The Elements of Euclid |
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Page 14
... less " than two right angles , these straight lines being continually 66 produced , shall at length meet upon that side on which are " the angles which are less than two right angles . See the " notes on prop . 29. of Book I ...
... less " than two right angles , these straight lines being continually 66 produced , shall at length meet upon that side on which are " the angles which are less than two right angles . See the " notes on prop . 29. of Book I ...
Page 16
... less . Let AB and C be the two giv en straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw a the straight line AD equal to C ; and from the ...
... less . Let AB and C be the two giv en straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw a the straight line AD equal to C ; and from the ...
Page 19
... less , and join DC ; there- 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 ...
... less , and join DC ; there- 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 ...
Page 26
... less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , ACD is greater a than the interior ...
... less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , ACD is greater a than the interior ...
Page 27
... less than two right angles , Therefore any two angles , & c . Q. E. D. PROP . XVIII , THEOR . 2.9 THE greater side ... less than it ; it is not equal , because then the angle ABC would be equal to the angle ACB ; but it is not ...
... less than two right angles , Therefore any two angles , & c . Q. E. D. PROP . XVIII , THEOR . 2.9 THE greater side ... less than it ; it is not equal , because then the angle ABC would be equal to the angle ACB ; but it is not ...
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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