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

### From inside the book

Results 1-5 of 41

Page 8

L. 7. 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

...

L. 7. 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 12

Again , since the

pair of opp . _ s are supplementary . Join AC , BD ; then in AS DEB , ABC , – DEB

= suppt . of BCD = 1 ABC , and DE , EB = AB , BC respectively ; .. DB = AC .

Again , since the

**four**_ s of the fig . are together equal to**four**rt . 2 $ , the otherpair of opp . _ s are supplementary . Join AC , BD ; then in AS DEB , ABC , – DEB

= suppt . of BCD = 1 ABC , and DE , EB = AB , BC respectively ; .. DB = AC .

Page 28

Then _ BCM = suppt . of - ACB = Z ECK , and A8 BCM , ECK are identically equal

( 1. 4 ) . Therefore sq . on EK = sq . on BM = sum of sqq . on BA , AM ( 1. 47 ] = sq .

on BA with

Then _ BCM = suppt . of - ACB = Z ECK , and A8 BCM , ECK are identically equal

( 1. 4 ) . Therefore sq . on EK = sq . on BM = sum of sqq . on BA , AM ( 1. 47 ] = sq .

on BA with

**four**times sq . on AC . ( iii ) Sq . on EK = sq . 28 KEY TO EUCLID . Page 29

( iii ) Sq . on EK = sq . on AB , with

with

five times sq . on AC = five times sq . on BC . 42. Let AB be divided at C ; from c ...

( iii ) Sq . on EK = sq . on AB , with

**four**times sq . on AC , sq . on FD = sq . on AC ,with

**four**times sq . on AB ; .. sum of sqq . on EK , FD = five times sq . on AB withfive times sq . on AC = five times sq . on BC . 42. Let AB be divided at C ; from c ...

Page 31

The diagonals of a par " , divide it into

inters ” . of the diagonals . Thus the problem is the same as in Ex . 10 , and the

required locus is a st . line through the inters . of the diagonals parl . to the given ...

The diagonals of a par " , divide it into

**four**equal A ' having their vertices at theinters ” . of the diagonals . Thus the problem is the same as in Ex . 10 , and the

required locus is a st . line through the inters . of the diagonals parl . to the given ...

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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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