The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 72
... ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles shall together be equal to two right angles . * Join AC , BD : and because the three angles of every triangle are equal to two right angles , the three ...
... ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles shall together be equal to two right angles . * Join AC , BD : and because the three angles of every triangle are equal to two right angles , the three ...
Page 77
... ABCD be a circle , of which the diameter is BC , and centre E ; and draw CA , dividing the circle into the segments ABC , ADC , and join BA , AD , DC : the angle in the semicircle BAC shall be a right angle ; and the angle in the ...
... ABCD be a circle , of which the diameter is BC , and centre E ; and draw CA , dividing the circle into the segments ABC , ADC , and join BA , AD , DC : the angle in the semicircle BAC shall be a right angle ; and the angle in the ...
Page 78
... ABC must be less than a right angle : and therefore the angle in a segment ABC greater than a semicircle , is less than a right angle . * And because ABCD is a quadrilateral figure in a circle , any two of its opposite angles are equal ...
... ABC must be less than a right angle : and therefore the angle in a segment ABC greater than a semicircle , is less than a right angle . * And because ABCD is a quadrilateral figure in a circle , any two of its opposite angles are equal ...
Page 79
... circle : the angles which BD makes with the touching line EF shall be equal to the angles in the alternate segments ... ABCD in the point B , and BA is drawn at right angles to the touching line from the point of con- tact B , the centre of ...
... circle : the angles which BD makes with the touching line EF shall be equal to the angles in the alternate segments ... ABCD in the point B , and BA is drawn at right angles to the touching line from the point of con- tact B , the centre of ...
Page 81
... circle ABC , the segment BAC is cut off , containing an angle equal to the given angle D. Which was to be done . PROP . XXXV . THEOR . If two straight lines cut one another within a circle , the See N. rectangle contained by the ...
... circle ABC , the segment BAC is cut off , containing an angle equal to the given angle D. Which was to be done . PROP . XXXV . THEOR . If two straight lines cut one another within a circle , the See N. rectangle contained by the ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore