The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 59
... half the line bisected , and of the square of the line made up of the half and the part produced . Let the straight line AB be bisected in Cand produced to the point D : the squares of AD , DB shall be double of the squares of AC , CD ...
... half the line bisected , and of the square of the line made up of the half and the part produced . Let the straight line AB be bisected in Cand produced to the point D : the squares of AD , DB shall be double of the squares of AC , CD ...
Page 60
... half * a right angle . For the same reason , each of the angles CEB , EBC , is half a right angle : there- fore AEB is a right angle . And because EBC is half a right angle , DBG is also * half a right angle , for they are vertically ...
... half * a right angle . For the same reason , each of the angles CEB , EBC , is half a right angle : there- fore AEB is a right angle . And because EBC is half a right angle , DBG is also * half a right angle , for they are vertically ...
Page 94
... half of the angle BGC , and the angle at D half of the angle EHF ; therefore the angle at A is equal † to the angle at D. Wherefore , in equal circles , & c . Q.E. D. † 20. 3 . +7 Ax . * 1. 3 . PROP . XXVIII . THEOR . In equal circles ...
... half of the angle BGC , and the angle at D half of the angle EHF ; therefore the angle at A is equal † to the angle at D. Wherefore , in equal circles , & c . Q.E. D. † 20. 3 . +7 Ax . * 1. 3 . PROP . XXVIII . THEOR . In equal circles ...
Page 114
... half of AD , and AF the half of AB , AE is equal to AF ; wherefore the sides opposite to these are equal , A viz . FG to GE : in the same manner it may be demonstrated that GH , GK are each of them equal to FG or GE : therefore 1 . 17 ...
... half of AD , and AF the half of AB , AE is equal to AF ; wherefore the sides opposite to these are equal , A viz . FG to GE : in the same manner it may be demonstrated that GH , GK are each of them equal to FG or GE : therefore 1 . 17 ...
Page 115
... half of DAB , and EBA the half of ABC ; the angle EAB is equal to the angle EBA ; +7 Ax wherefore the side EÂ is equal * to the side EB : * 6 . 1 . in the same manner it may be demonstrated that the straight lines EC , ED are each of ...
... half of DAB , and EBA the half of ABC ; the angle EAB is equal to the angle EBA ; +7 Ax wherefore the side EÂ is equal * to the side EB : * 6 . 1 . in the same manner it may be demonstrated that the straight lines EC , ED are each of ...
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