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

### From inside the book

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Page vi

Read , “ In any triangle , if a circle is described from the middle point of one side

as centre and with a radius equal to

touch the circles described on these sides as diameters . ” Page 235 , Ex . 18.

Read , “ In any triangle , if a circle is described from the middle point of one side

as centre and with a radius equal to

**half**the sum of the other two sides , it willtouch the circles described on these sides as diameters . ” Page 235 , Ex . 18.

Page 2

Bisect the given st . line , and with the

isosc . A as in Ex . 1 , page 13 . Page 25 . 3. Take a pt . X on CF , or CF produced

. Then DC = CE , CX is common , and < DCX = _ ECX , being rt . _ $ . ... DX = EX .

Bisect the given st . line , and with the

**half**line for the equal sides describe anisosc . A as in Ex . 1 , page 13 . Page 25 . 3. Take a pt . X on CF , or CF produced

. Then DC = CE , CX is common , and < DCX = _ ECX , being rt . _ $ . ... DX = EX .

Page 3

Page 29 . 1. In AABC let BC be produced both ways to X and Y. Then _ s ABC ,

ACB are supplementary to equal angles , and are therefore equal . 2. In the fig .

the _ * XOB , YOB together make up

Page 29 . 1. In AABC let BC be produced both ways to X and Y. Then _ s ABC ,

ACB are supplementary to equal angles , and are therefore equal . 2. In the fig .

the _ * XOB , YOB together make up

**half**the _ * AOB , BOC ; that is ,**half**of 2 rt . Page 11

Hence LBDC = the angle at A together with

A ABC let the external bisectors of $ B and C meet at F , and the internal bisectors

at E. Then by Ex . 2 , page 29 each of _ SEBF , ECF is a rt . L. 1. LF is the suppt ...

Hence LBDC = the angle at A together with

**half**the sum of the base angles . 7. InA ABC let the external bisectors of $ B and C meet at F , and the internal bisectors

at E. Then by Ex . 2 , page 29 each of _ SEBF , ECF is a rt . L. 1. LF is the suppt ...

Page 13

Page 74 . 1. Parm . AY =

be a diagonal of sq . ABCD . At B draw BE perp . to DB meeting DC produced in

E. Then _ CBE =

.

Page 74 . 1. Parm . AY =

**half**parm . AC , and AAZB =**half**parm . AY . 2. Let BDbe a diagonal of sq . ABCD . At B draw BE perp . to DB meeting DC produced in

E. Then _ CBE =

**half**a rt . L , and A * DCB , ECB are equal in all respects [ 1. 26 ).

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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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