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

### From inside the book

Results 1-5 of 64

Page 50

The

The pt . of contact is in the line of centres ( 111. 11 , 12 ] , .. the st . line drawn from

the pt . of contact perp . to the line of centres is a

The

**tangents**are perp . to the same diameter , and therefore parallel ( 1. 28 ] . 3.The pt . of contact is in the line of centres ( 111. 11 , 12 ] , .. the st . line drawn from

the pt . of contact perp . to the line of centres is a

**tangent**to both circles [ 111. Page 51

The chords of the outer which are

] and are bisected at the pt . of contact [ Ex . 4 , p . 181 ] . Hence the

is the halfchords , are equal . 4. The

The chords of the outer which are

**tangents**to the inner are equal [ Ex . 5 , p . 181] and are bisected at the pt . of contact [ Ex . 4 , p . 181 ] . Hence the

**tangents**, thatis the halfchords , are equal . 4. The

**tangent**at an extremity of a diameter is ... Page 52

Then OB , being perp . to

OB , ..LABO = LOAB . : . AB bisects L CAD . Draw DF perp . 15. Let o be centre ,

and let AT , BT ' be two equal

Then OB , being perp . to

**tangent**BD , is par . to AD . .. [ DAB = LABO . But OA =OB , ..LABO = LOAB . : . AB bisects L CAD . Draw DF perp . 15. Let o be centre ,

and let AT , BT ' be two equal

**tangents**at A and B. Then OT = OT ' [ III . 18 and 1. Page 53

Let the line drawn parallel to the '

given radius cut the centre ' line in Then O is the required centre . Two solutions .

20. Describe a O concentric with the given O , having its radius equal to the sum ...

Let the line drawn parallel to the '

**tangent**' line at a distance from it equal to thegiven radius cut the centre ' line in Then O is the required centre . Two solutions .

20. Describe a O concentric with the given O , having its radius equal to the sum ...

Page 56

Let

DC ( 111. 19 ] . But DC is also perp . to AB . ... DC bisects AB [ 111. 3. ] Hence arc

ADB is bisected at D [ 111. 30 ] . 2. Let CB be the quadrant , A the centre . On AB

...

Let

**tangent**at D be par . to AB . Then , if DC be perp . to**tangent**, the centre is inDC ( 111. 19 ] . But DC is also perp . to AB . ... DC bisects AB [ 111. 3. ] Hence arc

ADB is bisected at D [ 111. 30 ] . 2. Let CB be the quadrant , A the centre . On AB

...

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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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