Books Books 21 - 30 of 95 on The first of four magnitudes is said to have the same ratio to the second, which.... 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... A system of practical mathematics; being no.xvi. of a new series of school-books - Page 111
1845 ## The mechanical Euclid, containing the elements of mechanics and hydrostatics

William Whewell - 1837
...GEOMETRY. ELEMENTS or GEOMETRY. EUCLID, Books *i, *II, *III, IV. Book v. *Definition of Proportion. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when^ — any eq'wi-multiples whatsoever of the Jirst and third... ## Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...ratio that the third has to the fourth. 11. Magnitudes are said to be proportionals, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth, and so on, whatever... ## The Principles and Practice of Arithmetic: Comprising the Nature and Use of ...

John Hind - Arithmetic - 1840 - 224 pages
...in iheJifth Book of Euclid's Elements, that " Proportion is the Similitude of Ratios; and theJirst of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatever of the^rst and third being taken,... ## The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Ratio and proportion - 1841 - 98 pages
...of the four magnitudes, taken in the same manner. Euclid expresses this definition as follows : — 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,... ## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...mutual relation of two magnitudes of the " same kind to one another, in respect of quantity." IV. V. 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,... ## Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...the ratio of the third to the fourth. Definition of proportion according to Euclid, (Def. V., Book " 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... ## The principles of arithmetic. [Followed by] The principles of algebra

Wales Christopher Hotson - 1842
...:: a + c + e ... : 6 + d +/... 149. Geometrical Definition of Proportion. (Euclid, book v. def. 5). 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,... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...multiple of the third, when divided by the fourth, the four magnitudes are proportionals, or the first has the same ratio to the second that the third has to the fourth. We are now arrived very nearly at Euclid's definition ; for, let A, B, C, D be four proportionals,... ## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. V. 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,... 