The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 49
... rectangle , is said to be contained by any two of the straight lines which contain one of the right angles . II . A E In every parallelogram , any of the parallelo- grams about a diameter , together with the two com- plements , is ...
... rectangle , is said to be contained by any two of the straight lines which contain one of the right angles . II . A E In every parallelogram , any of the parallelo- grams about a diameter , together with the two com- plements , is ...
Page 50
... contained by the two straight lines , is equal to the rectangles contained by the undivided line , and the several ... rectangle contained by the straight lines A , BC shall be equal to the rectangle contained by A , BD , together with ...
... contained by the two straight lines , is equal to the rectangles contained by the undivided line , and the several ... rectangle contained by the straight lines A , BC shall be equal to the rectangle contained by A , BD , together with ...
Page 51
... rectangle contained by BA , for it is contained by DA , AC , of which AD is equal to AB ; and CE is contained by † 30 Def . AB , BC , for BE is equal to AB : therefore the rectangle contained by AB , AC , together with the rectangle AB ...
... rectangle contained by BA , for it is contained by DA , AC , of which AD is equal to AB ; and CE is contained by † 30 Def . AB , BC , for BE is equal to AB : therefore the rectangle contained by AB , AC , together with the rectangle AB ...
Page 52
... contained by AC , CB , for CD is equal to CB ; and DB is the square of BC : therefore the rectangle AB , BC is equal to the rectangle AC , CB , together with the square of BC . If therefore a straight line , & c . Q. E. D. PROP . IV ...
... contained by AC , CB , for CD is equal to CB ; and DB is the square of BC : therefore the rectangle AB , BC is equal to the rectangle AC , CB , together with the square of BC . If therefore a straight line , & c . Q. E. D. PROP . IV ...
Page 53
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal + + 30Def . to the rectangle AC , CB ; wherefore AG , GE are + 1ax . equal to twice the rectangle AC , CB ; and HF , CK are the squares of AC , CB ...
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal + + 30Def . to the rectangle AC , CB ; wherefore AG , GE are + 1ax . equal to twice the rectangle AC , CB ; and HF , CK are the squares of AC , CB ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole