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" IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Σελίδα 83
των Dennis M'Curdy - 1846 - 138 σελίδες
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 σελίδες
...Therefore, if there be three, &c. QED Beis to B : but A is A D B E C F A D B E PROP. XXII. THEOR. seeNote. IF there be any number of magnitudes, and as many others, which, takcn two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes...

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

John Mason Good - 1813
...fourth shall be greater than the sixth; and if equal, equal; and if less, less. Prop. XXII. Theor. If there be any number of magnitudes, and as many...which, taken two and two in order, have the same ratio; the first shall have to the last of the first magnitudes the «ame ratio which the first of the others...

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

Euclides - 1816 - 528 σελίδες
...Boon V. ,. • I ' -I . . * " / ' . t . •>!« ' . l:i •! : . I. I .1 * . PROP. XXIII. THEOR. SeeN. IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same...

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

John Mason Good - 1819
...fourth shall be greater than the sixth ; and if equal, equal ; and if less, less. Prop. XXII. Theor. If there be any number of magnitudes, and as many others, which, taken two and t«m in order, have the same ratio ; the first shall have to the last of the flrst magnitudes the same...

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

John Playfair - 1819 - 317 σελίδες
...sited by the words'' ex sequali," or " A, D, B, E, c, F. A, E, B, F, c, D, H. G, PROP. XXIII. THEOR. If there be any number of magnitudes, and as many others, which, taken twoand two, in a cross order, have the same ratio ; the first will have to the last of the first magnitudes...

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

John Playfair - 1819 - 333 σελίδες
...words " ex xquali," or " ex xquo." A, D, B, c, i E, F. A, B, F, c, D, H. E, G, PROP. XXIII. THEOR. Tf there be any number of magnitudes, and as many others, which, taken twoand two, in a cross order, have the same ratio ; the first will have to the last of the first magnitudes...

Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - 494 σελίδες
...that, if A be equal to Ci D is equal to F; and if Jess, less. ' 20 ••• .-/' PROP. XXII. THEOR. If there be any number of magnitudes, and as many others, which, taken two and two in order, are in the same ratio ; by ordinate equality, the ratio of the first, of the Jlrst magnitudes, to the...

Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - 494 σελίδες
...of A to B and of D to E being equal (Hyp.), A is to G, as D is to H (22. 5). PROP. XXIII. THEOR. ff there be any number of magnitudes, and as many others, which, taken two and two in perturbate order, are in the same ratio ; the ratio of the first, of tiie first magnitudes, to the...

The First Six Books with Notes

Euclid - 1822 - 179 σελίδες
...(i)JPrep£6. bate (1), and therefore if a be greater than c, d greater than/(2). PROP. XXXVIII. THEOR. If there be any number of magnitudes, and as many others, which taken two by two are in the same ratio but perturbate, they are ex aequali in the same ratio. First, let there...

An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...of the proposition may be shown, whatever be the number of magnitudes. QED 3«J PROP. XXIII. THEOR. If there be any number of magnitudes, and as many others, which, taken two and two in a cross order, have the same ratio ; the 6rst shall have to the last of the first magnitudes the same...




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