The Elements of Euclid |
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Page 19
... fore , 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 each ; and the angle DBC is equal to the angle ACB ; therefore the base DC is equal to ...
... fore , 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 each ; and the angle DBC is equal to the angle ACB ; therefore the base DC is equal to ...
Page 22
... fore the base AD is equal to the base DB , and the straight line AB is divided into two equal parts in the point D. Which was to be done . MA Α D B PROP . XI . PROB . TO draw a straight line at right angles to a given straight line ...
... fore the base AD is equal to the base DB , and the straight line AB is divided into two equal parts in the point D. Which was to be done . MA Α D B PROP . XI . PROB . TO draw a straight line at right angles to a given straight line ...
Page 24
... fore the angles DBA , ABC are equal to the three angles DBE , EBA , ABC ; but the angles CBE , EBD have been demonstrated to be equal to the same three angles ; and things that are equal to the same are equal to one another ; therefore ...
... fore the angles DBA , ABC are equal to the three angles DBE , EBA , ABC ; but the angles CBE , EBD have been demonstrated to be equal to the same three angles ; and things that are equal to the same are equal to one another ; therefore ...
Page 30
... fore FK is equal to A : again , because G is the centre of the 15. Def . circle LKH , GH is equal to GK ; but GH is equal to C ; therefore also GK is equal to C ; and FG is equal to B ; there- fore the three straight lines KF , FG , GK ...
... fore FK is equal to A : again , because G is the centre of the 15. Def . circle LKH , GH is equal to GK ; but GH is equal to C ; therefore also GK is equal to C ; and FG is equal to B ; there- fore the three straight lines KF , FG , GK ...
Page 47
... fore the angles MHG , HGL are equal to the angles HGF , HGL : but the angles MGH , HGL are equal to two right an- gles ; wherefore also the angles HGF , HGL are equal to two right angles , and FG is therefore in the same straight line ...
... fore the angles MHG , HGL are equal to the angles HGF , HGL : but the angles MGH , HGL are equal to two right an- gles ; wherefore also the angles HGF , HGL are equal to two right angles , and FG is therefore in the same straight line ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid 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 meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore