The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 89
... Ratio is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity . IV ... duplicate ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first ...
... Ratio is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity . IV ... duplicate ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first ...
Σελίδα 131
... duplicate ratio of that which be has to ef . Take bg a third proportional to bc , ef ( vi . 11 ) so that be is to ef as ef to bg , and join ga : then , because , as ab to bc , so de to ef ; alternately ( v . 16 ) ab is to de as bc to ef ...
... duplicate ratio of that which be has to ef . Take bg a third proportional to bc , ef ( vi . 11 ) so that be is to ef as ef to bg , and join ga : then , because , as ab to bc , so de to ef ; alternately ( v . 16 ) ab is to de as bc to ef ...
Σελίδα 132
... ratio which the polygons have ; and the polygon abcde has to the polygon fghkl the duplicate ratio of that which the side abhas to the side fg . 18 . Join be , ec , gl , lh : and because the polygon abcde is similar to the polygon fghkl ...
... ratio which the polygons have ; and the polygon abcde has to the polygon fghkl the duplicate ratio of that which the side abhas to the side fg . 18 . Join be , ec , gl , lh : and because the polygon abcde is similar to the polygon fghkl ...
Σελίδα 133
... duplicate ratio of that which the side ab has to the homo- logous side fg . Therefore also the polygon abcde has to the polygon fghkl the duplicate ratio of that which ab has to the homologous side fg . Wherefore similar polygons , & c ...
... duplicate ratio of that which the side ab has to the homo- logous side fg . Therefore also the polygon abcde has to the polygon fghkl the duplicate ratio of that which ab has to the homologous side fg . Wherefore similar polygons , & c ...
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ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle