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

### From inside the book

Results 6-10 of 33

Page 16

This follows at once from Ex . 8 , since

LACD is greater than DAC ; similarly L DBA is greater than - DAB . Hence the

sum of ...

This follows at once from Ex . 8 , since

**twice**the sum of the sides is greater than**twice**the sum of the medians . 10 . Let the median AD bisect BC . If AD > DC ,LACD is greater than DAC ; similarly L DBA is greater than - DAB . Hence the

sum of ...

Page 22

From B draw BC equal to N ; and on BC describe a ABFC , having BF equal to

EA equal to CE . Join BA . Then BA , BE , BC are the required lines . For BC = N ...

From B draw BC equal to N ; and on BC describe a ABFC , having BF equal to

**twice**M and CF equal to L. Bisect BF at E. Join CE , and produce it to A , makingEA equal to CE . Join BA . Then BA , BE , BC are the required lines . For BC = N ...

Page 26

BO and DO =

20. Draw BO part . to the diag . AC , and co parl . to AB ; then ABOC is a parm .

Also the perp . from Don Bo is equal to the sum of perp . from D on AC and perp ...

BO and DO =

**twice**the diff . between As AOB and DOA = 2 AAOC ( Ex . 18. ii . ] .20. Draw BO part . to the diag . AC , and co parl . to AB ; then ABOC is a parm .

Also the perp . from Don Bo is equal to the sum of perp . from D on AC and perp ...

Page 36

BE =

. to BC . Then by II . 4 , BC2 -- BX2 + XO2 + 2BX . ХС . To each of these equals

add 2. Ax ?. So that BC + 2AX ? = BX ? + AX® + XC ? + AX2 + 2BX . XC = AB ” +

...

BE =

**twice**the rectangle ABCD . 6. Let ABC be the given A. From A draw AX perp. to BC . Then by II . 4 , BC2 -- BX2 + XO2 + 2BX . ХС . To each of these equals

add 2. Ax ?. So that BC + 2AX ? = BX ? + AX® + XC ? + AX2 + 2BX . XC = AB ” +

...

Page 48

_ EAC =

because AE , BF are par ! . LACD _ BCG . :: DC , CG are in a st . line ; that is , the

st . line joining GD passes through c . 9. Let A , B be the centres of the two Os ;

and D ...

_ EAC =

**twice**- ACD . Similarly , L CBF =**twice**- BCG . But L EAC = L CBF ,because AE , BF are par ! . LACD _ BCG . :: DC , CG are in a st . line ; that is , the

st . line joining GD passes through c . 9. Let A , B be the centres of the two Os ;

and D ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

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

### Popular passages

Page 6 - BLACKIE— GREEK AND ENGLISH DIALOGUES FOR USE IN SCHOOLS AND COLLEGES. By JOHN STUART BLACKIE, Professor of Greek in the University of Edinburgh.

Page 13 - THE THIRD AND FOURTH COURSES, consisting of Long Vowels, and all the Double Vowels in the Language. 6d. 1 " These are admirable books, because they are constructed on a principle, and that the simplest principle on which it is possible to learn to read English."— SPECTATOR.

Page 13 - TAYLOR— WORDS AND PLACES; or, Etymological Illustrations of History, Ethnology, and Geography. By the Rev. ISAAC TAYLOR, MA Third and cheaper Edition, revised and compressed. With Maps. Globe 8vo. 6s.

Page 7 - FIRST GREEK READER. Edited after KARL HALM, with Corrections and large Additions by Professor JOHN EB MAYOR, MA, Fellow of St. John's College, Cambridge. New Edition, revised.

Page 26 - Crown 8vo. gr. 6d. GRAVITATION: an Elementary Explanation of the Principal Perturbations in the Solar System.

Page 17 - Also a Small Chart on a Card, price id. EASY LESSONS IN ARITHMETIC, combining Exercises in Reading, Writing, Spelling, and Dictation. Part I. for Standard I. in National Schools. Crown 8vo.

Page 25 - SHANN— AN ELEMENTARY TREATISE ON HEAT, IN RELATION TO STEAM AND THE STEAM-ENGINE. By G. SHANN, MA With Illustrations. Crown 8vo.

Page 10 - Hales.— LONGER ENGLISH POEMS. With Notes, Philological and Explanatory, and an Introduction on the Teaching of English. Chiefly for use in Schools. Edited by JW HALES, MA, Professor of English Literature at King's College, London, &c. &c. Fifth Edition. Extra fcap. 8vo. 4*.

Page 33 - Conflicts of Capital and Labour Historically and Economically considered. Being a History and Review of the Trade Unions of Great Britain, showing their Origin, Progress, Constitution, and Objects, in their Political, Social, Economical, and Industrial Aspects.

Page 13 - THE ENGLISH METHOD OF TEACHING TO READ. By A. SONNENSCHEIN and JMD MEIKLEJOHN, MA Fcap. 8vo. COMPRISING : THE NURSERY BOOK, containing all the Two-Letter Words in the Language, id. (Also in Large Type on Sheets for School Walls. 5*.) THE FIRST COURSE, consisting of Short Vowels with Single Consonants.