A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 8
... identically equal [ 1. 4 ] . 6 . .. _ DAC = 2 DCA , and hence △ DCB = △ DBC . = EC Let ABC be the rt . L. On BC describe an equilat . A BDC ; bisect DBC by BE ; then ABC is trisected by BD , BE . For DBC = two - thirds of a rt ...
... identically equal [ 1. 4 ] . 6 . .. _ DAC = 2 DCA , and hence △ DCB = △ DBC . = EC Let ABC be the rt . L. On BC describe an equilat . A BDC ; bisect DBC by BE ; then ABC is trisected by BD , BE . For DBC = two - thirds of a rt ...
Page 14
... equal in all respects [ 1. 4 ] . The other case is similar . S 3. It is easy to see that △ ACX , BCY are equal in ... IDENTICAL EQUALITY OF TRIANGLES . Page 90 . 1. Let the base BC be bisected by the perp . AD . DC , AD is common and ...
... equal in all respects [ 1. 4 ] . The other case is similar . S 3. It is easy to see that △ ACX , BCY are equal in ... IDENTICAL EQUALITY OF TRIANGLES . Page 90 . 1. Let the base BC be bisected by the perp . AD . DC , AD is common and ...
Page 15
... equal perps . drawn from ends of base Then in △ ABD , ACE , BD = CE , LADB = AEC [ Ax . 11 ] and the at A is common ... identically equal [ 1. 8 ] . 10. The △ ABD , BAC are equal in all respects [ 1. 8 ] . .. LABD = L BAC . .. △ AKB ...
... equal perps . drawn from ends of base Then in △ ABD , ACE , BD = CE , LADB = AEC [ Ax . 11 ] and the at A is common ... identically equal [ 1. 8 ] . 10. The △ ABD , BAC are equal in all respects [ 1. 8 ] . .. LABD = L BAC . .. △ AKB ...
Page 16
... equal to AD , join EC . Then △ ABD , EDC are identically equal [ 1. 4 ] and AB = CE . Now AC + CE > AE [ 1. 20 ] . That is , AB + AC > 2AD . 9. This follows at once from Ex . 8 , since twice the sum of the sides is greater than twice ...
... equal to AD , join EC . Then △ ABD , EDC are identically equal [ 1. 4 ] and AB = CE . Now AC + CE > AE [ 1. 20 ] . That is , AB + AC > 2AD . 9. This follows at once from Ex . 8 , since twice the sum of the sides is greater than twice ...
Page 17
... identically equal [ 1. 26 ] . S 6. The two formed are identically equal [ 1. 29 , 1. 26 ] . 7. Let O be pt . equidist . from the par1s . , and let POQ , XOY be drawn to cut them . Draw LOM perp . to the pars ; then △ LOP , MOQ are ...
... identically equal [ 1. 26 ] . S 6. The two formed are identically equal [ 1. 29 , 1. 26 ] . 7. Let O be pt . equidist . from the par1s . , and let POQ , XOY be drawn to cut them . Draw LOM perp . to the pars ; then △ LOP , MOQ 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
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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