The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
... angle which is contained by the straight lines ab , cb , is named the angle a bc , or cba ; that which is contained by a b , db , is named the angle abd , or dba ; and that which is con- tained by db , cb , is called the angle dbc , or ...
... angle which is contained by the straight lines ab , cb , is named the angle a bc , or cba ; that which is contained by a b , db , is named the angle abd , or dba ; and that which is con- tained by db , cb , is called the angle dbc , or ...
Σελίδα 5
... cb , are each of them equal to ab ; but things which are equal to the same are equal to one another ( 1 ax . ) ; therefore ca is equal to cb ; wherefore ca , ab , bc are equal to one another ; and the tri- angle abc is therefore ...
... cb , are each of them equal to ab ; but things which are equal to the same are equal to one another ( 1 ax . ) ; therefore ca is equal to cb ; wherefore ca , ab , bc are equal to one another ; and the tri- angle abc is therefore ...
Σελίδα 6
... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a b c to the angle def , and the angle a cb to dfe . Therefore , if two triangles have two sides of the one equal to two ...
... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a b c to the angle def , and the angle a cb to dfe . Therefore , if two triangles have two sides of the one equal to two ...
Σελίδα 7
... cb , each to each ; and the angle dbc is equal to the angle a cb ; therefore the base dc is equal to the base ab , and the triangle db c is equal to the triangle ( i . 4 ) a cb , the less to the greater ; which is absurd . Therefore ab ...
... cb , each to each ; and the angle dbc is equal to the angle a cb ; therefore the base dc is equal to the base ab , and the triangle db c is equal to the triangle ( i . 4 ) a cb , the less to the greater ; which is absurd . Therefore ab ...
Σελίδα 8
... cb , db , that are terminated in b . a bcd ; much greater Again , because cb is angle bcd ; but it has impossible . But if one of the produce a c , ad to a f Join cd ; then , in the case in which the vertex of each of the triangles is ...
... cb , db , that are terminated in b . a bcd ; much greater Again , because cb is angle bcd ; but it has impossible . But if one of the produce a c , ad to a f Join cd ; then , in the case in which the vertex of each of the triangles is ...
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a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle