The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 116
I. SIMILAR rectilineal figures are those which have their several angles equal , each to each , and the sides about the equal angles proportionals . Definition I. II . Reciprocal figures , viz . triangles and parallelograms , are such ...
I. SIMILAR rectilineal figures are those which have their several angles equal , each to each , and the sides about the equal angles proportionals . Definition I. II . Reciprocal figures , viz . triangles and parallelograms , are such ...
Σελίδα 124
In a right - angled triangle , if a perpendicular be drawn from the right angle to the base , the triangles on each side of it are similar to the whole triangle and to one another . Let a b c be a right - angled triangle , having the ...
In a right - angled triangle , if a perpendicular be drawn from the right angle to the base , the triangles on each side of it are similar to the whole triangle and to one another . Let a b c be a right - angled triangle , having the ...
Σελίδα 129
Upon a given straight line to describe a rectilineal figure similar , and similarly situated , to a given rectilineal figure . LET a b be the given straight line , and cdef the given rectilineal figure of four sides ; it is required ...
Upon a given straight line to describe a rectilineal figure similar , and similarly situated , to a given rectilineal figure . LET a b be the given straight line , and cdef the given rectilineal figure of four sides ; it is required ...
Σελίδα 130
Next , let it be required to describe upon a given straight line a b , a rectilineal figure similar , and similarly situated , to the rectilineal figure cdkef . Join de , and upon the given straight line ab describe the rectilineal ...
Next , let it be required to describe upon a given straight line a b , a rectilineal figure similar , and similarly situated , to the rectilineal figure cdkef . Join de , and upon the given straight line ab describe the rectilineal ...
Σελίδα 131
Similar triangles are to one another in the duplicate ratio of their homologous sides . LET a b c d e f be similar triangles , having the angle b equal to the angle e , and let a b be to bc , as de to ef , so that the side bc is ...
Similar triangles are to one another in the duplicate ratio of their homologous sides . LET a b c d e f be similar triangles , having the angle b equal to the angle e , and let a b be to bc , as de to ef , so that the side bc is ...
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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