The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 127
... proportionals . N. B. When four mag- ' nitudes are proportionals , it is usually ex- pressed by saying , the first is to the second , 6 as the third to the fourth . ' 6 VII . When of the equimultiples of four magnitudes ( taken as in ...
... proportionals . N. B. When four mag- ' nitudes are proportionals , it is usually ex- pressed by saying , the first is to the second , 6 as the third to the fourth . ' 6 VII . When of the equimultiples of four magnitudes ( taken as in ...
Page 128
... proportionals , the first is said to have to the third the duplicate 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 ...
... proportionals , the first is said to have to the third the duplicate 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 ...
Page 129
... proportionals.❜ XIII . Permutando , or alternando , by permutation or alternately . This word is used when there are four proportionals , and it is inferred that the first has the same ratio to the third which the second has to the ...
... proportionals.❜ XIII . Permutando , or alternando , by permutation or alternately . This word is used when there are four proportionals , and it is inferred that the first has the same ratio to the third which the second has to the ...
Page 130
... proportionals , and it is inferred , that the first is to its excess above the second , as the third to its excess above the fourth . Prop . E. Book 5 . XVIII . Ex æquali ( sc . distantiâ ) , or ex æquo , from equa- lity of distance ...
... proportionals , and it is inferred , that the first is to its excess above the second , as the third to its excess above the fourth . Prop . E. Book 5 . XVIII . Ex æquali ( sc . distantiâ ) , or ex æquo , from equa- lity of distance ...
Page 138
... proportionals , they are proportionals also when taken inversely . Let A be to B , as C is to D : then also in- versely B shall be to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A and C any equimultiples ...
... proportionals , they are proportionals also when taken inversely . Let A be to B , as C is to D : then also in- versely B shall be to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A and C any equimultiples ...
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