The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 2
... straight line . B D CE N. B. When several angles are at one point B , any ' one of them is expressed by three ... AB , CB , is named the angle ABC , or CBA ; that which is contained by AB , DB , is named the an- gle ABD , or DBA ; and ...
... straight line . B D CE N. B. When several angles are at one point B , any ' one of them is expressed by three ... AB , CB , is named the angle ABC , or CBA ; that which is contained by AB , DB , is named the an- gle ABD , or DBA ; and ...
Page 7
... 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 distance BA ...
... 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 distance BA ...
Page 9
... angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal † to DE : and AB ...
... angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal † to DE : and AB ...
Page 13
... 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 ... AB be the given straight line ; it is required to divide it into two equal parts . + Constr . Describe✶ upon it an ...
... 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 ... AB be the given straight line ; it is required to divide it into two equal parts . + Constr . Describe✶ upon it an ...
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 ...
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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