The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 17
... perpendicular to a given straight line of an unlimited length , from a given point without it . C Let AB bé the given straight line , which may be produced to any length both ways , and let C be a point with- out it . It is required to ...
... perpendicular to a given straight line of an unlimited length , from a given point without it . C Let AB bé the given straight line , which may be produced to any length both ways , and let C be a point with- out it . It is required to ...
Page 18
... perpendicular to the given straight line AB . † Const . * 8 . 1 . * Join CF , CG : and because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and ...
... perpendicular to the given straight line AB . † Const . * 8 . 1 . * Join CF , CG : and because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and ...
Page 62
... perpendicular be drawn from either of the acute angles to the opposite side produced , the square of the side subtending the obtuse angle , is greater than the squares of the sides containing the obtuse angle , by twice the rectangle ...
... perpendicular be drawn from either of the acute angles to the opposite side produced , the square of the side subtending the obtuse angle , is greater than the squares of the sides containing the obtuse angle , by twice the rectangle ...
Page 63
... perpendicular to BC produced : * 12 . 1 . the square of AB shall be greater than the squares of AC , CB , by twice ... perpendicular let fall upon it from the opposite angle , and the acute angle . Let ABC be any triangle , and the angle ...
... perpendicular to BC produced : * 12 . 1 . the square of AB shall be greater than the squares of AC , CB , by twice ... perpendicular let fall upon it from the opposite angle , and the acute angle . Let ABC be any triangle , and the angle ...
Page 84
... perpendicular to AF , and let it meet the circumference in H. And because AGD is a right angle , and DAG less than a right angle , DA is greater than DG : but DA +15 Def . is equal to DH ; therefore * 17. 1 . 1 . 19. 1 . DH is greater ...
... perpendicular to AF , and let it meet the circumference in H. And because AGD is a right angle , and DAG less than a right angle , DA is greater than DG : but DA +15 Def . is equal to DH ; therefore * 17. 1 . 1 . 19. 1 . DH is greater ...
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