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

### From inside the book

Results 6-10 of 39

Page 23

ON THE CONSTRUCTION OF

Let the given diff . be equal to AB and the hypotenuso equal ... Thus CBX is the

required

ON THE CONSTRUCTION OF

**TRIANGLES**WITH GIVEN PARTS . Page 107 . 2.Let the given diff . be equal to AB and the hypotenuso equal ... Thus CBX is the

required

**triangle**. 5. This is clearly a particular case of the preceding example . 6. Page 27

Let X , Y be the two given A $ . If they are not on equal bases , make a

equal to Y and having a base equal to that of x [ Ex . 21 , p . 111 ] . The

construction now follows easily by Ex . 16 ( i ) , p . 110 . 27. Through A draw AD

part . to BC ...

Let X , Y be the two given A $ . If they are not on equal bases , make a

**triangle**zequal to Y and having a base equal to that of x [ Ex . 21 , p . 111 ] . The

construction now follows easily by Ex . 16 ( i ) , p . 110 . 27. Through A draw AD

part . to BC ...

Page 28

Let ABC be a

through a pt . X in AB . Take BD a fifth part of BC [ Ex . 19 , p . 99 ) . Join AD , and

through X draw Xe to meet BC in E , so that ABXE = A ABD [ Ex . 21 , p . 111 ] . 40

.

Let ABC be a

**triangle**from which it is required to cut off a fifth part by a st . linethrough a pt . X in AB . Take BD a fifth part of BC [ Ex . 19 , p . 99 ) . Join AD , and

through X draw Xe to meet BC in E , so that ABXE = A ABD [ Ex . 21 , p . 111 ] . 40

.

Page 32

C1 , C , and there will be two

data . This last case however requires that Y shall be less than AB , for then both

pts . C1 , C , will lie on AZ on the same side of A. If one of these pts . C , lies on ...

C1 , C , and there will be two

**triangles**ABC1 , ABC , each of which satisfy thedata . This last case however requires that Y shall be less than AB , for then both

pts . C1 , C , will lie on AZ on the same side of A. If one of these pts . C , lies on ...

Page 37

Let ABC be the isosceles

the base BC produced . Join AQ , and draw AP perp . to BC . Then it may be

shewn by 1. 26 that BC is bisected at P. Hence by 11. 6 , BQ , QC + PO = PQ ?

Let ABC be the isosceles

**triangle**having its vertex at A , and let Q be any point inthe base BC produced . Join AQ , and draw AP perp . to BC . Then it may be

shewn by 1. 26 that BC is bisected at P. Hence by 11. 6 , BQ , QC + PO = PQ ?

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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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