The Elements of Euclid |
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Side 120
m AK Book V , multiple of CF , that AB is of CD ; therefore EB is the same mul . t
iple of FD , that AB is of CD . Therefore if one magnitude , & c . Q . E . D . PROP .
VI . THEOR . See N . TF two magnitudes be equimultiples of two others , and if ...
m AK Book V , multiple of CF , that AB is of CD ; therefore EB is the same mul . t
iple of FD , that AB is of CD . Therefore if one magnitude , & c . Q . E . D . PROP .
VI . THEOR . See N . TF two magnitudes be equimultiples of two others , and if ...
Side 312
Book v . had to C , the fame ratio that B has to C , then if any equimultiples
whatever of A and B be taken , and any multiple whatever of C ; if the multiple of
A be greater than the multiple of C , then , by the 5 . Def . of B . 5 . the multiple of B
is ...
Book v . had to C , the fame ratio that B has to C , then if any equimultiples
whatever of A and B be taken , and any multiple whatever of C ; if the multiple of
A be greater than the multiple of C , then , by the 5 . Def . of B . 5 . the multiple of B
is ...
Side 313
If A have to C a greater ratio than B to C , and if of A and B there be taken certain
equimultiples , and some multiple of C , then if the multiple of B be greater than
the multiple of C , the multiple of A is also greater than the same , is thus demon ...
If A have to C a greater ratio than B to C , and if of A and B there be taken certain
equimultiples , and some multiple of C , then if the multiple of B be greater than
the multiple of C , the multiple of A is also greater than the same , is thus demon ...
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added alſo altitude angle ABC angle BAC baſe becauſe Book caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet multiple muſt oppoſite parallel parallelogram perpendicular plane produced PROP proportionals Propoſition pyramid reaſon rectangle remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid angle ſphere ſquare ſquare of AC taken theſe third thro triangle ABC wherefore whole