The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 2
An obtuse angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . Obtuse . Acute . XIII . A term or boundary is the extremity of any thing . XIV .
An obtuse angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . Obtuse . Acute . XIII . A term or boundary is the extremity of any thing . XIV .
Σελίδα 4
Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . * IX . The whole is greater than its part .
Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . * IX . The whole is greater than its part .
Σελίδα 5
PROBLEM , From the greater of two given straight lines to cut off a part equal to the less , LET ab and c be the two given straight lines , d whereof a b is the greater . It is required to a cut off from a b , the greater , a part equal ...
PROBLEM , From the greater of two given straight lines to cut off a part equal to the less , LET ab and c be the two given straight lines , d whereof a b is the greater . It is required to a cut off from a b , the greater , a part equal ...
Σελίδα 6
to c , and from a b , the greater of two straight lines , a part a e has been cut off equal to c the less . Which was to be done . PROPOSITION IV . — THEOREM . If two triangles have two sides of the one equal to two sides of the other ...
to c , and from a b , the greater of two straight lines , a part a e has been cut off equal to c the less . Which was to be done . PROPOSITION IV . — THEOREM . If two triangles have two sides of the one equal to two sides of the other ...
Σελίδα 7
09 In bd take any point f , and from a e the greater , cut off ag equal ( i . 3 ) to a f , the less , and join fc , g b . Because a f is equal to ag , and a b to a c , the two sides fa , a c are equal to the two ga , a b , each to each ...
09 In bd take any point f , and from a e the greater , cut off ag equal ( i . 3 ) to a f , the less , and join fc , g b . Because a f is equal to ag , and a b to a c , the two sides fa , a c are equal to the two ga , a b , each to each ...
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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