The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 34
... parallel to the straight lineAB : and be- cause AB is parallel to CE , and AC meets them , the alternate angles BAC , * 29. 1. ACE , are equal . Again , because AB is parallel to CE , and BD falls upon them , the exterior +29 . 1. angle ...
... parallel to the straight lineAB : and be- cause AB is parallel to CE , and AC meets them , the alternate angles BAC , * 29. 1. ACE , are equal . Again , because AB is parallel to CE , and BD falls upon them , the exterior +29 . 1. angle ...
Page 35
... parallel . Let AB , CD be equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD : AC , BD shall be equal and parallel . C B * 13 . L Join BC ; and because AB is parallel to CD , and BC meets ...
... parallel . Let AB , CD be equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD : AC , BD shall be equal and parallel . C B * 13 . L Join BC ; and because AB is parallel to CD , and BC meets ...
Page 36
... parallel shown to be equal to it . lines , & c . Q. E.D. * 29 . l * 29. 1 . PROP . XXXIV . THEOR . The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into ...
... parallel shown to be equal to it . lines , & c . Q. E.D. * 29 . l * 29. 1 . PROP . XXXIV . THEOR . The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into ...
Page 37
... parallels , are equal to one another . 2d and Let the parallelograms ABCD , EBCF be See the upon the same base BC , and between the same d parallels AF , BC : the parallelogram ABCD figures . shall be equal to the parallelogram EBCF ...
... parallels , are equal to one another . 2d and Let the parallelograms ABCD , EBCF be See the upon the same base BC , and between the same d parallels AF , BC : the parallelogram ABCD figures . shall be equal to the parallelogram EBCF ...
Page 38
... parallel ; therefore EB , HC are both equal and parallel ; and therefore EBCH is at paral- lelogram ; and it is equal to ABCD , because they are upon the same base BC , and between the same parallels BC , AH : for the like reason , the ...
... parallel ; therefore EB , HC are both equal and parallel ; and therefore EBCH is at paral- lelogram ; and it is equal to ABCD , because they are upon the same base BC , and between the same parallels BC , AH : for the like reason , 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