The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 10
... Wherefore , from the given point c , in the given straight line a b , fc has been drawn at right angles to a b . Which was to be done . COR . By help of this problem , it may be demonstrated , that two straight lines cannot have a ...
... Wherefore , from the given point c , in the given straight line a b , fc has been drawn at right angles to a b . Which was to be done . COR . By help of this problem , it may be demonstrated , that two straight lines cannot have a ...
Σελίδα 12
... Wherefore , the angles which one straight line , & c . Q. E. D. PROPOSITION XIV . - THEOREM . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two ...
... Wherefore , the angles which one straight line , & c . Q. E. D. PROPOSITION XIV . - THEOREM . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two ...
Σελίδα 13
... wherefore the angle bae is equal to the angle ecf ; but the angle ecd is greater than the angle e cf ; therefore the angle a cd is greater than b a d g \ bae . In the same manner , if the side b c be bisected , it may be demon- strated ...
... wherefore the angle bae is equal to the angle ecf ; but the angle ecd is greater than the angle e cf ; therefore the angle a cd is greater than b a d g \ bae . In the same manner , if the side b c be bisected , it may be demon- strated ...
Σελίδα 14
... Wherefore the greater angle , & c . b C Q. E. D. PROPOSITION XX . THEOREM . Any two sides of a triangle are together greater than the third side . LET abc be a triangle ; any two sides of it together are greater than the third side ...
... Wherefore the greater angle , & c . b C Q. E. D. PROPOSITION XX . THEOREM . Any two sides of a triangle are together greater than the third side . LET abc be a triangle ; any two sides of it together are greater than the third side ...
Σελίδα 18
... Wherefore , if two triangles , & c . Q. E. D. PROPOSITION XXVI . - THEOREM . If two triangles have two angles of the one equal to two angles of the other , each to each , and one side equal to one side , viz . either the sides adjacent ...
... Wherefore , if two triangles , & c . Q. E. D. PROPOSITION XXVI . - THEOREM . If two triangles have two angles of the one equal to two angles of the other , each to each , and one side equal to one side , viz . either the sides adjacent ...
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a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle