The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 126
... Ratio is a mutual relation of two magnitudes " of the same kind to one another , in respect " of quantity . " IV . Magnitudes are said to have a ratio to one an- other , when the less can be multiplied so as to exceed the other . V. The ...
... Ratio is a mutual relation of two magnitudes " of the same kind to one another , in respect " of quantity . " IV . Magnitudes are said to have a ratio to one an- other , when the less can be multiplied so as to exceed the other . V. The ...
Page 127
... ratio to the second , which the third has to the fourth , when any equimultiples what- soever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than ...
... ratio to the second , which the third has to the fourth , when any equimultiples what- soever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than ...
Page 128
... ratio of that which it has to the second . XI . When four magnitudes are continual propor- tionals , the first is said to have to the fourth the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c ...
... ratio of that which it has to the second . XI . When four magnitudes are continual propor- tionals , the first is said to have to the fourth the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c ...
Page 129
... ratio compounded of the ratios of E to F , G to H , and K to L. XII . In proportionals , the antecedent terms are called homologous to one another , as also the con- sequents to one another . ' Geometers make use of the following ...
... ratio compounded of the ratios of E to F , G to H , and K to L. XII . In proportionals , the antecedent terms are called homologous to one another , as also the con- sequents to one another . ' Geometers make use of the following ...
Page 134
... ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth , viz . the equimultiple of the first shall have the ...
... ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth , viz . the equimultiple of the first shall have the ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole