The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter ...
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter ...
Σελίδα 24
... diameter is the straight line joining two of its opposite angles . Let a cd b be a parallelogram , of which bc is a diameter ; the oppo- site sides and angles of the figure are equal to one another ; and the diameter b c bisects it . a ...
... diameter is the straight line joining two of its opposite angles . Let a cd b be a parallelogram , of which bc is a diameter ; the oppo- site sides and angles of the figure are equal to one another ; and the diameter b c bisects it . a ...
Σελίδα 26
... diameter a b bisects it ( i . 34 ) ; and the triangle dbc is the half of the parallelogram dbcf , because the diameter dc bisects it : but the halves of equal things are equal ( 7 ax . ) ; therefore the triangle abc is equal to the ...
... diameter a b bisects it ( i . 34 ) ; and the triangle dbc is the half of the parallelogram dbcf , because the diameter dc bisects it : but the halves of equal things are equal ( 7 ax . ) ; therefore the triangle abc is equal to the ...
Σελίδα 28
... diameter a c divides it into two equal parts ; wherefore abcd is also double of the triangle e bc . Therefore , if a parallelogram , & c . Q. E. D. PROPOSITION XLII . - PROBLEM . To describe a parallelogram that shall be equal to a ...
... diameter a c divides it into two equal parts ; wherefore abcd is also double of the triangle e bc . Therefore , if a parallelogram , & c . Q. E. D. PROPOSITION XLII . - PROBLEM . To describe a parallelogram that shall be equal to a ...
Σελίδα 29
... diameter of any parallelogram , are equal to one another . LET abcd be a parallelogram , of which the diameter is a c , and eh , fg , the pa- rallelograms about a c , that is , through which ac passes , and bk , kd , the other ...
... diameter of any parallelogram , are equal to one another . LET abcd be a parallelogram , of which the diameter is a c , and eh , fg , the pa- rallelograms about a c , that is , through which ac passes , and bk , kd , the other ...
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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