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" 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 ... - Σελίδα 156
των Euclides - 1861
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 σελίδες
...permutation, or alternately; this word is used when there are four proportionals, and it is See N. inferred, that the first has the same ratio to the...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,...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 σελίδες
...XIV. 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. 16th of this book. XV. Invertendo, by inversion : when there are four proportionals, and...

Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 493 σελίδες
...products AD and BC still obtains. PROP. VIII. THEOR. Numbers are likewise proportional by alternation, or the first is to the third as the second to the fourth. Let A: B : : C : 1); then alternately A : C : : B : D. !For the extreme terms are here still retained,...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 σελίδες
...Permutando, or alternando, by premutation, or alternately; this See Note, word is used when there are four proportionals, and it is inferred, that the first...or that the first is to the third, as the second to |he fourth: as is shown in the 16th prop. of this sth book. XIV. luvertendo, by inversion: when there...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813
...or alternando, by permutation, or alternately; this word is ч-ed when there are four proportional*, and it is inferred, that the first has the same ratio to the third, « hicli the •econd has to the fourth; or that the first is to the third, as the second to the fourth:...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...alternando, by permutation, or alternately. This word is used when there are four proportionals, and See N. it is inferred, that the first has the same ratio...to the fourth; or that the first is to the third, us the second to the fourth : As is shown in the ICth prop. of this 5th book. XIV. Invertendo, by inversion...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 σελίδες
...Permutando, or alternando, by permutation, or alternately. gee N. 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,...

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 σελίδες
...XIV. 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. XV. Invertendo, by inversion : When there are four proportionals, and...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 516 σελίδες
...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,...

The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821
...alternando ; when it is concluded, that if there be four magnitudes of the same kind proportionals, the first is to the third as the second to the fourth. Note. In this the antecedents are compared with one another, and the consequents with one another;...




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