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The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Elements of Geometry - Page 136
by George Albert Wentworth - 1881 - 250 pages

## The elementary geometry of the right line and circle

William Alexander Willock - Circle - 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...equimultiples whatsoever of the second and fourth being taken, if the equimultiples of the first and third together exceed, or are equal to, or are less...

## 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...

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

Robert Potts - Geometry - 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...

## Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 452 pages
...into three, and also into five equal parts. 6. When is the first of four magnitudes said to have the the same ratio to the second which the third has to the fourth ? Prove that triangles which have the same altitude are to one another as their bases. Show also that...

## The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 pages
...two magnitudes of the same kind to one another, in respect of quantity, is called their ratio. XXX. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fouitl', when any equimultiples whatsoever of the first and third i being taken, ai;d any equimultiples...

## First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879 - 414 pages
...rectilineal figures. Explain homologous, alternando, ex sequali. When is the first of four magnitudes said to have the same ratio to the second which the third has to the fourth ? 7. In a right angled triangle, if a perpendicular be drawn from the right angle to the base, the...

## Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880 - 68 pages
...triangle, pentagon, and hexagon. 7. Give Euclid's definition of ratio. When is the first of four magnitudes said to have the same ratio to the second which the third has to the fourth ? 8. The sides about the equal angles of equiangular triangles are proportional. If a straight line...

## The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...together. [V. Definition 5. Wherefore, if any number &c. Q.EJ>. PROPOSITION 13. THEOREM. If the first have the same ratio to the second which the third has to the fourth, but the third to the fourth a greater ratio than the fifth to the si.cth, thefirst shall have to ths...