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" THEOR. IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth... "
The First Six Books of the Elements of Euclid, with a Commentary and ... - Σελίδα 107
των Euclid, Dionysius Lardner - 1828 - 324 σελίδες
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 σελίδες
...Stc. PROP. C. THEOR. See N. IF the first be the same multiple of the second, or the same part of it, that the third is of the .fourth ; the first is to...the fourth. Let the first A be the same multiple of B the second, that C the-third is of the fourth D : A is to B as C is to D. Take of A and C any equimultiples...

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

John Playfair - 1806 - 311 σελίδες
...QED Bookv, PROP. B. THEOR. IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth, the first is to the second as the third to the fourth. First, if mA and mB be equimultiples of the magnitudes A and B, mA : A : : »iB : B....

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

Euclid - 1810 - 518 σελίδες
...PROP. C. THEOR. See Note. IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth; the first is to the second, as the third is to the fourth. A E Let the first A be the same multiple of B the second, that C the third is of the fourth D: A is...

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

John Mason Good - 1813
...inversely. Prop. C. Theor. If the first be the same multiple of the second, or the same part of it, that the third is of the fourth; the first is to the second, a* the third is to the fourth. Prop. D. Theor. If the fust be to the second as the third to the fourth,...

Easy Introduction to Mathematics, Τόμος 2

Charles Butler - 1814
...PROPORTION. 83. The foregoing articles treat of the properties of what is called DIRECT PROPORTION, where the first is to the second as the third is to the fourth ; but when the terms are so arranged, ' It must he understood, tbat what we have delivered on proportion,...

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

Euclides - 1816 - 528 σελίδες
...D H PROP. C. THEOR. Se«N. IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to...the fourth. Let the first A be the same multiple of B the second, that C the third is of the fourth D : A is to B as C is to D. Take of A and C any equimultiples...

A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - 410 σελίδες
...THEOREM. If the first of four magnitudes be the same multiple of the second, or the same part ofit, that the third is of the fourth, the first is to the second, as the third is to the fourth. First, let A •= pB, and C = pD ; then A : B :: C:D. Let there be taken of A and C any equi-multiples...

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

John Playfair - 1819 - 333 σελίδες
...&c. Q, ED PROP. B. THEOR. If the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second as the third to the fourth. First, if mA, mB be equimultiples of the magnitudes A and :B, mA : A : : mB : B. Take...

An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...: rB. QED PROr. C. THEOR. If the first be (lie same multiple of the second,' or the same part of it that the third is of the fourth ; the first is to the second as the third is to the fourth. DEMONSTRATION. t 1. Supposing m lo be any integer greater than unity, let w»A the lirst be the same...

An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...: rB. QED PROP. C. THEOfl. If the first be the satne multiple of the second, or 1he same part of it that the third is of the fourth ; the first is to. the second as the third is to the fourth. DEMONSTRATION. I. Supposing m to be any integer greater than unity, let mA the first be the same multiple...




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