Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple... "
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... - Page 458
by Sir John Leslie - 1809 - 493 pages
Full view - About this book

Elementary Algebra

James Hamblin Smith - 1870 - 452 pages
...representing the ratios must be equal. Euclid's test is given in Book v. Def. 5, where it stands thus: " The first of four magnitudes is said to have the same...equimultiples whatsoever of the first and third being takeu and any equimultiples whatsoever of the second and fourth : " If the multiple of the first be...
Full view - About this book

Elementary algebra

James Hamblin Smith - 1872 - 454 pages
...representing the ratios must be equal. Euclid-s test is given in Book v. Def. 5, where it stands thus: " The first of four magnitudes is said to have the same...whatsoever of the first and third being taken and auy equimultiples whatsoever of the second and fourth : " If the multiple of the first be less than...
Full view - About this book

Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 pages
...only one hitherto devised that applies equally to commensurable and incommensurable quantities ; " the first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equi-multiples whatsoever of the first and third being taken,...
Full view - About this book

Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - 1874 - 80 pages
...third is also greater than that of the fourth. The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have the same...the second which the third has to the fourth, when the first is the same multiple, part, or fraction of the second which the third is of the fourth '...
Full view - About this book

Euclid, book v. proved algebraically, so far as it relates to commensurable ...

Charles Lutwidge Dodgson - 1874 - 96 pages
...third is also greater than that of the fourth. The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have the same...the second which the third has to the fourth, when the first is the same multiple, part, or fraction of the second which the third is of the fourth '...
Full view - About this book

Euclidian Geometry

Francis Cuthbertson - 1874 - 400 pages
...be compared with one which differs from the latter by less than any assignable quantity. DEFINITION. The first of four magnitudes is said to have the same...the second which the third has to the fourth when, if the first be divided into any number whatever of equal parts and the third be divided into the same...
Full view - About this book

The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...ratio to the second, than the fifth has to the sixth. PROPOSITION 14.— Theorem. If the first has the same ratio to the second which the third has to the fourth ; then, if the first be greater than the third, the second shall be greater than the fourth ; ana if...
Full view - About this book

The elementary geometry of the right line and circle

William Alexander Willock - 1875 - 196 pages
...OAv OB, be proportional, and the following statement hold good:— If there be four magnitudes, and any equimultiples whatsoever of the first and third...being taken, and any equimultiples whatsoever of the second and fourth being taken, if the equimultiples of the first and third together exceed, or are...
Full view - About this book

The Elements of Euclid, with Many Additional Propositions and Explanatory ...

Euclid - 1876 - 240 pages
...Or, to bring it still nearer to the language of Euclid's definition: — The first of four magnitades is said to have the same ratio to the second, which...equimultiples whatsoever of the first and third being taken, the second is contained as often in the equimultiple of the first, as the fourth is contained in the...
Full view - About this book

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 446 pages
...any integers, m,*l. mA. or m/ll : na, : : m/f, : na,. That i«, if the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the game ratio to any equimultiples...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF