The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 34
... parallelograms be inscribed in a given parallelo- gram , the diameters of all the figures shall cut one another in the same point . 26. In a parallelogram the diameters bisect each other . BOOK II . DEFINITIONS . I. EVERY right - angled ...
... parallelograms be inscribed in a given parallelo- gram , the diameters of all the figures shall cut one another in the same point . 26. In a parallelogram the diameters bisect each other . BOOK II . DEFINITIONS . I. EVERY right - angled ...
Σελίδα 35
Euclides. BOOK II . DEFINITIONS . I. EVERY right - angled parallelogram is said to be contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any of the parallelograms about a ...
Euclides. BOOK II . DEFINITIONS . I. EVERY right - angled parallelogram is said to be contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any of the parallelograms about a ...
Σελίδα 37
... parallelograms about the diameter of a square are likewise squares . PROPOSITION V. - THEOREM . If a straight line be divided into two equal parts , and also into two unequal parts , the rectangle contained by the unequal parts ...
... parallelograms about the diameter of a square are likewise squares . PROPOSITION V. - THEOREM . If a straight line be divided into two equal parts , and also into two unequal parts , the rectangle contained by the unequal parts ...
Σελίδα 40
... parallelogram co ; therefore also bn is equal to gr ; and the four rectangles bn , ck , gr , rn are there- fore equal to one another , and so are quadruple of one of them ck . Again , because cb is equal to bd , and that bd is equal ...
... parallelogram co ; therefore also bn is equal to gr ; and the four rectangles bn , ck , gr , rn are there- fore equal to one another , and so are quadruple of one of them ck . Again , because cb is equal to bd , and that bd is equal ...
Σελίδα 45
... parallelogram bcde equal to the rectilineal figure a . If then the sides of it , be , ed , are equal to one another , it is a square , and what was required is now done . are not equal , produce one of them be to f , and make ef equal ...
... parallelogram bcde equal to the rectilineal figure a . If then the sides of it , be , ed , are equal to one another , it is a square , and what was required is now done . are not equal , produce one of them be to f , and make ef equal ...
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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