 | John Mason Good - 1819 - 800 σελίδες
...equal to these others, or equimultiples of them. Prop. A. Theor. If the first of four macnltudei has to the second the same ratio which the third has to the fourth; then, if the fine be greater than the second, the third is als» greater than the fointh; and, if equal, equal ;... | |
 | John Playfair - 1819 - 350 σελίδες
...; therefore (def 5. 5.) A : B : : A+C+E : B+D+F. Therefore, &c, QED PROP. XIII. THEOR. If thejlrst have to the second the same ratio which the third has to tht fourth, but the third to the fourth a greater ratio than the fifth has to the sixth ; the first... | |
 | Euclid, Robert Simson - 1821 - 514 σελίδες
...number of magnitudes. Therefore, if there be any number, &c. QED PROP. XXIV. THEOR. IF the first has to the second the same ratio which the third has to the fourth; and the fifth to the second, the same ratio which the sixth has to the fourth; the first and fifth... | |
 | Miles Bland - 1821 - 898 σελίδες
...three of which are in arithmetic and the last three in harmonic progression ; prove that the first has to the second the same ratio which the third has to the fourth. ч 18. The sum of three terms of an harmonic progression, whose first term is -, is = — ; determine... | |
 | James Ryan, Robert Adrain - 1824 - 542 σελίδες
...E : H. In like manner we may proceed for any number ot magnitudes. QED PROP. XXIV. If the first has to the second the same ratio which the third has to the fourth ; and the fifth to the se••ond the same ratio which the sixth has to the fourth ; the first and... | |
 | James Ryan - 1824 - 550 σελίδες
...H. In like manner we may proceed for any number of magnitudes. QED tt PROP. xxiv. I/ the first has to the second the same ratio which the third has to the fouttY\ -, *a& v\» fe.Wtv \x> V^^ wtcond the same ratio vrtucVi V\ia %vs.\Xx \\a& \» fourth; the... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...equimultiples of A, C, E, and L, •I, N equimultiples of B, D, F; if PROP. XIII. THEOR. If the ßrst has to the second the same ratio which the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the sixth ; the ßrst shall also... | |
 | Euclides - 1826 - 226 σελίδες
...the second a less ratio than the third has to the fourth." "Prop. i. If the first of four magnitudes have to the second the same ratio which the third has to the fourth; then, if the first be equal to the second, the third is equal to the fourth; if greater, greater; if less, less." Dr. Robertson... | |
 | Euclid - 1826 - 234 σελίδες
...then delivers the propositions, which are the following : "Prop. i. If the first of four magnitudes have to the second the same ratio which the third has to the fourth ; then, if the first be equal to the second, the third is equal to the fourth ; if greater, greater ; if less, less." " Prop.... | |
 | James Ryan - 1826 - 430 σελίδες
...: nA : : rB : nB. PROF. A. THEOR. If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then if the first be greater than the second, the third is also greater than the fourth ; if equal, equal ; and if less, less. DEMONSTRATION.... | |
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THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the... 
