The Elements of Euclid |
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Page 28
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the tri- angle , but shall contain a greater angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side ...
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the tri- angle , but shall contain a greater angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side ...
Page 36
... draw a straight line through a given point pa- rallel to a given straight line . Let A be the given point , and BC the given straight line ; it is required to draw a straight line ... drawn through the given point A parallel to THE ELEMENTS.
... draw a straight line through a given point pa- rallel to a given straight line . Let A be the given point , and BC the given straight line ; it is required to draw a straight line ... drawn through the given point A parallel to THE ELEMENTS.
Page 48
... draw a AC at right angles to AB ; and make b AD equal to AB , and through the point D draw DE parallel to AB , and through B draw BE parallel to AD ; there- fore ADEB is a parallelogram : whence AB is equal d to DE , and AD to BE : but ...
... draw a AC at right angles to AB ; and make b AD equal to AB , and through the point D draw DE parallel to AB , and through B draw BE parallel to AD ; there- fore ADEB is a parallelogram : whence AB is equal d to DE , and AD to BE : but ...
Page 63
... drawn from any of the acute angles to the opposite side produced , the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle , by twice the rectangle contained by the side ...
... drawn from any of the acute angles to the opposite side produced , the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle , by twice the rectangle contained by the side ...
Page 68
... drawn from any point in the circumference of the segment , to the extremities of the straight line which is the base of the segment . IX . And an angle is said to insist or stand upon the circumference intercepted between the straight ...
... drawn from any point in the circumference of the segment , to the extremities of the straight line which is the base of the segment . IX . And an angle is said to insist or stand upon the circumference intercepted between the straight ...
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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