The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 1
A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . IX . A plane rectilineal angle is the inclination of two straight lines to one another , which meet ...
A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . IX . A plane rectilineal angle is the inclination of two straight lines to one another , which meet ...
Σελίδα 3
Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . a I. Let it be granted that a DEFINITIONS . 3.
Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . a I. Let it be granted that a DEFINITIONS . 3.
Σελίδα 4
... meets two straight lines , so as to make the two interior angles on the same side of it taken together less than two right angles , these straight lines being continually produced , shall at length meet upon that side on which are ...
... meets two straight lines , so as to make the two interior angles on the same side of it taken together less than two right angles , these straight lines being continually produced , shall at length meet upon that side on which are ...
Σελίδα 20
For , if it be not parallel , a b and cd being produced shall meet either towards b , d , or towards a , c : let them be produced and meet towards b , d in the point g ; therefore gef is a triangle , and its exterior angle a efis ...
For , if it be not parallel , a b and cd being produced shall meet either towards b , d , or towards a , c : let them be produced and meet towards b , d in the point g ; therefore gef is a triangle , and its exterior angle a efis ...
Σελίδα 21
... do meet ( 12 ax :) together if continually produced ; therefore the straight lines a b , cd , if produced far enough , shall meet ; but they never meet , since they are parallel by the hypothesis ; therefore the angle agh is not ...
... do meet ( 12 ax :) together if continually produced ; therefore the straight lines a b , cd , if produced far enough , shall meet ; but they never meet , since they are parallel by the hypothesis ; therefore the angle agh is not ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole