 | Euclid - 1835 - 540 pages
...« here applied to two.' QED PROP. II. THEOR. //' the first magnitude be the same multiple of tlie second that the third is of the fourth, and the fifth...the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second, that the third together... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...holds in any number of magnitudes, which v— ~v-^ ' here applied to two.' QED PROP. II. THEOR. Jf the first magnitude be the same multiple of the second...of the fourth, and the fifth the same multiple of tJie second that the sixth is of the fourth ; then shall the first together with the fifth be the same... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...hold, if the number of magnitudes were greater than two. Therefore, if any number, &c. PROP. II. THEOR. IF the first magnitude be the same multiple of the...the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second, that the third together... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...demonstration holds in any number of ' magnitudes which was here applied to two.' QED PROP. II. THEOR. D IF the first magnitude be the same multiple of the...of the second that the sixth is of the fourth; then shall the first together with the fifth be the same multiple of the second, that the third together... | |
 | Euclid - Geometry - 1838 - 470 pages
...demonstration holds in any number of ' magnitudes which was here applied to two.' QED PROP. II. THEOR. Ir the first magnitude be the same multiple of the second...the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second, that the third together... | |
 | Oliver Byrne - Mathematics - 1841 - 140 pages
...the same multiple of а + t, + c + d + , &f., that m а is of а, т b is of b, &c. PROP. II. THEO. If the first magnitude be the same multiple of the...of the second that the sixth is of the fourth, then shall the first, together with the fifth, be the same multiple of the second that the third, together... | |
 | Euclides - Geometry - 1841 - 378 pages
...demonstration holds in any number of mag' nitudes, which was here applied to two.' QED PROP. II. THEOR. If the first magnitude be the same multiple of the...the same multiple of the second that the sixth is ofthefowth; then shall the first together with the fifth be the same multiple of the second, that the... | |
 | Oliver Byrne - Mathematics - 1841 - 144 pages
...the third and sixth together, is of b the fourth. PROP. III. THEO. If the first of four magnitudes be the same multiple of the second that the third is of the fourth, and if any equimultiples whatever of the first and third be taken, those shall be equimultiples ; one of... | |
 | Philip Kelland - Algebra - 1843 - 168 pages
...propositions are omitted in the Fifth Element ; such as " four magnitudes are proportional when the first is the same multiple of the second that the third is of the fourth."* Truths of this kind are clear by their own light from the arithmetical notion of proportion, but are... | |
 | Euclid - Geometry - 1845 - 218 pages
...demonstration holds in any number of magnitudes, which was here applied to two.' QED PROPOSITION II. THEOB. — If the first magnitude be the same multiple of the...the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second, that the third together... | |
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If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; then shall... 
