The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 1
... taken , the straight line between them lies wholly in that superficies . VIII . A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . IX . A plane rectilineal ...
... taken , the straight line between them lies wholly in that superficies . VIII . A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . IX . A plane rectilineal ...
Σελίδα 4
... taken from equals , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the same , are equal to one ...
... taken from equals , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the same , are equal to one ...
Σελίδα 49
... taken in the circumference of a circle , the straight line which joins them shall fall within the circle . LET a b c be a circle , and a , b any two points in the circumference ; the straight line drawn from a to b shall fall within the ...
... taken in the circumference of a circle , the straight line which joins them shall fall within the circle . LET a b c be a circle , and a , b any two points in the circumference ; the straight line drawn from a to b shall fall within the ...
Σελίδα 51
... taken in the diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and ...
... taken in the diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and ...
Σελίδα 52
... taken , & c . Q. E. D. PROPOSITION VIII . - THEOREM . If any point be taken without a circle , and straight lines be drawn from it to the circumference , whereof one passes through the centre ; of those which fall upon the concave ...
... taken , & c . Q. E. D. PROPOSITION VIII . - THEOREM . If any point be taken without a circle , and straight lines be drawn from it to the circumference , whereof one passes through the centre ; of those which fall upon the concave ...
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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