The first six books of the Elements of Euclid, with numerous exercises |
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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 19
Let the straight line ef , which falls upon the two straight lines a b , cd , make the alternate angles a ef , efd equal to one another ; ab is parallel to cd . For , if it be not parallel , a b BOOK I. 19 PROP . XXVII .
Let the straight line ef , which falls upon the two straight lines a b , cd , make the alternate angles a ef , efd equal to one another ; ab is parallel to cd . For , if it be not parallel , a b BOOK I. 19 PROP . XXVII .
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
If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the ...
If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the ...
Σελίδα 22
To draw a straight line through a given point parallel to a given straight line . LET a be the given point , and bc the given straight line ; it is required to draw a straight line through the point a , parallel to the straight line ...
To draw a straight line through a given point parallel to a given straight line . LET a be the given point , and bc the given straight line ; it is required to draw a straight line through the point a , parallel to the straight line ...
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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