , 1. 26 ) . 7. Let o be pt . equidist ... 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 ] . 8. ... 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 ] . 8. ... Then AS ABE , CDF are

**identically equal**( 1.### What people are saying - Write a review

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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 double 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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