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

### From inside the book

Results 1-5 of 34

Page 5

... of AB , BC , CA. 10 , Let ABCD be the quadril .; BD , AC its diags .; then AB +

BC > AC ; AD + DC > AC . Hence perim . > twice diag . AC . Similarly perim . >

twice diag . BD . That is , twice perim . > twice sum of diagonals . Let the

of A ...

... of AB , BC , CA. 10 , Let ABCD be the quadril .; BD , AC its diags .; then AB +

BC > AC ; AD + DC > AC . Hence perim . > twice diag . AC . Similarly perim . >

twice diag . BD . That is , twice perim . > twice sum of diagonals . Let the

**bisector**of A ...

Page 6

Let o be any pt . on

AOQ are clearly equal in all respects [ 1. 26 ] ; .. OP = OQ . 4. Here angles at O

are equal [ 1. 15 ) ; LAXO = BYO , being rt . 28 ; and AO = OB ; .. As AOX , BOY

are ...

Let o be any pt . on

**bisector**of BAC ; OP , OQ perps . on AC , AB ; then As AOP ,AOQ are clearly equal in all respects [ 1. 26 ] ; .. OP = OQ . 4. Here angles at O

are equal [ 1. 15 ) ; LAXO = BYO , being rt . 28 ; and AO = OB ; .. As AOX , BOY

are ...

Page 8

Let the

suppt . of LABC . 8. Let ABCD be the quadril . with _ 8 at D and C bisected by DO

, CO . Then twice the sum of _ S DOC , ODC , OCD = 4 rt . L $ -- the of the four ...

Let the

**bisectors**be BO , CO ; then - BOC = suppt . of sum of _ S OBC , OCB =suppt . of LABC . 8. Let ABCD be the quadril . with _ 8 at D and C bisected by DO

, CO . Then twice the sum of _ S DOC , ODC , OCD = 4 rt . L $ -- the of the four ...

Page 11

In A ABC let the external

the suppt ... But if px is greater than Py , let the

and ...

In 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 isthe suppt ... But if px is greater than Py , let the

**bisector**of the - XOY meet Px in Q ;and ...

Page 44

Let the

DC and LADB = L ADC [ 1. 4 ) . .. AD passes through the centre . 3. If the chords

are not par ? . , bisect each at rt . 2 are par . , join their extremities : and bisect ...

Let the

**bisector**of < BAC cut BC in D. Then in As ADB , ADC , it follows that DB =DC and LADB = L ADC [ 1. 4 ) . .. AD passes through the centre . 3. If the chords

are not par ? . , bisect each at rt . 2 are par . , join their extremities : and bisect ...

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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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