The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 131
... similar triangles , & c . Q. E. D. COR . From this it is manifest , that if three straight lines be propor- tionals , as the first is to the third , so is any triangle upon the first to a similar and similarly described triangle upon ...
... similar triangles , & c . Q. E. D. COR . From this it is manifest , that if three straight lines be propor- tionals , as the first is to the third , so is any triangle upon the first to a similar and similarly described triangle upon ...
Σελίδα 132
... similar triangles , whereof each to each has the same ratio which the polygons have ; and the polygon abcde has to the polygon fghkl the duplicate ratio of that which the side a b has to the side fg . Join be , ec , gl , 1h and because ...
... similar triangles , whereof each to each has the same ratio which the polygons have ; and the polygon abcde has to the polygon fghkl the duplicate ratio of that which the side a b has to the side fg . Join be , ec , gl , 1h and because ...
Σελίδα 133
... similar polygons , & c . Q. E. D. COR . 1. In like manner , it may be proved , that similar four - sided figures , or of any number of sides , are one to another in the duplicate ratio of their homologous sides , and it has already been ...
... similar polygons , & c . Q. E. D. COR . 1. In like manner , it may be proved , that similar four - sided figures , or of any number of sides , are one to another in the duplicate ratio of their homologous sides , and it has already been ...
Σελίδα 134
... similar ( vi . def . 1 ) to b . Q. E. D. PROPOSITION XXII . - THEOREM . If four straight lines be proportionals , the similar rectilineal figures similarly described upon them shall also be proportionals ; and if the similar recti ...
... similar ( vi . def . 1 ) to b . Q. E. D. PROPOSITION XXII . - THEOREM . If four straight lines be proportionals , the similar rectilineal figures similarly described upon them shall also be proportionals ; and if the similar recti ...
Σελίδα 135
... similar to the whole and to one another , LET abcd be a parallelogram , of which the diameter is a c ; and eg , hk the parallelograms about the diameter . The parallelograms eg , h k are similar both to the whole parallelogram a bcd ...
... similar to the whole and to one another , LET abcd be a parallelogram , of which the diameter is a c ; and eg , hk the parallelograms about the diameter . The parallelograms eg , h k are similar both to the whole parallelogram a bcd ...
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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