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" Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth. "
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... - Page 155
by Sir John Leslie - 1809 - 493 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 pages
...5th book. XIV. Invertendo, by inversion ; when there are four proportionals, and it is inferred, that the second is to the first as the fourth to the third. Prop. B, book 5. XV. Componendo, by composition ; when there are four proportionals, and it is inferred,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 pages
...this book. XV. Invertendo, by inversion : when there are four proportionals, and it is inferred, that the second is to the first as the fourth to the third. Prop. A. book 5. XVI. Componendo, by composition : when there are four proportionals, and it is inferred,...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...Book V. 14. Invertendo, by inversion: when there are four proportionals, and it is inferred, tliat the se-cond is to the first, as the fourth to the third. Prop. B. Book V. 15. Componendo, by composition, »hen there are four proportional», and it is inferred,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...5th book. XIV. Invertendo by inversion ; when there are four proportionals, and it is inferred, that the second is to the first, as the fourth to the third. Prop. B. Book 5. XV. Componendo, by composition; when there are four proportionals, and it is ini'erred,...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...this Book. XV. Invertendo, by inversion : When there are four proportionals, and it is inferred, that the second is to the first, as the fourth to the third. Prop. A. Book 5. XVI. C.omponendo, by composition : When there are four proportionals, and it is inferred,...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ...

Sir John Leslie - 1820 - 488 pages
...by transposing or interchanging its extreme and mean terms.— On this principle are founded the twp following theorems. PROP. VII. THEOR. The terms of...consequently the same equality of products AD and BC (V. 2.) still obtains. PROP. VIII. THEOR. Numbers are proportional by alternation, or the first is...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ...

Sir John Leslie - 1820 - 482 pages
...following theorems. i > PROP. VII. THEOR. I f ! The terms of an analogy are proportional by inversiont or the second is to the first, as the fourth to the third,,. .. , ..i .,; .. ,,.', i , „ ..... .1. i Let A : B : : C : D ; then inversely B 1 A ': It) : (X For...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 pages
...the 5th Book. 15. By invertendo ; when it is concluded that if there be four magnitudes proportional, the second is to the first as the fourth to the third. Note. Here the antecedent is made consequent, and the consequent antecedent. If A : B : : C : D then...
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The First Six Books with Notes

Euclid - 1822 - 222 pages
...proved in Prop. 33. B. 5. 15. By inversion, when we inter that if there be four magnitudes proportional, the second is to the first as the fourth to the third. Prop. 20. 16. By composition, when we infer that if there be four magnitudes proportional, the sum...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 508 pages
...16 prop, of t.his book. 17- Inverting; when it is inferred, if four magnitudes be proportional, that the second is to the first, as the fourth to the third ; as is shewn in Thcor. 3 at 15th of this book18. Compounding; when it is inferred, if four magnitudes...
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