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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: The Errors, by which Theon, Or Others, Have Long Ago ...

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...firft ; and therefore D is lefs than F. Therefore if there be three, &c. Q._E. D. PROP. XXII. THEOR, TF there be any number of magnitudes, and as many others, which taken two and two in order have the fame ratio ; the firft fhall have to the laft of the firft magnitudes the fame ratio which the firft...

## The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

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...Therefsre, i( there be any number, &c. Q^ED BC FG D. H. PROP. Book V. PROP. XXIII. THEO R. SeeK. TF there be any number of magnitudes, and as many others, which taken two and two, in a crofs order, have the fame ratio ; the firft mall have to the laft of the firft magnitudes the fame...

## The First Six Books: Together with the Eleventh and Twelfth

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...of magnitudes. Theiefore, if there be any number, &c. Q^ED K a P IUO P. v. PROP. XXIII. THEO R. K. IF there be any number of magnitudes, and as many others, which, taken two and two, in a crofs order, have the fame ratio ; the firft mail have to the laft of the firft magnitudes the fame...

## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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...if there be any number, &c. Q;_, ED • Book V. SeeN. a. if- Jkn ft 4ii. J. PROP. XXIII. THEO R. TF there be any number of magnitudes, and as many ,*, others, which, taken two and two, in a crofs order, have the fame ratio ; the firft lhall have to the laft of the firft magnitudes the fame...

## Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

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...the demonftration extended to any number of magnitudes. Therefore, Scc. Q^ ED PROP. XXIII. THEO R. IF there be any number of magnitudes, and as many others, which, taken two and two, in a crofs order, have the fame ratio; the firft (hall have to the laft of the firft magnitudes the fame...

## The Elements of Mathematical Analysis, Abridged: For the Use of Students ...

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...л . /Yj _ V -'HI ^n<^ ^° 4I>' v/batever be the number of magnitudes. PROPOSITION XXIIL— THEOREM. If there be any number of magnitudes, and as many others, which taken two and two inordinately, have the fame ratio ; then, by perturberate equality (Def. XX.), the firft mall have...

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

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...as E to H ; and fo on, whatever be the number of magnitudes. Wherefore, &c. Q^ED PROP. XXIII. THEOR. IF there be any number of magnitudes, and as many others, which, taken two and two, in a crofs order, have the fame ratio ; the firll mail have to the laft of the firft magnitudes the fame...

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

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...therefore, by the firft cafe, fince C > A, F > D, that is, D < F. Therefore. . f RO P. ^XXII. THEO R. IF there be any number of magnitudes, and as many...others, which, taken two and two in order, have the fame ratio ; the firft will have to the laft of the firft magnitudes, the fame ratio which the firft...

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

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...F>D, that is, D<F. Therefore, &c. QED But A : B : : : : D : E, and : E : De, and, PROP. XXII. THEOK. IF there be any number of magnitudes, and as many...which, taken two and two in order, have the same ratio ; the first will have to the last of the first magnitudes the same ratio which the first of the others...

## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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...whatever be the number of magnitudes. Therefore, if there be any number, &c. QED 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 first shall have to the last of the first magnitudes the same...