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" IF the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second; the third is the same multiple, or the same part of the fourth... "
The First Six Books of the Elements of Euclid, with a Commentary and ... - Σελίδα 107
των Euclid, Dionysius Lardner - 1828 - 324 σελίδες
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 σελίδες
...taken separately, be proportionals, see N. they shall also be proportionals when taken joindy, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth....

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 σελίδες
...magnitudes, taken separately, be proportionals, they will also be proportionals when taken jointly, that is, if the first be to the second as the third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth....

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813
...taken separately, he proportionals, they shall also be proportionals, when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall he to the second, as the third and fourth together to the fourth....

Easy Introduction to Mathematics, Τόμος 1

Charles Butler - 1814
...one or two more particulars will require an explanation. If four numbers are proportionals, that is, if the first be to the second as the third to the fourth, then will the first be to the third аз the second to the fourth; and this accounts for the usual...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...is to B, as C is to D: Therefore, if the first be the same multiple, A. &c. QED CD H PROP. D. THEOR. IF the first be to the second as the third to the s«- N. fourth, and if the first be a multiple or part of the second ; the third is the same multiple,...

A Philosophical and Mathematical Dictionary: Containing an ..., Τόμος 2

Charles Hutton - 1815 - 628 σελίδες
...equal to the fourth; if greater, greater; if less, less." " Prop. 2. If the first df four magnitudes be to the second as the third to the fourth, and if any equimultiples whatever of the first and third be taken, and also any equimultiples of the second...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 σελίδες
...is to B, as C is to D : Therefore, if the first be the same multiple, A. &c. QED CI) PROP. D. THEOR. IF the first be to the second as the third to the See N. fourth, and if the first be a multiple or part of the second ; the third is the same multiple,...

An Elementary Treatise on Algebra

Bewick Bridge - 1818 - 227 σελίδες
...с : b : d, and b : d :; a.: c. cd cd, с а Тн. 5. "If there be six proportional quantities, and the " first be to the second as the third to the fourth ; and the third " to the fourth as the fifth to the sixth ; then will the first " be to the second as the...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 σελίδες
...demonstrated, A : C : : B : D, and inversely (A. 5.) C : A : : D : B. Therefore, &c. q. ED PROP. C. THEOE. If the first be to the second as the third to the fourth ; and if the first be a multiple or a part of the second, ihe third is the same multiple or the same part of the fourth. Let A : B : :...

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 σελίδες
...magnitudes, taken separately, be proportionals, they will also be proportionals -when taken jointly, that is, if the first be to the second as the third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth....




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