The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 52
... common to the triangles bef , cef , the two sides be , ef are equal to the two ce , ef ; but the angle bef is greater than the angle cef ; therefore the base bf is greater ( i . 24 ) than the base fc : for the same reason cf is greater ...
... common to the triangles bef , cef , the two sides be , ef are equal to the two ce , ef ; but the angle bef is greater than the angle cef ; therefore the base bf is greater ( i . 24 ) than the base fc : for the same reason cf is greater ...
Σελίδα 53
... common to the triangles emd , fmd ; em , md are equal to fm , md : but the angle emd is greater than the angle fmd ; therefore the base ed is greater than the base fd ( i . 24 ) . In like manner it may be shewn that fd is greater than ...
... common to the triangles emd , fmd ; em , md are equal to fm , md : but the angle emd is greater than the angle fmd ; therefore the base ed is greater than the base fd ( i . 24 ) . In like manner it may be shewn that fd is greater than ...
Σελίδα 55
... common part fg ; there- fore the remainder a g is greater than the remainder gh . But ag is equal to gd ; therefore gd is greater than gh , the less than the greater , which is impossible . h rd * ક Therefore the straight line which ...
... common part fg ; there- fore the remainder a g is greater than the remainder gh . But ag is equal to gd ; therefore gd is greater than gh , the less than the greater , which is impossible . h rd * ક Therefore the straight line which ...
Σελίδα 59
... common to the two triangles aeb , fed therefore the base df is equal to the base ab ; and the tri- angle fed to the triangle aeb , and the other angles to the other angles ( i . 4 ) : therefore the angle e ba is equal to the angle e df ...
... common to the two triangles aeb , fed therefore the base df is equal to the base ab ; and the tri- angle fed to the triangle aeb , and the other angles to the other angles ( i . 4 ) : therefore the angle e ba is equal to the angle e df ...
Σελίδα 64
... common to the tri- angles a de , cde , the two sides ad , de are equal to the two cd , de , · each to each ; and the angle ade is equal to the angle cde , for each of them is a right angle ; therefore the base ae is equal ( i . 4 ) to ...
... common to the tri- angles a de , cde , the two sides ad , de are equal to the two cd , de , · each to each ; and the angle ade is equal to the angle cde , for each of them is a right angle ; therefore the base ae is equal ( i . 4 ) to ...
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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