The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 30
... falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines shall be pa- rallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate ...
... falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines shall be pa- rallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate ...
Page 31
... fall upon two parallel straight See the lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the position interior and opposite upon the same side ; and Oct. Ed . likewise the two interior angles ...
... fall upon two parallel straight See the lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the position interior and opposite upon the same side ; and Oct. Ed . likewise the two interior angles ...
Page 32
... falling upon them , make the in- terior angles on the same side less than two * 12 Ax . right angles , will meet together if continually See the produced ; therefore the straight lines AB , CD , this pro- if produced far enough , will ...
... falling upon them , make the in- terior angles on the same side less than two * 12 Ax . right angles , will meet together if continually See the produced ; therefore the straight lines AB , CD , this pro- if produced far enough , will ...
Page 34
... falls upon them , the exterior +29 . 1. angle ECD is equal to the interior and opposite angle ABC but the angle ACE was shown to be equal to the angle BAC ; therefore the whole +2 Ax .. exterior angle ACD is equal † to the two interior ...
... falls upon them , the exterior +29 . 1. angle ECD is equal to the interior and opposite angle ABC but the angle ACE was shown to be equal to the angle BAC ; therefore the whole +2 Ax .. exterior angle ACD is equal † to the two interior ...
Page 43
... ; and produce FG to H ; and through A draw * AH parallel * 31 . 1 . to BG or EF , and join HB . Then , because the straight line HF falls upon the parallels AH , * 29 . 1. EF , the angles AHF , BOOK I PROP . XLIV . 43.
... ; and produce FG to H ; and through A draw * AH parallel * 31 . 1 . to BG or EF , and join HB . Then , because the straight line HF falls upon the parallels AH , * 29 . 1. EF , the angles AHF , BOOK I PROP . XLIV . 43.
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