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" This word is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which the second has to the fourth ; or that the first is to the third as the second to the fourth : as is shown in Prop. "
The elements of plane geometry; or, The first six books of Euclid, ed. by W ... - Σελίδα 68
των Euclides - 1863
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John Radford YOUNG - 1855 - 218 σελίδες
...quantities of the same kind are in proportion, they are also in proportion when taken alternately ; that is, the first is to the third as the second to the fourth. Let a : b '.: c '. d, that is, •=•=-;. Multiply by -, then -=-;: that oa ' cca is, o : c '. '....

A Treatise on Elementary and Higher Algebra

Theodore Strong - 1859 - 570 σελίδες
...a proportion are all of the same kind, they will be proportional when taken alternately ; that is, the first is to the third as the second to the fourth. The same things being supposed ; since — = --., we shall OD have — = ^ or mA : nC : : mB : nD,...

The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 σελίδες
...permutation, or alternately ; this word is used when there are four proportionals, and it is inferred, that the first has the same ratio to the third, which...third, as the second to the fourth : as is shown in the 16th proposition of this book. 15. Invertendo, by inversion ; when there are four proportionals,...

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

Robert Potts - 1860 - 380 σελίδες
...permutation, or alternately. This words is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which...first is to the third as the second to the fourth : a» is shewn in Prop. XVI. of this Fifth Book. XIV. Invertendo, by inversion ; when there are four...

Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 σελίδες
...permutation, or alternately. This word is used when there are fpur proportionals, and it is inferred that the first has the same ratio to the third which...fourth ; as is shown in Prop. 16 of this fifth book. Thus, IfA:B = C:D, or 1:2 = 3:6; then alternando A: C = B : D; or 1:3 = 2:6. "Alternate ratio is the...

The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - 1862 - 104 σελίδες
...permutation or alternately. This word is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which...is to the third as the second to the fourth : as is shewn in Prop. xvi. of this fifth book. If a : Ъ ; ; с ; ¿/'permutando" or" alternando" a : с '...

The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 σελίδες
...permutation or alternately. This word is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which the second has to tho fourth ; or that the first is to the third as the second to the fourth : as is shewn in Prop. xvi....

The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 σελίδες
...permutation or alternately. This word is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which...as the second to the fourth : as is shown in Prop. xvi. of this Fifth Book. xrv. Invertendo, by inversion ; when there are four proportionals, and it...

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

Robert Potts - 1865 - 528 σελίδες
...permutation, or alternately. This word is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which...is to the third as the second to the fourth : as is shewn in Prop. xvi. of this Fifth Book. XTV. Invertendo, by inversion ; when there are four proportionals,...

A Dictionary of Science, Literature, & Art: Comprising the ..., Τόμος 1

William Thomas Brande, George William Cox - 1865 - 978 σελίδες
...the first of four lit? magnitudes be to the second as the third is to the fourth, then alternately the first is to the third as the second to the fourth. Alternation. A term formerly nsed for what is now called pcrnuttatitsn. [PERMCTV TIO3Î.] Althaea (Or....




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