A Supplement to the Elements of EuclidJ. Deighton and Sons, Cambridge and G and W. B. Whittaker, Ave-Maria-Lane, 1819 - 410 sider |
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Resultat 1-5 av 15
Side 278
... magnitudes ; and since ( hyp . ) A > B , twice A > twice B ; .. ( hyp , and 5 def . 5. ) twice C > twice D ; .. C > D . In like manner it can be shewn , if A = B , that C = D ; and if A < B , that C < D. " PROP . II . 2. THEOREM . If ...
... magnitudes ; and since ( hyp . ) A > B , twice A > twice B ; .. ( hyp , and 5 def . 5. ) twice C > twice D ; .. C > D . In like manner it can be shewn , if A = B , that C = D ; and if A < B , that C < D. " PROP . II . 2. THEOREM . If ...
Side 279
... magnitudes be the same multiple of the second , or the same part of it , that the third is of the fourth , the first is to the second , as the third is to the fourth . First , let A = pB , and C = pD ; then A : B :: C : D . Let there be ...
... magnitudes be the same multiple of the second , or the same part of it , that the third is of the fourth , the first is to the second , as the third is to the fourth . First , let A = pB , and C = pD ; then A : B :: C : D . Let there be ...
Side 280
... magnitudes be a multiple , or a part , of the se- cond , the third is the same multiple , or the same part , of the fourth . If A : B :: C : D , and if A = pB , then C = pD . For ( hyp . and S. 3. 5. ) A : B :: pD : D ; and ( hyp . ) A ...
... magnitudes be a multiple , or a part , of the se- cond , the third is the same multiple , or the same part , of the fourth . If A : B :: C : D , and if A = pB , then C = pD . For ( hyp . and S. 3. 5. ) A : B :: pD : D ; and ( hyp . ) A ...
Side 281
... magnitudes have a greater ratio to the second than the third has to the fourth , the second shall have to the first ... magnitude such that ( E : B ) :: ( C : D ) ; and since ( hyp . ) ( A : B ELEMENTS OF EUCLID . 281.
... magnitudes have a greater ratio to the second than the third has to the fourth , the second shall have to the first ... magnitude such that ( E : B ) :: ( C : D ) ; and since ( hyp . ) ( A : B ELEMENTS OF EUCLID . 281.
Side 282
... magnitudes , of the same kind , have a greater ratio to the second than the third has to the fourth , the first shall have to the third a greater ratio than the second has to the fourth . If ( A : B ) be greater than ( C : D ) , then is ...
... magnitudes , of the same kind , have a greater ratio to the second than the third has to the fourth , the first shall have to the third a greater ratio than the second has to the fourth . If ( A : B ) be greater than ( C : D ) , then is ...
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Vanlige uttrykk og setninger
ABCD base BC bisect centre chord circle ABC circle described circumference constr decagon describe a circle describe the circle diameter distance divided double draw a straight draw E equi equiangular equilateral and equiangular F draw find a point finite straight line given circle given finite straight given point given ratio given square given straight line half hypotenuse inscribed isosceles less Let AB Let ABC lines be drawn magnitudes manifest manner meet the circumference number of equal number of sides parallel to BC parallelogram pass perimeter point G polygon PROBLEM produced PROP rectangle contained rectilineal figure remaining sides required to describe required to draw rhombus right angles segment semi-diameter straight line joining tangent THEOREM three given touch the circle trapezium vertex