A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 50
... tangent to both circles [ III . 16 ] . 4. The radius from the pt . of contact of the inner is perp . to the tangent [ III . 18 ] , and .. bisects the chord of the outer [ III . 3 ] . 5. The tangents to the inner are chords of the outer ...
... tangent to both circles [ III . 16 ] . 4. The radius from the pt . of contact of the inner is perp . to the tangent [ III . 18 ] , and .. bisects the chord of the outer [ III . 3 ] . 5. The tangents to the inner are chords of the outer ...
Page 51
... tangents to the 3. The chords of the outer inner are equal [ Ex . 5 , p . 181 ] and are bisected at the pt . of contact [ Ex . 4 , p . 181 ] . Hence the tangents , that is the half- chords , are equal . 4. The tangent at an extremity of ...
... tangents to the 3. The chords of the outer inner are equal [ Ex . 5 , p . 181 ] and are bisected at the pt . of contact [ Ex . 4 , p . 181 ] . Hence the tangents , that is the half- chords , are equal . 4. The tangent at an extremity of ...
Page 52
... tangent BD , DAB = LABO . But OA = OB , .. LABO L OAB . .. AB bisects = CAD . 15. Let O be centre , and let AT , BT ' be two equal tangents at A and B. Then OTOT ' [ III . 18 and 1. 4 ] . .. locus of T is circle with centre O. 16. See ...
... tangent BD , DAB = LABO . But OA = OB , .. LABO L OAB . .. AB bisects = CAD . 15. Let O be centre , and let AT , BT ' be two equal tangents at A and B. Then OTOT ' [ III . 18 and 1. 4 ] . .. locus of T is circle with centre O. 16. See ...
Page 53
... tangent ' line at a distance from it equal to the given radius cut the ' centre ' line in Then O is the required centre . Two solutions . O. SO 20. Describe a concentric with the given O , having its radius equal to the sum or ...
... tangent ' line at a distance from it equal to the given radius cut the ' centre ' line in Then O is the required centre . Two solutions . O. SO 20. Describe a concentric with the given O , having its radius equal to the sum or ...
Page 56
... tangent at D be parl . to AB . Then , if DC be perp . to tangent , the centre is in DC [ III . 19 ] . But DC .. DC bisects AB [ III . 3. ] Hence arc ADB is is also perp . to AB . bisected at D [ III . 30 ] . On AB describe 2. Let CB be ...
... tangent at D be parl . to AB . Then , if DC be perp . to tangent , the centre is in DC [ III . 19 ] . But DC .. DC bisects AB [ III . 3. ] Hence arc ADB is is also perp . to AB . bisected at D [ III . 30 ] . On AB describe 2. Let CB be ...
Other editions - View all
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
A. W. VERRALL AABC AB² ABCD AC² angles Assistant Master AX² BC² bisector bisects Cambridge centre chord circle circum College concyclic constant describe diam diameter diff draw ELEMENTARY equiangular equilat FASNACHT Fcap fixed point G. E. FASNACHT given base given point given ratio given st GREEK Hence identically equal inscribed intersect Introduction and Notes ISAAC TODHUNTER isosceles Join Let ABC LL.D locus M.A. BOOK meet middle point middle pt orthocentre Owens College par¹ parm pedal triangle perp plane produced Prof Professor Radical Axis radius equal rect respectively segment shewn sides Similarly sum of sqq tangent touch Translated triangle Trinity College vert vols
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