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 Βιβλία Βιβλία 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
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 σελίδες
...H. In the same manner is the demonstration extended to any number of magnitudes. 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 will have to the last of the first magnitudes the same... ## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 σελίδες
...last of the first magnitudes, the same ratio which the first of the others has to the last. XXIII. 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 will have to the last of the first magnitudes the same... ## The Element of Geometry

John Playfair - 1836 - 114 σελίδες
...therefore ^=^ , or A : B : : E : F. JJ r D r PROP. XVI. THEOR. If there be any number of quantities, and as many others, which taken two and two in order have the same ratio, the first shall have to the laist of the first quantities the same ratio which the first of the others... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 471 σελίδες
...: E, therefore, by the first case, since C^A, F^^D, that is, Therefore, &c. QED PROP. XXII. THEOR. If there be any number of magnitudes, and as many others, which, taken two and tico in order, have the same ratio ; the first will have to the last of tlie jirst magnitudes, the... ## Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...same manner is the demonstration extended to any number of magnitudes. PROPOSITION XXIII. THEOREM. 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... ## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 σελίδες
...the number of magnitudes. Therefore, if there be any number of magnitudes, &c. 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 has to the last of the first magnitudes the same ratio... ## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 σελίδες
...: A : : F : E, therefore, by this first case, since C 7 A, F 7 D, that is, D/F. PROP. XXII. THEOR. If there be any number of magnitudes, and as many others, which, taken two ana two in order, have the same ratio ; the first will have to the last of the first magnitudes, the... ## The Elements of Euclid

Euclid - 1838 - 416 σελίδες
...first ; and therefore D is less than F. Therefore, if there be three, &c. QED PROP. XXII. THEOR. Ir there be any number of magnitudes, and as many others,...which, taken two and two in 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... ## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 σελίδες
...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... ## Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...H. In the same manner is the demonstration extended to any number of magnitudes. PROP. XXIII. THEOR. If there be any number of magnitudes, and as many others, which, taken two and two, irregularly, have the same ratio ; the first will have to the last of the first series of magnitudes...