The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 3
... off by the diameter . 66 XIX . " A segment of a circle is the figure contained by a straight line , and the circumference it " cuts off . " XX . Rectilineal figures are those which are contained by B 2 BOOK I. - DEFINITIONS . 3 XII. ...
... off by the diameter . 66 XIX . " A segment of a circle is the figure contained by a straight line , and the circumference it " cuts off . " XX . Rectilineal figures are those which are contained by B 2 BOOK I. - DEFINITIONS . 3 XII. ...
Page 17
... segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw + BE at +11 . 1- right angles to AB ; and because ABC is a straight line , the angle CBE is * equal to ...
... segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw + BE at +11 . 1- right angles to AB ; and because ABC is a straight line , the angle CBE is * equal to ...
Page 68
... segment of a circle is the figure contained by a straight line and the circumference it cuts off . VII . " The angle of a segment is that which is con- tained by the straight line and the circumfer- ence . " VIII . An angle in a segment ...
... segment of a circle is the figure contained by a straight line and the circumference it cuts off . VII . " The angle of a segment is that which is con- tained by the straight line and the circumfer- ence . " VIII . An angle in a segment ...
Page 69
... segments of circles are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . * Draw within it any ...
... segments of circles are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . * Draw within it any ...
Page 88
... segment BAED : the angles BÅD , BED shall be equal to one another . B C E First , let the segment BAED be greater than a semicircle . Take + F , the centre of the circle ABCD , and join BF , FD : and because the angle BFD is at the ...
... segment BAED : the angles BÅD , BED shall be equal to one another . B C E First , let the segment BAED be greater than a semicircle . Take + F , the centre of the circle ABCD , and join BF , FD : and because the angle BFD is at the ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole