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

### From inside the book

Results 6-10 of 49

Page 19

Let the diagonals

CY = 2EF [ Ex . 17 , p . 98 ] = DB + BQ , since E is the middle pt . of the diagonals (

Ex . 5 , p . 64 ] . 22. From D in base BC let DE , DF be drawn perp . to AC , AB ...

Let the diagonals

**intersect**in E , and let EF be perp . to the given line . Then AX +CY = 2EF [ Ex . 17 , p . 98 ] = DB + BQ , since E is the middle pt . of the diagonals (

Ex . 5 , p . 64 ] . 22. From D in base BC let DE , DF be drawn perp . to AC , AB ...

Page 21

... the angle of an equilat . A. Through P and a draw st . lines par ! to AC , BD

meeting AB in X and Y and

o be the given pt . , THEOREMS AND EXAMPLES ON BOOK I. PAGES 101 , 102.

21.

... the angle of an equilat . A. Through P and a draw st . lines par ! to AC , BD

meeting AB in X and Y and

**intersecting**in Z. Then XYZ is the required A. 16 . Leto be the given pt . , THEOREMS AND EXAMPLES ON BOOK I. PAGES 101 , 102.

21.

Page 25

37 ] ; .. ARBX AQCX . Again A ABQ = ABQC ; .. by taking away the equal AS RBX

, QCX , the area AQXR = ABXC . 13 . Let ABCD be the quad ' . , and P , Q , R , S

the middle points of the sides AB , BC , CD , DA . Draw AC , BD

37 ] ; .. ARBX AQCX . Again A ABQ = ABQC ; .. by taking away the equal AS RBX

, QCX , the area AQXR = ABXC . 13 . Let ABCD be the quad ' . , and P , Q , R , S

the middle points of the sides AB , BC , CD , DA . Draw AC , BD

**intersecting**at o . Page 26

( ii ) If o is within 4 DAB and its opp . vert . L , then AO

that the perp . from c on OA is equal to the diff . of the perps . drawn from B and D

to OA ( Ex . 20 , p . 99 ) . Therefore since the As OAC , OAD , OAB are on the

same ...

( ii ) If o is within 4 DAB and its opp . vert . L , then AO

**intersects**the parm . ; sothat the perp . from c on OA is equal to the diff . of the perps . drawn from B and D

to OA ( Ex . 20 , p . 99 ) . Therefore since the As OAC , OAD , OAB are on the

same ...

Page 30

... touches at one , or does not meet it at all . IX . On Loci . Page 117 . 4. The locus

is a concentric circle whose radius is equal to the sum or difference of the radius

of given circle and the given distance . 5. Let OA , OB be the two

... touches at one , or does not meet it at all . IX . On Loci . Page 117 . 4. The locus

is a concentric circle whose radius is equal to the sum or difference of the radius

of given circle and the given distance . 5. Let OA , OB be the two

**intersecting**st ...### 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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