The Elements of Euclid |
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Page 15
... straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the dis- tance AB , describe the circle BCD , and from the centre B , at the distance BA , describe ...
... straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the dis- tance AB , describe the circle BCD , and from the centre B , at the distance BA , describe ...
Page 16
... straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . a 2. 1 . PROP . III . PROB . FROM the greater of two given straight lines to ...
... straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . a 2. 1 . PROP . III . PROB . FROM the greater of two given straight lines to ...
Page 21
... given rectilineal angle , that is , to di- vide it into two equal angles ... straight line AF bisects the angle BAC . sides EA , AF , Because AD is equal ... straight line AF , he base DF is ; therefore thè to the angle B D E Co & L given ...
... given rectilineal angle , that is , to di- vide it into two equal angles ... straight line AF bisects the angle BAC . sides EA , AF , Because AD is equal ... straight line AF , he base DF is ; therefore thè to the angle B D E Co & L given ...
Page 22
... 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 , from a given point in the same . Let AB be , a given ...
... 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 , from a given point in the same . Let AB be , a given ...
Page 23
... straight line , the angle DBE is equal to the angle EBA ; where- fore the angle DBE is equal to the angle CBE , the ... given straight line of an unlimited length , from a given ) point without it . zi Let AB be the given straight line ...
... straight line , the angle DBE is equal to the angle EBA ; where- fore the angle DBE is equal to the angle CBE , the ... given straight line of an unlimited length , from a given ) point without it . zi Let AB be the given 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