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

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Page 23

( See

the construction and proof given on p . 90 , it is shewn that AX = XC , and BX =

BC . Thus CBX is the required triangle . 5. This is clearly a particular case of the ...

( See

**Note**to Ex . 1. ] 3. See fig . on p . 89. Let AB be the given sum , then usingthe construction and proof given on p . 90 , it is shewn that AX = XC , and BX =

BC . Thus CBX is the required triangle . 5. This is clearly a particular case of the ...

Page 43

And as P is a fixed point , Q is determined . 41. This is the same as dividing a line

externally in medial section . ( See Ex . 21 , p . 146 , and p . 139 ,

Draw the rect . ABDH , contained by THEOREMS AND EXAMPLES ON BOOK II .

And as P is a fixed point , Q is determined . 41. This is the same as dividing a line

externally in medial section . ( See Ex . 21 , p . 146 , and p . 139 ,

**note**. ] 42 .Draw the rect . ABDH , contained by THEOREMS AND EXAMPLES ON BOOK II .

Page 66

ABCD be the quad ' . , and P , Q , R , S the points of contact of the sides AB , BC ,

CD , DA . Then AS = AP [ 111. 17 , Cor . ] and DS = DR ; : . by addition AD = AP ...

**NOTE**. The LPOQ = one rt . gle + half the < at A. ( See Ex . 36 , p . 228. ] 7. LetABCD be the quad ' . , and P , Q , R , S the points of contact of the sides AB , BC ,

CD , DA . Then AS = AP [ 111. 17 , Cor . ] and DS = DR ; : . by addition AD = AP ...

Page 67

11 and 12 ] . And AP + BP = 11-13 +12 + 13 = 1 ] + 72 .

special case of the following : If any two circles are touched one internally and

one externally by a third circle , the sum or difference of the distances of this ...

11 and 12 ] . And AP + BP = 11-13 +12 + 13 = 1 ] + 72 .

**NOTE**. This problem is aspecial case of the following : If any two circles are touched one internally and

one externally by a third circle , the sum or difference of the distances of this ...

Page 82

same O. 39. Let the bisectors meet at X. Then PAB , QBA together = two rt .

angles ( 1. 29 ] . :: LXAB , XBA together = one rt . angle ( Hyp . ] . :: LAXB is a rt .

angle ( 1.

**NOTE**. The locus of 1 in Ex . 36 and the locus of 1 , are conjugate arcs of thesame O. 39. Let the bisectors meet at X. Then PAB , QBA together = two rt .

angles ( 1. 29 ] . :: LXAB , XBA together = one rt . angle ( Hyp . ] . :: LAXB is a rt .

angle ( 1.

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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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