The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 9
... join FC , GB . Because AF is equal to † AG , and AB to ‡ AC , the + Constr . two sides FA , AC are equal to the two GA , AB , each to each : and they contain the angle FAG common to Hyp . * 4 . 1 . * 3 Ax . * BOOK I. PROP . IV . V. 9.
... join FC , GB . Because AF is equal to † AG , and AB to ‡ AC , the + Constr . two sides FA , AC are equal to the two GA , AB , each to each : and they contain the angle FAG common to Hyp . * 4 . 1 . * 3 Ax . * BOOK I. PROP . IV . V. 9.
Page 10
... join DC : therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides , DB , BC are equal to the two AC , CB , each to J 4. 1 . each ; and the angle DBC 10 EUCLID'S ELEMENTS .
... join DC : therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides , DB , BC are equal to the two AC , CB , each to J 4. 1 . each ; and the angle DBC 10 EUCLID'S ELEMENTS .
Page 13
... join DE , and upon it describe * an equila- * 1. 1 . teral triangle DEF ; then join AF : the straight line AF shall bisect the angle BAC . A A B F E † Constr . Because AD is equal + to AE , and AF is common to the two triangles DAF ...
... join DE , and upon it describe * an equila- * 1. 1 . teral triangle DEF ; then join AF : the straight line AF shall bisect the angle BAC . A A B F E † Constr . Because AD is equal + to AE , and AF is common to the two triangles DAF ...
Page 14
... join FC . The straight line FC drawn from the given point C , shall be at right angles to the given straight line AB . * A D ER Because DC is equal † to CE , and FC common to the two triangles DCF , ECF ; the two sides DC , CF , are ...
... join FC . The straight line FC drawn from the given point C , shall be at right angles to the given straight line AB . * A D ER Because DC is equal † to CE , and FC common to the two triangles DCF , ECF ; the two sides DC , CF , are ...
Page 15
... join CH . The straight line CH , drawn from the given point C , shall be perpendicular to the given straight line AB . * * * Join CF , CG : and because FH is equal † to HG , and + Constr . HC common to the two triangles FHC , GHC , the ...
... join CH . The straight line CH , drawn from the given point C , shall be perpendicular to the given straight line AB . * * * Join CF , CG : and because FH is equal † to HG , and + Constr . HC common to the two triangles FHC , GHC , the ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore