Books Books 51 - 60 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 elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...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,... ## Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - Geometry - 1862 - 98 pages
...their homologous sides are proportional. 2. Magnitudes are called proportionals when the first has the same ratio to the second, that the third has to the fourth, the fifth to the sixth, etc. The first terms of the several equal ratios are called the antecedents,... ## The school edition. Euclid's Elements of geometry, the first six books, by R ...

Robert Potts - 1864
...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,... ## The college Euclid: comprising the first six and the parts of the eleventh ...

...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,... ## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...to G as J7 is to H. [V. Definition 5. Wherefore, if the first &c. QEB COROLLARY. Also if the first have the same ratio to the second that the third has to the fourth, then any equimultiples whatever of the first and third shall have the same ratio to the second and... ## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...greater ratio to the second than the fifth has to the sixth. PROPOSITION 14. THEOREM. If the first have the same ratio to the second that the third has to the fourth, then if the first be greater than the third the second shall be greater than the fourth; anil if equal,... ## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...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,... ## Practical Arithmetic: By Induction and Analysis

Joseph Ray - Arithmetic - 1857 - 320 pages
...PROPORTION. ART. 197. Proportion is an equality of ratios. Four numbers are proportional, when the first has the same ratio to the second that 'the third has to the fourth. REVIEW. — 194. How is a ratio affected by multiplying the consequent, or dividing the antecedent?... ## A Treatise on Elementary Algebra

1869
...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 ratio to the second which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken... 