The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 10
AB to DE , and AC to DF ; CE F the angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite , shall be equal ...
AB to DE , and AC to DF ; CE F the angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite , shall be equal ...
Page 14
Again , because CB is Hyp . equalt to DB , the angle BDC is equal * to the angle BCD ; but BDC has been proved to be greater than the same BCD : which is impossible . ... The angle BAC shall be equal to the angle EDF .
Again , because CB is Hyp . equalt to DB , the angle BDC is equal * to the angle BCD ; but BDC has been proved to be greater than the same BCD : which is impossible . ... The angle BAC shall be equal to the angle EDF .
Page 15
To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle ... DEF ; then join AF : the straight line AF shall bisect the A angle BAC . Because AD is equalt to AE , DA E ...
To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle ... DEF ; then join AF : the straight line AF shall bisect the A angle BAC . Because AD is equalt to AE , DA E ...
Page 21
Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be greater than either of the interior opposite angles CBA , BAC . Bisect * AC in E , join А BE and produce it to F , F and make EF equal t to ...
Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be greater than either of the interior opposite angles CBA , BAC . Bisect * AC in E , join А BE and produce it to F , F and make EF equal t to ...
Page 22
In like manner , it may be demonstrated , that BAC , ACB , as also CÁB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. angle BĆA PROP . XVIII . THEOR . The greater side of every triangle is opposite lo ...
In like manner , it may be demonstrated , that BAC , ACB , as also CÁB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. angle BĆA PROP . XVIII . THEOR . The greater side of every triangle is opposite lo ...
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Common terms and phrases
altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole
Bibliographic information
| Title | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
| Author | Euclid |
| Editors | Robert Simson, Samuel Maynard |
| Translated by | Robert Simson |
| Publisher | Longman, Orme, Brown, Green, and Longmans, 1838 |
| Original from | University of Iowa |
| Digitized | 13 Jul 2015 |
| Length | 328 pages |
| Export Citation | BiBTeX EndNote RefMan |