The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 34
... triangle have its exterior angle and one of its opposite interior angles ... twice the line joining the vertex and the middle of the base .. 21. Each ... rectangle are equal to one another . 25. If any number of parallelograms be ...
... triangle have its exterior angle and one of its opposite interior angles ... twice the line joining the vertex and the middle of the base .. 21. Each ... rectangle are equal to one another . 25. If any number of parallelograms be ...
Página 37
... twice the rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of ab is equal to the squares of ac , cb , and to twice the rectangle con- tained by ac , cb . Upon ab describe ( i ...
... twice the rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of ab is equal to the squares of ac , cb , and to twice the rectangle con- tained by ac , cb . Upon ab describe ( i ...
Página 39
... twice the rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of ab , bc are equal to twice the rectangle ab ...
... twice the rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of ab , bc are equal to twice the rectangle ab ...
Página 43
... rectangle cf , fa , together with the square of a e , is equal to f the squares of ba , ae : take away the square of ... twice the rectangle contained by the side upon which , when produced , the perpendicular falls , and the ...
... rectangle cf , fa , together with the square of a e , is equal to f the squares of ba , ae : take away the square of ... twice the rectangle contained by the side upon which , when produced , the perpendicular falls , and the ...
Página 44
... square of ac , opposite to the angle b , is less than the squares of cb , b , a , by twice the rectangle cb , bd . a First , let ad fall within the triangle abc ; and because the straight line cb is divided into two parts in the point d ...
... square of ac , opposite to the angle b , is less than the squares of cb , b , a , by twice the rectangle cb , bd . a First , let ad fall within the triangle abc ; and because the straight line cb is divided into two parts in the point d ...
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Términos y frases comunes
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