The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 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 a gh 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 a gh is not unequal to the angle ghd , that is , it is equal ...
Σελίδα 22
... produce the straight line ea to f Because the straight line ad , which meets the two straight lines bc , ef , makes ... produced to d ; the exterior angle a cd is equal to the two interior and opposite angles cab , abc , and the three ...
... produce the straight line ea to f Because the straight line ad , which meets the two straight lines bc , ef , makes ... produced to d ; the exterior angle a cd is equal to the two interior and opposite angles cab , abc , and the three ...
Σελίδα 26
... Produce ad both ways to the points e , f , and through b draw ( i . 31 ) be parallel to ca ; and through c draw cf parallel to bd ; therefore each of the figures ebca , dbcf is a paral- lelogram ; and ebca is equal ( i . 35 ) to dbcf ...
... Produce ad both ways to the points e , f , and through b draw ( i . 31 ) be parallel to ca ; and through c draw cf parallel to bd ; therefore each of the figures ebca , dbcf is a paral- lelogram ; and ebca is equal ( i . 35 ) to dbcf ...
Σελίδα 29
... produce fg to h ; and through a draw ( i . 31 ) ah parallel to bg or ef , and join h b . Then , because the straight line hf falls upon the pa- rallels ah ... produced ; let them meet in k , and through BOOK I. PROPS . XLIII . , XLIV . 29 29.
... produce fg to h ; and through a draw ( i . 31 ) ah parallel to bg or ef , and join h b . Then , because the straight line hf falls upon the pa- rallels ah ... produced ; let them meet in k , and through BOOK I. PROPS . XLIII . , XLIV . 29 29.
Σελίδα 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 a g , me are the parallelograms about ...
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 a g , me are the parallelograms about ...
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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