The Elements of Euclid |
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Page 71
... circle two straight lines cut one another which do not both pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both ...
... circle two straight lines cut one another which do not both pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both ...
Page 73
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
Page 80
... ABCD be a circle , of which the diameter is AD , and the centre E ; and let BC be nearer to the centre than FG ; AD is greater than any straight line BC . which is not a diameter , and BC greater than FG . From the centre draw EH , EK ...
... ABCD be a circle , of which the diameter is AD , and the centre E ; and let BC be nearer to the centre than FG ; AD is greater than any straight line BC . which is not a diameter , and BC greater than FG . From the centre draw EH , EK ...
Page 85
Euclid Robert Simson. 18 Let.ABC be a circle , and BEC an angle at the centre , and Book III . BAC an angle at the circumference , which have the same cir- cumference BC for their base ; the angle BEC is double of the angle BAC . / a A E ...
Euclid Robert Simson. 18 Let.ABC be a circle , and BEC an angle at the centre , and Book III . BAC an angle at the circumference , which have the same cir- cumference BC for their base ; the angle BEC is double of the angle BAC . / a A E ...
Page 86
... circle , are together equal to two right angles . Let ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right angles . D Join AC , BD ; and because the three angles of every tri ...
... circle , are together equal to two right angles . Let ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right angles . D Join AC , BD ; and because the three angles of every tri ...
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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