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

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Page 30

Therefore the locus of D is a circle whose centre is the

radius is half the given length of the rod . 8. Let ACB be a rt . angled o on AB as

hypotenuse . Then , if AB is bisected at D , CD is constant , being equal to half of

AB .

Therefore the locus of D is a circle whose centre is the

**fixed**pt . C and whoseradius is half the given length of the rod . 8. Let ACB be a rt . angled o on AB as

hypotenuse . Then , if AB is bisected at D , CD is constant , being equal to half of

AB .

Page 31

Then since the area of the 2 is constant , A must move on a

BC . Let AX be the median bisecting BC ; then if o is the inters ” . of medians AO =

20X [ Ex . 4 , p . 105 ] . Draw AD perp . to BC and in it take AP = 2PD Ex . 19 , p .

Then since the area of the 2 is constant , A must move on a

**fixed**st . line par !. toBC . Let AX be the median bisecting BC ; then if o is the inters ” . of medians AO =

20X [ Ex . 4 , p . 105 ] . Draw AD perp . to BC and in it take AP = 2PD Ex . 19 , p .

Page 41

AX is constant ; and x is a

at X. 31. Since CB is a median of the AACD , :: DC ? + CAP = 2AB ” + 2BC ? [ Ex .

24 , p . 147 ] . But CAP = AB ? ( Hyp . ] .. DC2 = AB ? + 2BC ?. 32. Let ABC be a ...

AX is constant ; and x is a

**fixed**point ; .. the locus of A is a circle , whose centre isat X. 31. Since CB is a median of the AACD , :: DC ? + CAP = 2AB ” + 2BC ? [ Ex .

24 , p . 147 ] . But CAP = AB ? ( Hyp . ] .. DC2 = AB ? + 2BC ?. 32. Let ABC be a ...

Page 43

And as P is a

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 .

And as P is a

**fixed**point , Q is determined . 41. This is the same as dividing a lineexternally 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 61

... while A remains

coincides with the perp . from A to the tangent at A ; and always passes through C

. 2. Let AB be the common chord of two O $ whose centres are Then EF bisects

AB ...

... while A remains

**fixed**, and B approaches A. Then the perp . EF ultimatelycoincides with the perp . from A to the tangent at A ; and always passes through C

. 2. Let AB be the common chord of two O $ whose centres are Then EF bisects

AB ...

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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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