The Elements of Euclid |
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the first and third have the fame ratio to the fecond and fourth . Book V. and in like manner the firft and the third have the fame ratio to any equimultiples whatever of the fecond and fourth . Let A the first have to B the fecond ...
the first and third have the fame ratio to the fecond and fourth . Book V. and in like manner the firft and the third have the fame ratio to any equimultiples whatever of the fecond and fourth . Let A the first have to B the fecond ...
Página 120
Book V. multiple of CF , that AB is of CD ; therefore EB is the fame mul tiple of FD , that AB is of CD . Therefore if one magnitude , & c . Q. E. D. See N. IF PROP . VI . THEOR . F two magnitudes be equimultiples of two others , and if ...
Book V. multiple of CF , that AB is of CD ; therefore EB is the fame mul tiple of FD , that AB is of CD . Therefore if one magnitude , & c . Q. E. D. See N. IF PROP . VI . THEOR . F two magnitudes be equimultiples of two others , and if ...
Página 123
D. THEO R. F the first be to the fecond as the third to the fourth , See N. and if the first be a multiple , or part of the fecond ; the third is the fame multiple , or the fame part of the fourth .
D. THEO R. F the first be to the fecond as the third to the fourth , See N. and if the first be a multiple , or part of the fecond ; the third is the fame multiple , or the fame part of the fourth .
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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