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

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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 half the sum of the other two sides , it will

touch the circles described on these sides as

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 will

touch the circles described on these sides as

**diameters**. ” Page 235 , Ex . 18. Page 48

Draw the parallel

ACD , .. ext . _ EAC ... Let A be any pt . on the circumference : ACB the

AD any other chord . Then CB = CD ; .. AB = AC + CD > AD . And if AF is nearer to

...

Draw the parallel

**diameters**DAE , FBG . Then , because AD = AC , .. LADC = LACD , .. ext . _ EAC ... Let A be any pt . on the circumference : ACB the

**diameter**,AD any other chord . Then CB = CD ; .. AB = AC + CD > AD . And if AF is nearer to

...

Page 50

Draw a

either extremity of the

the tangents , ( i ) and ( ii ) , required . 2. The tangents are perp . to the same

Draw a

**diameter**( i ) at right angles to , ( ii ) par . to the given straight line . Ateither extremity of the

**diameter**draw a line perp . to the**diameter**. These will bethe tangents , ( i ) and ( ii ) , required . 2. The tangents are perp . to the same

**diameter**... Page 51

The tangent at an extremity of a

par !. to it are bisected by the

. to the given st . line through the given pt . [ 111. 19 ] . 6. The required locus is ...

The tangent at an extremity of a

**diameter**is perp . to the**diameter**. .. the chordspar !. to it are bisected by the

**diameter**[ 111. 3 ] . 5. The required locus is the perp. to the given st . line through the given pt . [ 111. 19 ] . 6. The required locus is ...

Page 52

Let BCD be given 0 , EBF the given

and equal to the required length . Join AE cutting the o in D. to ED meeting EBF

in F. Then the tangent DF = AB , the given length . Hence F is the required pt . 17.

Let BCD be given 0 , EBF the given

**diameter**produced . Draw BA perp . to EBand equal to the required length . Join AE cutting the o in D. to ED meeting EBF

in F. Then the tangent DF = AB , the given length . Hence F is the required pt . 17.

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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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