The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 48
... extremities of the straight line which is the base of the segment . IX . And an angle is said to insist or stand upon the circumference intercepted between the straight lines that contain the angle . Definitions VIII . and IX . X. The ...
... extremities of the straight line which is the base of the segment . IX . And an angle is said to insist or stand upon the circumference intercepted between the straight lines that contain the angle . Definitions VIII . and IX . X. The ...
Σελίδα 58
... extremity of it , falls without the circle ; and no straight line can be drawn between that straight line and the circumference from the ex- tremity , so as not to cut the circle ; or , which is the same thing , no straight line can ...
... extremity of it , falls without the circle ; and no straight line can be drawn between that straight line and the circumference from the ex- tremity , so as not to cut the circle ; or , which is the same thing , no straight line can ...
Σελίδα 59
... extremity of it , touches the circle ; and that it touches it only in one point , because if it did meet the circle in two , it would fall within it ( iii . 2 ) . Also , it is evident that there can be but one straight line which ...
... extremity of it , touches the circle ; and that it touches it only in one point , because if it did meet the circle in two , it would fall within it ( iii . 2 ) . Also , it is evident that there can be but one straight line which ...
Σελίδα 69
... extremity of the diameter a e , a d is drawn at right angles to a e , there- fore a d ( iii . 16. cor . ) touches the circle ; and because ab drawn from the point of contact a cuts the circle , the angle dab is equal to the angle in the ...
... extremity of the diameter a e , a d is drawn at right angles to a e , there- fore a d ( iii . 16. cor . ) touches the circle ; and because ab drawn from the point of contact a cuts the circle , the angle dab is equal to the angle in the ...
Σελίδα 72
... drawn at right angles to a diameter , from the extremity of it , touches ( iii . 16 ) the circle : therefore bd touches the circle abc . Wherefore , if from a EXERCISES ON BOOK III . SECT . I. - PROBLEMS 72 THE ELEMENTS OF EUCLID .
... drawn at right angles to a diameter , from the extremity of it , touches ( iii . 16 ) the circle : therefore bd touches the circle abc . Wherefore , if from a EXERCISES ON BOOK III . SECT . I. - PROBLEMS 72 THE ELEMENTS OF EUCLID .
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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