The Elements of Euclid |
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Página 45
F a ftraight line be divided into any two parts , the rectangle contained by the whole and one of the parts , is equal to the rectangle contained by the two parts , together with the square of the forefaid part .
F a ftraight line be divided into any two parts , the rectangle contained by the whole and one of the parts , is equal to the rectangle contained by the two parts , together with the square of the forefaid part .
Página 159
To divide a given ftraight line fimilarly to a given divided straight line , that is , into parts that shall have the fame ratios to one another which the parts of the divided given straight line have . Let AB be the straight line given ...
To divide a given ftraight line fimilarly to a given divided straight line , that is , into parts that shall have the fame ratios to one another which the parts of the divided given straight line have . Let AB be the straight line given ...
Página 252
IF there be two pyramids of the fame altitude , upon triangular bafes , and each of them be divided into two equal pyramids fimilar to the whole pyramid , and alfo into two equal prifms ; and if each of these pyra- mids be divided in ...
IF there be two pyramids of the fame altitude , upon triangular bafes , and each of them be divided into two equal pyramids fimilar to the whole pyramid , and alfo into two equal prifms ; and if each of these pyra- mids be divided in ...
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added alfo alſo altitude angle ABC angle BAC bafe baſe becauſe bifected Book Book XI circle circle ABCD circumference common cone cylinder defcribed Definition demonftrated diameter divided double draw drawn equal equal angles equiangular equimultiples excefs fame fame multiple fecond fegment fhall fhewn fides fimilar firft firſt folid folid angle fore four fourth fquare fquare of BC ftraight line given angle given ftraight line given in fpecies given in pofition given magnitude given ratio greater Greek half join lefs magnitude manner meet oppofite parallel parallelogram perpendicular plane produced PROP Propofition proportionals pyramid reafon rectangle remaining right angles ſphere taken THEOR theſe third thro triangle ABC wherefore whole