A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements: Books I.- VI. and XI.Macmillan, 1905 - 229 pages |
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Page 190
... that each of the ranges of points consisting of one external and two internal centres of similitude are collinear , and also that the three external centres are collinear . EXAMPLES ON POLE AND POLAR . Page 395 . 1. 190 KEY TO EUCLID .
... that each of the ranges of points consisting of one external and two internal centres of similitude are collinear , and also that the three external centres are collinear . EXAMPLES ON POLE AND POLAR . Page 395 . 1. 190 KEY TO EUCLID .
Page 191
... polar of B passes through P , .. the polar of P passes through B. Hence the polar of P passes through both A and B ; that is , AB is the polar of P. 2 . Let P be the intersection of the given st . lines PQ , PR , and let A and B be ...
... polar of B passes through P , .. the polar of P passes through B. Hence the polar of P passes through both A and B ; that is , AB is the polar of P. 2 . Let P be the intersection of the given st . lines PQ , PR , and let A and B be ...
Page 192
... polar of P : that is , the polar of P passes through Q. 6. Let P and O be the centres of the two " which intersect at A , B and let OP cut AB at Q. Join PA , PB . 8 Then since the " are orthogonal , PA and PB touch the C ( 0 ) at A and ...
... polar of P : that is , the polar of P passes through Q. 6. Let P and O be the centres of the two " which intersect at A , B and let OP cut AB at Q. Join PA , PB . 8 Then since the " are orthogonal , PA and PB touch the C ( 0 ) at A and ...
Page 193
... polar of X. 10. Let C and D be the points inverse to A and B respec- tively , and let AX , BY be the perps . from A ... Polar , the polar of P passes through both p and p ' : that is , RQ is the polar of P. Similarly it may be shewn that ...
... polar of X. 10. Let C and D be the points inverse to A and B respec- tively , and let AX , BY be the perps . from A ... Polar , the polar of P passes through both p and p ' : that is , RQ is the polar of P. Similarly it may be shewn that ...
Page 194
... polar of P , .. PO is perp . to QR [ Def . ii . p . 391 ] . Similarly RO is perp . to PQ , and consequently Qo is perp . to PR [ Ex . 19 , p . 242 ] . That is , O is the orthocentre of the PQR . 14. Let A , P , B , Q be a harmonic range ...
... polar of P , .. PO is perp . to QR [ Def . ii . p . 391 ] . Similarly RO is perp . to PQ , and consequently Qo is perp . to PR [ Ex . 19 , p . 242 ] . That is , O is the orthocentre of the PQR . 14. Let A , P , B , Q be a harmonic range ...
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
AB² ABCD AC² angles AP² arc AC AX² base BC BC² bisector bisects centre chord circum collinear common tangent concyclic constant cutting the given diagonals diam diameter diff draw drawn equiangular equilat fixed point given base given point given ratio given st greater half Hence identically equal inscribed intersect isosceles Join Let AB Let ABC Let AX locus middle point middle pt orthocentre par¹ parm pass pedal triangle perp plane polar produced Radical Axis radius equal rect respectively rhombus segment shewn sides Similarly solutions subtended sum of sqq tangent touch triangle vert vertex