 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 ,fourth; or that the first is to the...  Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Page 156by Euclides - 1861Full view - About this book
 | Mathematics - 1836 - 488 pages
...15. Permutando, or alternando, by permutalion, or alternately ; this word is used when there are four proportionals, and it is inferred, that the first...first is to the third as the second to the fourth. 16. Invertendo, by inversion : when there are four proportionals, and it is inferred, that the second... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...above ART. is called INVERTENDO, or Inversion. ART. 171. In a series of four proportional right lines, the first is to the third as the second to the fourth. In the above diagram, AB is to EF as CD to GH. DEM. By ART. 100, the rectangle under AB and GH is equal... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...terms.' 14. Alternately : f this word is used when there are four proportionals of the same kind : and it is inferred, that the first has the same ratio...third, as the second to the fourth : as is shown in the 16th proposition of this book. 15. By inversion : when there are four proportionals, and it is... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...XIII. Permutando, or alternando, by permutation, or alternately ; this word is used when there are four proportionals, and it is inferred, that the first...third, as the second to the fourth; as is shown in the 16th prop, of this 5th book.* XIV. Invertendo, by inversion ; when there are four proportionals,... | |
 | Euclides - 1838 - 264 pages
...terms of a proportion are all of the same kind, they are proportional when taken ALTERNATELY, that is, the first is to the third as the second to the fourth. Let the proportion be A : B :: C : D; then also A : C :: B : D. For take mA, mB any equimultiples of... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...inversion, when the second is to the first as the fourth to the third ; (328.) By alternation, when the first is to the third as the second to the fourth ; (329.) By composition, when the sum of the first and second is to the second, as the sum of the third... | |
 | Euclides - Geometry - 1841 - 378 pages
...XIII. Permutando, or alternando, by permutation, or alternately. This word is used when there are four proportionals, and it is inferred, that the first...third, as the second to the fourth; as is shown in the 16th Prop, of this fifth Book. XIV. Invertendo, by inversion: when there are four proportionals,... | |
 | Oliver Byrne - Mathematics - 1841 - 140 pages
...technical term permutando, or alternando, by permutation or alternately, is used when there are four proportionals, and it is inferred that the first has...; or that the first is to the third as the second is to the fourth : as is shown in the following proposition : — Let • : A : : О : Д, by " permuntando... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...14. Permutando, or alternando, by permutation, or alternately ; this word is used when there are four proportionals, and it is inferred, that the first...first is to the third as the second to the fourth : See Prop. 16. of this Book. 15. Invertendo, by inversion : When there are four proportionals, and... | |
 | Euclides - 1845 - 546 pages
...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...as the second to the fourth : as is shown in Prop. xvi. of this fifth book. XIV. Invertendo, by inversion ; when there are four proportionals, and it... | |
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