The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 4
... a given finite straight line . LET ab be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre a , at the distance ab , describe ( 3 post . ) the circle bcd , and from the centre b , at ...
... a given finite straight line . LET ab be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre a , at the distance ab , describe ( 3 post . ) the circle bcd , and from the centre b , at ...
Σελίδα 5
... given straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the given point , and be the given straight line ; it is required to draw ...
... given straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the given point , and be the given straight line ; it is required to draw ...
Σελίδα 9
... straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal to ef ... given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal angle , it is ...
... straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal to ef ... given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal angle , it is ...
Σελίδα 10
... straight line fc drawn from the given point c is at right angles to the given straight line a b . a d e b Because dc is equal to ce , and fc common to the two triangles d cf , ecf ; the two sides dc , cf , are equal to the two ec , cf ...
... straight line fc drawn from the given point c is at right angles to the given straight line a b . a d e b Because dc is equal to ce , and fc common to the two triangles d cf , ecf ; the two sides dc , cf , are equal to the two ec , cf ...
Σελίδα 11
Euclides. PROPOSITION XII . — PROBLEM . To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . LET a b be the given straight line , which may be produced to any length both ...
Euclides. PROPOSITION XII . — PROBLEM . To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . LET a b be the given straight line , which may be produced to any length both ...
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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