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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 ... - Page 83
by Dennis M'Curdy - 1846 - 138 pages

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

Euclid - Geometry - 1810 - 518 pages
...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) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 722 pages
...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 pages
...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) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 740 pages
...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 pages
...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 ...

Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...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 ...

Rev. John Allen - Astronomy - 1822 - 508 pages
...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 ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...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...