The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 7
... a given finite straight line . Let AB be the given straight line ; it is required to de- scribe an equilateral triangle upon AB . From the centre A , at the distance AB , describe * the circle BCD , and from the centre B , at the ...
... a given finite straight line . Let AB be the given straight line ; it is required to de- scribe an equilateral triangle upon AB . From the centre A , at the distance AB , describe * the circle BCD , and from the centre B , at the ...
Page 8
... straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . From the greater of two given straight lines to cut off a ...
... straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . From the greater of two given straight lines to cut off a ...
Page 13
... given rectilineal angle , that is , to divide it into two equal angles . Let ... straight line AF shall bisect the angle BAC . A A B F E † Constr . Because ... given rectilineal angle BAC is bisected by the straight line AF . Which was to ...
... given rectilineal angle , that is , to divide it into two equal angles . Let ... straight line AF shall bisect the angle BAC . A A B F E † Constr . Because ... given rectilineal angle BAC is bisected by the straight line AF . Which was to ...
Page 14
... 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 equal to the two ...
... 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 equal to the two ...
Page 15
... 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 two sides FH ...
... 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 two sides FH ...
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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