The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 36
... rectangle * ab , a d C f bac , shall be equal to the square of a b . e Upon ab describe ( i . 46 ) the square adeb , and through e draw ( i . 31 ) cf , parallel to ad or be . Then ae is equal to the rectangles af , ce ; and ae is the ...
... rectangle * ab , a d C f bac , shall be equal to the square of a b . e Upon ab describe ( i . 46 ) the square adeb , and through e draw ( i . 31 ) cf , parallel to ad or be . Then ae is equal to the rectangles af , ce ; and ae is the ...
Σελίδα 37
... rectangle con- tained by ac , cb . Upon ab describe ( i . 46 ) the square adeb , and join bd , and through c draw ( i . 31 ) cgf parallel to ad or be , and through g draw hk parallel to ab orde . And because cf is parallel to ad , and ...
... rectangle con- tained by ac , cb . Upon ab describe ( i . 46 ) the square adeb , and join bd , and through c draw ( i . 31 ) cgf parallel to ad or be , and through g draw hk parallel to ab orde . And because cf is parallel to ad , and ...
Σελίδα 38
Euclides. and into two unequal parts at the point d ; the rectangle ad , db , together with the square of cd , is equal to the square of cb . Upon cb describe ( i . 46 ) the square cefb , join be , and through d draw ( i . 31 ) dhg ...
Euclides. and into two unequal parts at the point d ; the rectangle ad , db , together with the square of cd , is equal to the square of cb . Upon cb describe ( i . 46 ) the square cefb , join be , and through d draw ( i . 31 ) dhg ...
Σελίδα 39
Euclides. angle ad , db , together with the square of cb , is equal to the gnomon cmg , and the figure 18 ; but the gnomon cmg and 1g make up the whole figure cefd , which is the square of cd ; therefore the rectangle ad , db , together ...
Euclides. angle ad , db , together with the square of cb , is equal to the gnomon cmg , and the figure 18 ; but the gnomon cmg and 1g make up the whole figure cefd , which is the square of cd ; therefore the rectangle ad , db , together ...
Σελίδα 40
... rectangle ck is equal ( i . 36 ) to bn , and gr to rn ; but ck is equal ( i . 43 ) to rn , because they are the ... ad : therefore four times the rectangle ab , bc , together with the square of ac , is equal to the square of a d ...
... rectangle ck is equal ( i . 36 ) to bn , and gr to rn ; but ck is equal ( i . 43 ) to rn , because they are the ... ad : therefore four times the rectangle ab , bc , together with the square of ac , is equal to the square of a d ...
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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