The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 6
If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and ...
If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and ...
Σελίδα 14
Any two sides of a triangle are together greater than the third side . 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 ...
Any two sides of a triangle are together greater than the third side . 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 ...
Σελίδα 15
Therefore , if from the ends of , & c . Q. E. D. PROPOSITION XXII . — PROBLEM . To make a triangle of which the sides shall be equal to three given straight lines , but any two whatever of these must be greater than the third ( i ...
Therefore , if from the ends of , & c . Q. E. D. PROPOSITION XXII . — PROBLEM . To make a triangle of which the sides shall be equal to three given straight lines , but any two whatever of these must be greater than the third ( i ...
Σελίδα 18
a b to de , and ac b f to df , and the third angle bac to the third angle edf . For , if a b be not equal to de , one of them must be the greater . Let a b be the greater of the two , and make bg equal to de , and join gc ; therefore ...
a b to de , and ac b f to df , and the third angle bac to the third angle edf . For , if a b be not equal to de , one of them must be the greater . Let a b be the greater of the two , and make bg equal to de , and join gc ; therefore ...
Σελίδα 19
4 ) to the base d f , and the third angle bac to the third angle ed f . Next , let the sides which are opposite to equal angles in each triangle be equal to one another , viz . a b to de ; likewise in this case , the other sides shall ...
4 ) to the base d f , and the third angle bac to the third angle ed f . Next , let the sides which are opposite to equal angles in each triangle be equal to one another , viz . a b to de ; likewise in this case , the other sides shall ...
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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