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

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Page 2

Then AS ABD , BCD have their sides

Similarly for the other pair of angles . 5. Here L YAB - = _ YBA ; and _ XAB LXBA ;

.. XAY : L XBY . Join XY , then it easily follows that A XAY = AXBY in all respects .

6 .

Then AS ABD , BCD have their sides

**respectively**equal ; .. DAB = _ DCB .Similarly for the other pair of angles . 5. Here L YAB - = _ YBA ; and _ XAB LXBA ;

.. XAY : L XBY . Join XY , then it easily follows that A XAY = AXBY in all respects .

6 .

Page 3

Let D , E , F be middle pts . of BC , CA , AB

AF = BF , AE = BD , and _FAE = ZFBD . : . FE = FD . Similarly DE = FE = FD . 10.

In A8 CBF , BCE , CF = BE by constr . , BC is common , and - FCB = · EBC , : .

Let D , E , F be middle pts . of BC , CA , AB

**respectively**; then in AS AFE , BFD ,AF = BF , AE = BD , and _FAE = ZFBD . : . FE = FD . Similarly DE = FE = FD . 10.

In A8 CBF , BCE , CF = BE by constr . , BC is common , and - FCB = · EBC , : .

Page 7

Let PQ , QR be par to AB , BC

PQO = int . opp . Z ABQ , and L RQO = int . opp . L CBQ . Hence the sum or diff . of

_ $ PQO , RQO = the sum or diff . of * AB , CBQ ; .. – PQR - ABC . Similarly for the

...

Let PQ , QR be par to AB , BC

**respectively**. Join BQ and produce it to 0. Then <PQO = int . opp . Z ABQ , and L RQO = int . opp . L CBQ . Hence the sum or diff . of

_ $ PQO , RQO = the sum or diff . of * AB , CBQ ; .. – PQR - ABC . Similarly for the

...

Page 8

...

and AD = DB ; .. DF = AE . [ 1. 26. ] Also from the As EDC , FDC , it may be shewn

that DF = EC [ 1. 26 ] . .. AE EC . Hence the A ' DEA , DEC are identically equal ...

...

**respectively**. Then in A8 AED , DFB , LADE = int . DBF . rt . — AED = rt . DFB ,and AD = DB ; .. DF = AE . [ 1. 26. ] Also from the As EDC , FDC , it may be shewn

that DF = EC [ 1. 26 ] . .. AE EC . Hence the A ' DEA , DEC are identically equal ...

Page 10

... two sides might be produced in either direction . Hence the no . of

constructions is 2 x 2 x 2 , or 8 . Exceptional case , when A is situated at the

vertex of an equilat . A on BC . 2. In fig . to Prop . 15 let EX , EY bisect _ S BEC ,

AED

... two sides might be produced in either direction . Hence the no . of

constructions is 2 x 2 x 2 , or 8 . Exceptional case , when A is situated at the

vertex of an equilat . A on BC . 2. In fig . to Prop . 15 let EX , EY bisect _ S BEC ,

AED

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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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