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

### From inside the book

Page 5

Hence

Hence

**twice**the sum of OA , OB , OC > the sum 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 . 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

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 . Page 9

And the sum of all the _s of these As =

And the sum of all the _s of these As =

**twice**as many rt . as the fig . has sides . . : . the at the vertices together with 8 rt . _ $ =**twice**as many rt . - as the fig . has sides . Page 64 . The sum of each pair of adjacent _ is equal ... Page 13

DB = BE , and ADBE =

DB = BE , and ADBE =

**twice**A DCB = given square . 3 . AS AXB , BYC are each of them half of given parm . 4. Through p draw XY par ! to AB or DC . Then AAPB is half parm . Ay , and A DPC is half parm . XC . Page 75 . 1. Page 14

The other case is similar . 3. It is easy to see that AS ACX , BCY are equal in all respects [ 1. 4 ] . .. AX = BY . Similarly BY = cz . 4. Let BD be the diagonal of sq . ABCD . Then DB = sum of sqq . on DC , BC =

The other case is similar . 3. It is easy to see that AS ACX , BCY are equal in all respects [ 1. 4 ] . .. AX = BY . Similarly BY = cz . 4. Let BD be the diagonal of sq . ABCD . Then DB = sum of sqq . on DC , BC =

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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 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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