The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 74
... circumference , FA shall be the greatest , and FD , the other part of the diameter AD , shall be the least : and of the others , FB shall be greater than FC , and FC greater than FG . Join BE , CE , GE : and because two sides of a ...
... circumference , FA shall be the greatest , and FD , the other part of the diameter AD , shall be the least : and of the others , FB shall be greater than FC , and FC greater than FG . Join BE , CE , GE : and because two sides of a ...
Page 75
... circumference ; and BF is greater than CF , and CF than GF . Also , there can be drawn only two equal straight lines from the point F to the circumfer- ence , one upon each side of the shortest line FD . At the point E , in the straight ...
... circumference ; and BF is greater than CF , and CF than GF . Also , there can be drawn only two equal straight lines from the point F to the circumfer- ence , one upon each side of the shortest line FD . At the point E , in the straight ...
Page 76
... circumference , one upon each side of the least line . Let ABC be a circle , and D any point without it , from which let the straight lines DA , DE , DF , DC be drawn to the circumference , where- of DA passes through the centre . Of ...
... circumference , one upon each side of the least line . Let ABC be a circle , and D any point without it , from which let the straight lines DA , DE , DF , DC be drawn to the circumference , where- of DA passes through the centre . Of ...
Page 77
... circumference , one upon each side of the least line . At the point M , in the straight line MD , make the angle DMB equal to the angle DMK , † 23.1 . and join DB : and because MK is equal to MB , and MD common to the triangles KMD ...
... circumference , one upon each side of the least line . At the point M , in the straight line MD , make the angle DMB equal to the angle DMK , † 23.1 . and join DB : and because MK is equal to MB , and MD common to the triangles KMD ...
Page 78
... circumference , and DC is greater * than DB , F and DB greater than DA : but + Hyp . they are likewise † equal , which is impossible : therefore E is not the centre of the circle +3.3 . 1 . * 9.3 . DE B ABC . In like manner it may be ...
... circumference , and DC is greater * than DB , F and DB greater than DA : but + Hyp . they are likewise † equal , which is impossible : therefore E is not the centre of the circle +3.3 . 1 . * 9.3 . DE B ABC . In like manner it may be ...
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