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 183
... rect . AB , CD + rect . BC , AD = rect . AC , BD , rect . ( AB + BC ) , AD = rect . AC , BD [ 11. 1 ] , .. AB + BC BD AC : AD = = constant . THEOREMS ON HARMONIC SECTION . Page 387 . 1. ( EXERCISES ON BOOK VI . PAGE 383 . 183.
... rect . AB , CD + rect . BC , AD = rect . AC , BD , rect . ( AB + BC ) , AD = rect . AC , BD [ 11. 1 ] , .. AB + BC BD AC : AD = = constant . THEOREMS ON HARMONIC SECTION . Page 387 . 1. ( EXERCISES ON BOOK VI . PAGE 383 . 183.
Page 184
Books I.- VI. and XI. Henry Sinclair Hall. THEOREMS ON HARMONIC SECTION . Page 387 . 1. ( i ) Let A , P , B , Q be a harmonic range , and S the vertex of the pencil . Through P draw aPb par . to SQ meeting SA , SB at a and b . Now ...
Books I.- VI. and XI. Henry Sinclair Hall. THEOREMS ON HARMONIC SECTION . Page 387 . 1. ( i ) Let A , P , B , Q be a harmonic range , and S the vertex of the pencil . Through P draw aPb par . to SQ meeting SA , SB at a and b . Now ...
Page 185
... harmonic pencil be formed by joining a point S to the harmonic range A , P , B , Q ; then any transversal shall be cut harmonically by this pencil . Through P draw any transversal aPbq , and also the trans- versal hPk par1 . to SQ ...
... harmonic pencil be formed by joining a point S to the harmonic range A , P , B , Q ; then any transversal shall be cut harmonically by this pencil . Through P draw any transversal aPbq , and also the trans- versal hPk par1 . to SQ ...
Page 186
... harmonic pencil , But .. A , p , b , q ' is a harmonic range [ Ex . 2 ] . A , p , b , q is a harmonic range [ hyp . ] ; .. q and q ' are coincident ; or , Qq passes through S ; that is , PP , Bp , Qq are concurrent . Similarly it may be ...
... harmonic pencil , But .. A , p , b , q ' is a harmonic range [ Ex . 2 ] . A , p , b , q is a harmonic range [ hyp . ] ; .. q and q ' are coincident ; or , Qq passes through S ; that is , PP , Bp , Qq are concurrent . Similarly it may be ...
Page 188
... harmonic [ p . 385 ] . 5. Taking the fig . and the results of Ex . 33 , p . 302 , we have from the similar △ ASO , aNO , SO NO SA : Na - circum . - radius : nine - point - radius . .. O is the external centre of similitude of the two ...
... harmonic [ p . 385 ] . 5. Taking the fig . and the results of Ex . 33 , p . 302 , we have from the similar △ ASO , aNO , SO NO SA : Na - circum . - radius : nine - point - radius . .. O is the external centre of similitude of the two ...
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