A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 2
... Let BDCE in BC the base of isosc . A ABC . Then △ ABD , ACE are equal in all respects [ 1. 4 ] . = DC , 4. Let BD be a diagonal of a quadril . which has AB BC = DA . Then △ ABD , BCD have their sides respectively equal ; .. 2 DAB = _ ...
... Let BDCE in BC the base of isosc . A ABC . Then △ ABD , ACE are equal in all respects [ 1. 4 ] . = DC , 4. Let BD be a diagonal of a quadril . which has AB BC = DA . Then △ ABD , BCD have their sides respectively equal ; .. 2 DAB = _ ...
Page 3
... let BC be produced both ways to X and Y. Then ABC , ACB are supplementary to equal angles , and are therefore equal . 8 2. In the fig . the XOB , YOB together make up half the < S AOB , BOC ; that is , half of 2 rt . . 3. Since XOY is a ...
... let BC be produced both ways to X and Y. Then ABC , ACB are supplementary to equal angles , and are therefore equal . 8 2. In the fig . the XOB , YOB together make up half the < S AOB , BOC ; that is , half of 2 rt . . 3. Since XOY is a ...
Page 4
... ABC , S .. ABC , ACB are together less than △ AXC , AXB ; that is , less than 2 rt . 3 ( 1. 13 ] . Page 38 . S 1. A △ must have two acute 4o [ 1. 17 ] . .. the rt . is the greatest , and has the greatest side opposite to it . = 2. Let ABC ...
... ABC , S .. ABC , ACB are together less than △ AXC , AXB ; that is , less than 2 rt . 3 ( 1. 13 ] . Page 38 . S 1. A △ must have two acute 4o [ 1. 17 ] . .. the rt . is the greatest , and has the greatest side opposite to it . = 2. Let ABC ...
Page 7
... Let PQ drawn par1 . to base BC cut the sides in X and Y. Then 4 AXP , AYQ are respectively equal to the alt . ACB , and these are equal since the A is isosceles . OB . ABC , 2. Let AOB be bisected by OP , and from P draw PQ par1 . to ...
... Let PQ drawn par1 . to base BC cut the sides in X and Y. Then 4 AXP , AYQ are respectively equal to the alt . ACB , and these are equal since the A is isosceles . OB . ABC , 2. Let AOB be bisected by OP , and from P draw PQ par1 . to ...
Page 8
... Let ABC be the A ; produce BC to X and Y ; then LXBA = < LYCA = .. the 2 ext . △ 3 = the three 3. Let XP be XP , AQ meet at O. 8 BAC and BCA ; 8 3 CBA , BAC . of together with BAC . perp . to AP , and XQ perp . to AQ ; also let Then ...
... Let ABC be the A ; produce BC to X and Y ; then LXBA = < LYCA = .. the 2 ext . △ 3 = the three 3. Let XP be XP , AQ meet at O. 8 BAC and BCA ; 8 3 CBA , BAC . of together with BAC . perp . to AP , and XQ perp . to AQ ; also let Then ...
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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