Books Books 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) cyclopædia, 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) cyclopædia, 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... ## The First Six Books with Notes

Euclid - 1822 - 179 pages
...(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... 