The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Results 6-10 of 48
Page 24
... angle BDC greater than the angle BAC . Produce BD to E ; and because two sides of a * 20 . 1. triangle * are greater than the third side , the two sides BA , AE , of the triangle ABE are greater than BE . To each of these add EC ...
... angle BDC greater than the angle BAC . Produce BD to E ; and because two sides of a * 20 . 1. triangle * are greater than the third side , the two sides BA , AE , of the triangle ABE are greater than BE . To each of these add EC ...
Page 26
... angle ; it is required to make an angle at the given point A in the given straight line AB , that shall be equal to the given angle DCE . rectilineal AA În CD , CE , take any D4 points D , E , and join DE ... angle BAC 26 EUCLID'S ELEMENTS .
... angle ; it is required to make an angle at the given point A in the given straight line AB , that shall be equal to the given angle DCE . rectilineal AA În CD , CE , take any D4 points D , E , and join DE ... angle BAC 26 EUCLID'S ELEMENTS .
Page 27
... angle BAC is equal to the angle EDG ; therefore the hase BC is equal * to the base EG . And because DG is equal + Const . * 4.1 . G to DF , the angle DFG is equal to the angle DGF ; but the angle * E . 1 . DGF is greater than the angle ...
... angle BAC is equal to the angle EDG ; therefore the hase BC is equal * to the base EG . And because DG is equal + Const . * 4.1 . G to DF , the angle DFG is equal to the angle DGF ; but the angle * E . 1 . DGF is greater than the angle ...
Page 28
... angle BAC is not equal to the angle EDF : neither is it less , because then * 24 . 1. the base BC would be less than the base EF : Hyp . but it is not ; therefore the angle BAC is not less than the angle EDF : and it was shown that it ...
... angle BAC is not equal to the angle EDF : neither is it less , because then * 24 . 1. the base BC would be less than the base EF : Hyp . but it is not ; therefore the angle BAC is not less than the angle EDF : and it was shown that it ...
Page 29
... angle , ABC is equal to the angle DEF ; therefore the base + Hyp . AC is equal to the base DF , and the third angle * 4 . 1 . BAC to the third angle EDF . Next , let the sides which are opposite to equal angles in each triangle be equal ...
... angle , ABC is equal to the angle DEF ; therefore the base + Hyp . AC is equal to the base DF , and the third angle * 4 . 1 . BAC to the third angle EDF . Next , let the sides which are opposite to equal angles in each triangle be equal ...
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