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

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Results 6-10 of 32

Page 58

_ S. .. BD , CE are par . and _ S DAB , EAC are in ( i ) coincident and in ( ii ) opp .

vertical . Hence the remaining _ S ABD , ACE are equal ( 1. 32 ] : i . e . the

segments DBA , ECA are

os at A.

_ S. .. BD , CE are par . and _ S DAB , EAC are in ( i ) coincident and in ( ii ) opp .

vertical . Hence the remaining _ S ABD , ACE are equal ( 1. 32 ] : i . e . the

segments DBA , ECA are

**similar**. 4 . Draw T'AT the common tangent to the twoos at A.

Page 68

Proceeding in a

common to the two locus - circles satisfy the conditions . There are two solutions ,

one solution or no solution according as the loci - circles intersect , touch one ...

Proceeding in a

**similar**manner with the second circle , we see that the pointscommon to the two locus - circles satisfy the conditions . There are two solutions ,

one solution or no solution according as the loci - circles intersect , touch one ...

Page 79

2 FDX is bisected by BD : and so on for the other _s of the pedal A. The latter part

of the proposition may be solved in a

227 , since the < 8 AFO , AEO are rt . angles ( hyp . ) , .. the four points A , F , 0 ...

2 FDX is bisected by BD : and so on for the other _s of the pedal A. The latter part

of the proposition may be solved in a

**similar**manner . 23 . For , with the fig . of p .227 , since the < 8 AFO , AEO are rt . angles ( hyp . ) , .. the four points A , F , 0 ...

Page 84

DXB is constant , and D , B are fixed points . .. the locus of x is a 0 , the segment

on DB being

the rulers . Then PXQA is a rectangle . ..AX = PQ , which is constant , and the ...

DXB is constant , and D , B are fixed points . .. the locus of x is a 0 , the segment

on DB being

**similar**to the segment ACB . 46. Let A be the point of intersection ofthe rulers . Then PXQA is a rectangle . ..AX = PQ , which is constant , and the ...

Page 87

... intersection of the two Oo , AD , AE the two diams . , and let the line through A

meet the Osat X and Y. Then in the AS AXD , AYE L DAX = L EAY [ Hyp . ) , and _

AXD = L AYE [ 111. 31 ] ; .. LADX = LAEY ( 1. 32 ] . . : . the segments are

... intersection of the two Oo , AD , AE the two diams . , and let the line through A

meet the Osat X and Y. Then in the AS AXD , AYE L DAX = L EAY [ Hyp . ) , and _

AXD = L AYE [ 111. 31 ] ; .. LADX = LAEY ( 1. 32 ] . . : . the segments are

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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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