The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 20
... produced do not meet towards b , d . In like manner it may be demonstrated , that they do not meet towards a , c , but those straight lines which meet neither way , though produced ever so far , are parallel ( 35 def . ) to one another ...
... produced do not meet towards b , d . In like manner it may be demonstrated , that they do not meet towards a , c , but those straight lines which meet neither way , though produced ever so far , are parallel ( 35 def . ) to one another ...
Página 21
... produced ; therefore the straight lines ab , cd , if produced far enough , shall meet ; but they never meet , since they are parallel by the hypothesis ; therefore the angle agh is not unequal to the angle ghd , that is , it is equal ...
... produced ; therefore the straight lines ab , cd , if produced far enough , shall meet ; but they never meet , since they are parallel by the hypothesis ; therefore the angle agh is not unequal to the angle ghd , that is , it is equal ...
Página 22
... produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles . LET abc be a triangle , and let one of its sides bc be produced to d ...
... produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles . LET abc be a triangle , and let one of its sides bc be produced to d ...
Página 29
... produced far enough : therefore hb , fe shall meet if produced ; let them meet in k , and through BOOK I. PROPS . XLIII . , XLIV . 29.
... produced far enough : therefore hb , fe shall meet if produced ; let them meet in k , and through BOOK I. PROPS . XLIII . , XLIV . 29.
Página 30
Euclides. produced ; let them meet in k , and through k draw kl , parallel to ea or fh , and produce ha , gb to the points 1 , m : then hlkf is a paral- lelogram , of which the diameter is hk , and ag , me are the parallelograms about hk ...
Euclides. produced ; let them meet in k , and through k draw kl , parallel to ea or fh , and produce ha , gb to the points 1 , m : then hlkf is a paral- lelogram , of which the diameter is hk , and ag , me are the parallelograms about hk ...
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Términos y frases comunes
ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle