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

### From inside the book

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Page 2

A

of a quadril . which has AB = DC , BC = DA . Then AS ABD , BCD have their sides

respectively equal ; .. DAB = _ DCB . Similarly for the other pair of angles . 5.

A

**ABC**. AS ABD , ACE are equal in all respects ( 1. 4 ] . 4.**Let**BD be a diagonalof a quadril . which has AB = DC , BC = DA . Then AS ABD , BCD have their sides

respectively equal ; .. DAB = _ DCB . Similarly for the other pair of angles . 5.

Page 3

In AS BAY , CAX , at A is common and BA , AY = CA , AX . As are equal in all

respects ; .. _ ABY = = LACY . But

isosceles . Again AB = AC and AO is common , and BO = OC ; .. 4 BAO = Z CAO .

In AS BAY , CAX , at A is common and BA , AY = CA , AX . As are equal in all

respects ; .. _ ABY = = LACY . But

**ABC**= L ACB ; .. OBC = LOCB ; that is , BOC isisosceles . Again AB = AC and AO is common , and BO = OC ; .. 4 BAO = Z CAO .

**Let**... Page 4

A if produced , and are cut by another st . line BC , the interior angles on the

same side , viz . <

Prop .

rt .

A if produced , and are cut by another st . line BC , the interior angles on the

same side , viz . <

**ABC**, ACB are together less than 2 rt . 28 . 2. In the fig . to theProp .

**let**CB be produced to E. Then the 28 DCA , ACB , CBA , ABE together = 4rt .

Page 7

PQO = int . opp . Z ABQ , and L RQO = int . opp . L CBQ . Hence the sum or diff . of

_ $ PQO , RQO = the sum or diff . of * AB , CBQ ; .. – PQR -

...

**Let**PQ , QR be par to AB , BC respectively . Join BQ and produce it to 0. Then <PQO = int . opp . Z ABQ , and L RQO = int . opp . L CBQ . Hence the sum or diff . of

_ $ PQO , RQO = the sum or diff . of * AB , CBQ ; .. – PQR -

**ABC**. Similarly for the...

Page 8

S ( ii ) Let AX be drawn to a pt . in base BC ; then ext . L AXC = sum of int . _ * X.

BA , BAX ; and L AXB = sum of _ * XAC , ACX . Thus the three _ 8 of A are

together equal to sum of < $ AXB , AXC , that is to 2 rt . _ $ . 2.

S ( ii ) Let AX be drawn to a pt . in base BC ; then ext . L AXC = sum of int . _ * X.

BA , BAX ; and L AXB = sum of _ * XAC , ACX . Thus the three _ 8 of A are

together equal to sum of < $ AXB , AXC , that is to 2 rt . _ $ . 2.

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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 |

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### 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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