The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 24
... reason , the ex- terior angle CEB of the triangle ABE is greater than BAC and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
... reason , the ex- terior angle CEB of the triangle ABE is greater than BAC and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
Page 37
... reason EF is equal to BC ; where- fore AD is equal to EF ; and DE is common ; * ] Ax . therefore the whole , or the remainder , AE is equal to the whole , or the remainder , DF : AB * 2 or 3 also is equal to DC ; therefore the two EA ...
... reason EF is equal to BC ; where- fore AD is equal to EF ; and DE is common ; * ] Ax . therefore the whole , or the remainder , AE is equal to the whole , or the remainder , DF : AB * 2 or 3 also is equal to DC ; therefore the two EA ...
Page 38
... reason , the parallelogram EFGH is equal to the same EBCH : therefore the parallelogram ABCD is +1 Ax . equal to EFGH . Wherefore parallelograms , & c . Q. E. D. + Dcí . St. 1 . * 35 . 1 . * PROP . XXXVII . THEOR . Triangles upon the ...
... reason , the parallelogram EFGH is equal to the same EBCH : therefore the parallelogram ABCD is +1 Ax . equal to EFGH . Wherefore parallelograms , & c . Q. E. D. + Dcí . St. 1 . * 35 . 1 . * PROP . XXXVII . THEOR . Triangles upon the ...
Page 43
... reason , the triangle KGC is equal to the triangle KFC . Therefore , because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC : the triangle AEK together with the triangle KGC is equal † +2 Ax to the triangle ...
... reason , the triangle KGC is equal to the triangle KFC . Therefore , because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC : the triangle AEK together with the triangle KGC is equal † +2 Ax to the triangle ...
Page 47
... reason , AB and AH are in the D E same straight line . And because the angle DBC is equal to the angle +11 Ax . FBA , each of them being a right † angle , add to † 30Def . each the angle ABC ; therefore the whole angle * DBA is equal to ...
... reason , AB and AH are in the D E same straight line . And because the angle DBC is equal to the angle +11 Ax . FBA , each of them being a right † angle , add to † 30Def . each the angle ABC ; therefore the whole angle * DBA is equal to ...
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