The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 11
LET a b be the given straight line , which may be produced to any length both ways , and let c be a point without it . It is required to draw a straight line perpendicular to a b from the point c . Take any point d upon the other side ...
LET a b be the given straight line , which may be produced to any length both ways , and let c be a point without it . It is required to draw a straight line perpendicular to a b from the point c . Take any point d upon the other side ...
Σελίδα 13
If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . LET a b c be a triangle , and let its side bc be produced to d , the exterior с angle a cd is greater than either of the ...
If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . LET a b c be a triangle , and let its side bc be produced to d , the exterior с angle a cd is greater than either of the ...
Σελίδα 14
LET a b c be a triangle ; any two sides of it together are greater than the . third side , viz . the sides ba , ac greater than the side bc ; and a b , b c greater than a c ; and b c , ca greater than a b . Produce ba to the point d ...
LET a b c be a triangle ; any two sides of it together are greater than the . third side , viz . the sides ba , ac greater than the side bc ; and a b , b c greater than a c ; and b c , ca greater than a b . Produce ba to the point d ...
Σελίδα 15
... c , the ends of the side b c of the triangle a bc , to the point d within it ; bd and dc are less than the other two sides ba , a c of the triangle , but contain an angle bdc greater than the angle bac . Produce bd to e ...
... c , the ends of the side b c of the triangle a bc , to the point d within it ; bd and dc are less than the other two sides ba , a c of the triangle , but contain an angle bdc greater than the angle bac . Produce bd to e ...
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 ...
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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