A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 42
... intersecting at O. OA = 20X , OB = 20Y , OC = 2oz [ Ex . 4 , p . 105 ] , A BOC , OB2 + OC2 = 2BX2 + 20x2 . Then and from the Again from also from △ COA , OC2 + OA2 = 2cy2 + 20Y2 , AAOB , OA2 + OB2 = 2AZ2 + 2oz2 . .. by addition 20A2 + ...
... intersecting at O. OA = 20X , OB = 20Y , OC = 2oz [ Ex . 4 , p . 105 ] , A BOC , OB2 + OC2 = 2BX2 + 20x2 . Then and from the Again from also from △ COA , OC2 + OA2 = 2cy2 + 20Y2 , AAOB , OA2 + OB2 = 2AZ2 + 2oz2 . .. by addition 20A2 + ...
Page 45
... intersect in A , B. Let CAD , EBF be par1 . st . lines cutting the one circle in C , E and the other in D , F. Then the st . line through the centre of ABEC perp . to the chords AC , BE bisects these chords in P and Q , say . Similarly ...
... intersect in A , B. Let CAD , EBF be par1 . st . lines cutting the one circle in C , E and the other in D , F. Then the st . line through the centre of ABEC perp . to the chords AC , BE bisects these chords in P and Q , say . Similarly ...
Page 46
... intersect in O , the centre of the Because AO BO , . ' . △ OAB = L OBA . = .. LOAD = L ODA ; .. whole DAB = sum of $ ABD , ADB ; .. △ DAB is a rt . ≤ [ 1. 32 ] . = 3. Let C , D be the centres of two O intersecting in A. Draw AX perp ...
... intersect in O , the centre of the Because AO BO , . ' . △ OAB = L OBA . = .. LOAD = L ODA ; .. whole DAB = sum of $ ABD , ADB ; .. △ DAB is a rt . ≤ [ 1. 32 ] . = 3. Let C , D be the centres of two O intersecting in A. Draw AX perp ...
Page 55
... intersect at rt . s in X. LAXD : < " ABD , BAC together , .. the arcs AD , BC subtend at the circumferences together equal to a rt . 2. And AXB = ACB , CBD together , .. the arcs AB , CD subtend at the circumference Ls together equal to ...
... intersect at rt . s in X. LAXD : < " ABD , BAC together , .. the arcs AD , BC subtend at the circumferences together equal to a rt . 2. And AXB = ACB , CBD together , .. the arcs AB , CD subtend at the circumference Ls together equal to ...
Page 63
... intersect at A , B ; and let PAQ , XAY be two st . lines equally inclined to AB and terminated by the Through B draw P'BQ ' par1 . to PQ . Then P'Q ' PQ [ Ex . 12 , p . 156 ] . Now the XAB = the P'BA ; whence it may be shewn XA = P'B ...
... intersect at A , B ; and let PAQ , XAY be two st . lines equally inclined to AB and terminated by the Through B draw P'BQ ' par1 . to PQ . Then P'Q ' PQ [ Ex . 12 , p . 156 ] . Now the XAB = the P'BA ; whence it may be shewn XA = P'B ...
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 |
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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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