The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 24
Again , because the exterior angle of a triangle * is greater than the interior and opposite angle , the exterior angle DC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is ...
Again , because the exterior angle of a triangle * is greater than the interior and opposite angle , the exterior angle DC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is ...
Page 37
1 . for the same reason EF is equal to BC ; wherefore AD is equal * to EF ; and DE is common therefore the whole , or the remainder , AE is equal * to the whole , or the remainder , DF : AB * 2 or 3 also is equalf to DC ; therefore the ...
1 . for the same reason EF is equal to BC ; wherefore AD is equal * to EF ; and DE is common therefore the whole , or the remainder , AE is equal * to the whole , or the remainder , DF : AB * 2 or 3 also is equalf to DC ; therefore the ...
Page 38
... and between the same parallels BC , AH : for the like reason , .the parallelogram EFGH is equal to the same EBCH : therefore the parallelogram ABCD is +1 Ax . equal t to EFGH . Wherefore parallelograms , & c . Q. E. D. , * St. 1 .
... and between the same parallels BC , AH : for the like reason , .the parallelogram EFGH is equal to the same EBCH : therefore the parallelogram ABCD is +1 Ax . equal t to EFGH . Wherefore parallelograms , & c . Q. E. D. , * St. 1 .
Page 43
Again , because EKHA is a parallelogram , the diameter of which is AK , the triangle AEK is equalt to the triangle AHK ; +34 1 . and for the same reason , the triangle KGC is equal to the triangle KFC . Therefore , because the triangle ...
Again , because EKHA is a parallelogram , the diameter of which is AK , the triangle AEK is equalt to the triangle AHK ; +34 1 . and for the same reason , the triangle KGC is equal to the triangle KFC . Therefore , because the triangle ...
Page 47
... opposite sides of AB , make with it at the point F A the adjacent angles > K equal to two right angles ; Bi IC therefore CA is in the same straight line * with AG : for the same reason , AB and AH are in the D same straight line .
... opposite sides of AB , make with it at the point F A the adjacent angles > K equal to two right angles ; Bi IC therefore CA is in the same straight line * with AG : for the same reason , AB and AH are in the D same straight line .
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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |
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 |