The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 171
... plane , when it makes right angles with every straight line in that plane which meets it . IV . A plane is perpendicular to a plane , when the straight lines drawn in one of the planes perpendicular to the common section of the two planes ...
... plane , when it makes right angles with every straight line in that plane which meets it . IV . A plane is perpendicular to a plane , when the straight lines drawn in one of the planes perpendicular to the common section of the two planes ...
Page 172
... plane to a plane is the acute angle contained by two straight lines drawn from any the same point of their common section at right angles to it , one upon one plane , and the other upon the other plane . VII . Two planes are said to ...
... plane to a plane is the acute angle contained by two straight lines drawn from any the same point of their common section at right angles to it , one upon one plane , and the other upon the other plane . VII . Two planes are said to ...
Page 174
... plane , and another part above it . If it be possible , let AB , part of the straight line ABC , be in the plane , and the part BC above it : and since the straight line AB is in the plane , it can be produced in that plane : let it be ...
... plane , and another part above it . If it be possible , let AB , part of the straight line ABC , be in the plane , and the part BC above it : and since the straight line AB is in the plane , it can be produced in that plane : let it be ...
Page 175
... plane , the straight line * BC is in it : * 7 Def . 1 . therefore there are two straight lines , ABC , ABD in the same plane that have a common segment AB ; * which is impossible . Therefore , one part , & c . Q.E.D. * Cor . 11.1 . PROP ...
... plane , the straight line * BC is in it : * 7 Def . 1 . therefore there are two straight lines , ABC , ABD in the same plane that have a common segment AB ; * which is impossible . Therefore , one part , & c . Q.E.D. * Cor . 11.1 . PROP ...
Page 176
... plane which passes through them , that is , to the plane in which they are . Let the straight line EF stand at right angles to each of the straight lines AB , CD , in E , the point of their intersection : EF shall also be at right ...
... plane which passes through them , that is , to the plane in which they are . Let the straight line EF stand at right angles to each of the straight lines AB , CD , in E , the point of their intersection : EF shall also be at right ...
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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