The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 4
Euclides. POSTULATES . I. Let it be granted that a straight line may be drawn ... LET ab be the given straight line ; it is required to describe an ... abc shall be an equilateral triangle . Because the point a is the centre of ...
Euclides. POSTULATES . I. Let it be granted that a straight line may be drawn ... LET ab be the given straight line ; it is required to describe an ... abc shall be an equilateral triangle . Because the point a is the centre of ...
Σελίδα 5
... abc is therefore equilateral , and it is described upon the given straight line ab . 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 ...
... abc is therefore equilateral , and it is described upon the given straight line ab . 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 ...
Σελίδα 6
... LET abc , def be two triangles , which have the two sides ab , ac equal to the two sides de , df , each to each , viz . ab to de , and acto df ; and the angle bac equal to the angle edf , the base be shall be equal to the base ef ; and ...
... LET abc , def be two triangles , which have the two sides ab , ac equal to the two sides de , df , each to each , viz . ab to de , and acto df ; and the angle bac equal to the angle edf , the base be shall be equal to the base ef ; and ...
Σελίδα 7
... LET abc be a triangle having the angle abc equal to the angle acb ; the side ab is also equal to the side ac . For , if ab be not equal to ac , one of them is greater than the other : let ab be the greater ; and from it cut ( i . 3 ) ...
... LET abc be a triangle having the angle abc equal to the angle acb ; the side ab is also equal to the side ac . For , if ab be not equal to ac , one of them is greater than the other : let ab be the greater ; and from it cut ( i . 3 ) ...
Σελίδα 8
... let there be two triangles acb , ad b , upon the same base a b , and upon the same side of it , which have their ... LET abc , def be two triangles , having the two sides ab , ac , equal to the two sides de , df , each to each 8 ...
... let there be two triangles acb , ad b , upon the same base a b , and upon the same side of it , which have their ... LET abc , def be two triangles , having the two sides ab , ac , equal to the two sides de , df , each to each 8 ...
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ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle