The Elements of Euclid |
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Página 292
B. 1 . this part must therefore have been added to Prop . 5. upon account of fome Propofition betwixt the 5. and 13. but none of these stand in need of it , except the 7. Propofition , on account of which it has been added . befides the ...
B. 1 . this part must therefore have been added to Prop . 5. upon account of fome Propofition betwixt the 5. and 13. but none of these stand in need of it , except the 7. Propofition , on account of which it has been added . befides the ...
Página 361
The limitation within the inverted commas is not in the Greek text , but is now neceffarily added ; and the fame must be under- ftood in all the Propofitions of the Book which depend upon this fecond Propofition , where it is not ...
The limitation within the inverted commas is not in the Greek text , but is now neceffarily added ; and the fame must be under- ftood in all the Propofitions of the Book which depend upon this fecond Propofition , where it is not ...
Página 3
THE fum and difference of two magnitudes being given , to find them . TH given , Half the given fum added to half the given difference , will be the greater , and half the difference fubtracted from half the fum , will be the lefs .
THE fum and difference of two magnitudes being given , to find them . TH given , Half the given fum added to half the given difference , will be the greater , and half the difference fubtracted from half the fum , will be the lefs .
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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