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

### From inside the book

Results 1-5 of 74

Page vii

Exx . 38 and 39 are removed to page 382 , where they

and 60 . For Ex . 38 read , “ Given the base and vertical angle of a triangle , shew

that one angle and one side of the pedal triangle are constant . " For Ex . 39 read

...

Exx . 38 and 39 are removed to page 382 , where they

**take**the place of Exx . 59and 60 . For Ex . 38 read , “ Given the base and vertical angle of a triangle , shew

that one angle and one side of the pedal triangle are constant . " For Ex . 39 read

...

Page 2

Page 25 . 3.

common , and < DCX = _ ECX , being rt . _ $ . ... DX = EX . Page 27 . 1. Let A be

the vertex and BC the base bisected at D. Then BD = DC , AD is common , and

AB = AC .

Page 25 . 3.

**Take**a pt . X on CF , or CF produced . Then DC = CE , CX iscommon , and < DCX = _ ECX , being rt . _ $ . ... DX = EX . Page 27 . 1. Let A be

the vertex and BC the base bisected at D. Then BD = DC , AD is common , and

AB = AC .

Page 5

BC is less than BA and AC together ;

is less than BA . 8. Let ABCD be a quadril . whose sides BA , CD meet in O. Then

AO and OD are together > AD . .. the sum of OA , AB , BC , CD , OD > the sum of ...

BC is less than BA and AC together ;

**take**AC from both , then diff . of BC and ACis less than BA . 8. Let ABCD be a quadril . whose sides BA , CD meet in O. Then

AO and OD are together > AD . .. the sum of OA , AB , BC , CD , OD > the sum of ...

Page 9

. Thus the interior angles are together equal to 6 rt . 28 .. the int . s together with 4

rt . į 8 = 10 rt . L's . Similarly the corollary may be proved for a fig . of any ...

**Take**the fig . on p . 60 . Join DA , DB ; then the five - sided fig . is divided into 3 As. Thus the interior angles are together equal to 6 rt . 28 .. the int . s together with 4

rt . į 8 = 10 rt . L's . Similarly the corollary may be proved for a fig . of any ...

Page 12

ABCD = ACDF . .. AS EAB , AKB together = A $ CDF , DKC . 2. See solution to Ex

. 3 on p . 65 . 3. Let AB be the base of given A ABC , and let PQ be the st . line in ...

**Take**away AKD from each and the remainders are equal . ( 2 ) AEAB A ABC =ABCD = ACDF . .. AS EAB , AKB together = A $ CDF , DKC . 2. See solution to Ex

. 3 on p . 65 . 3. Let AB be the base of given A ABC , and let PQ be the st . line in ...

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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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