The Elements of Euclid |
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Page 11
... circle . XVII . A diameter of a circle is a straight line drawn through the cen- tre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off ...
... circle . XVII . A diameter of a circle is a straight line drawn through the cen- tre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off ...
Page 15
... circle BCD , and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in which the circles cut one the circles another , draw the straight lines b CA , CB to the points A , B ; ABC shall be an ...
... circle BCD , and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in which the circles cut one the circles another , draw the straight lines b CA , CB to the points A , B ; ABC shall be an ...
Page 16
... circle CGH , BC is equal e to BG ; and because D is the centre of the circle GKL , e 15. Def . DL is equal to DG , and DA , DB , parts of them , are equal ; therefore the remainder AL is equal to the remainder f BG : but it has been ...
... circle CGH , BC is equal e to BG ; and because D is the centre of the circle GKL , e 15. Def . DL is equal to DG , and DA , DB , parts of them , are equal ; therefore the remainder AL is equal to the remainder f BG : but it has been ...
Page 29
... circle DKL ; and ' from the centre G , at the distance GH , describe banother circle HLK ; and join KF , KG ; the triangle KFG has its sides equal to D the three straight lines A , B , C. See Note . a_20.1 . a 3. 1 . E G H b 3. Post . L ...
... circle DKL ; and ' from the centre G , at the distance GH , describe banother circle HLK ; and join KF , KG ; the triangle KFG has its sides equal to D the three straight lines A , B , C. See Note . a_20.1 . a 3. 1 . E G H b 3. Post . L ...
Page 67
... circles be applied to one another , so that ' their centres coincide , the circles must likewise coincide , since " the straight lines from the centers are equal . ' II . A straight line is said to touch a circle when it meets the circle ...
... circles be applied to one another , so that ' their centres coincide , the circles must likewise coincide , since " the straight lines from the centers are equal . ' II . A straight line is said to touch a circle when it meets the circle ...
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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