The Doctrine of Proportion Clearly Developed, On a Comprehensive, Original, And Very Easy System; Or, the Fifth book of Euclid Simplified
The Doctrine of Proportion Clearly Developed, On a Comprehensive, Original, And Very Easy System; Or, the Fifth book of Euclid Simplified
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In our eReader you can find the full English version of the book. Read The Doctrine of Proportion Clearly Developed, On a Comprehensive, Original, And Very Easy System; Or, the Fifth book of Euclid Simplified Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Doctrine of Proportion Clearly Developed, On a Comprehensive, Original, And Very Easy System; Or, the Fifth book of Euclid Simplified
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To quickly assess the difficulty of the text, read a short excerpt:
If the first has the same ratio, &c.
Let A : B t=z C : D.
If A cr> => or "3 C, then will B c-, zz, or -3 D.
First, let A c- C, then it is evident A B ==■ c B' but 4 = C C C B ' .-. C B c- CD, and .-. B r - D.
In the same way it may be readily shown, if A be 31 or -^ C, B will be 3: or -3 D.
Digitized by Google 41 PROP. XV. THEO.
Magnitudes have the same ratio to one another which their equimultiples have.
Let ^_) and [_J be two magnitudes ; then, O • D :• M' O : M' □• For o ^ D = o = n = 0''U} ...•'. = n:'-40 = 4Qa2B.v.).
And as the same reasoning is generally applicable, we have O^D*.: M'0:M'Q .*. Magnitudes have the same ratio, &c.
Let A and B be two numbers, and C and D equimultiples of them, A : B :: C : D.
Let C ^z n A and D zz: « B ; then it is evident that A : B I ! n A : n B> r A n A '^^ B = 7b • Digitized by Google 42 DEFINITION XIII.
The technical term permutando, or altemando, by permutation or alternately, 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 is to the fourth : as is shown in the following proposi- tion : — Let • : A : : O : A, by *' permuntando " or "altemando '* it is inferred • : O : I A : A.
What to read after The Doctrine of Proportion Clearly Developed, On a Comprehensive, Original, And Very Easy System; Or, the Fifth book of Euclid Simplified?
You can find similar books in the "Read Also" column, or choose other free books by Byrne, Oliver to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
If the first has the same ratio, &c.
Let A : B t=z C : D.
If A cr> => or "3 C, then will B c-, zz, or -3 D.
First, let A c- C, then it is evident A B ==■ c B' but 4 = C C C B ' .-. C B c- CD, and .-. B r - D.
In the same way it may be readily shown, if A be 31 or -^ C, B will be 3: or -3 D.
Digitized by Google 41 PROP. XV. THEO.
Magnitudes have the same ratio to one another which their equimultiples have.
Let ^_) and [_J be two magnitudes ; then, O • D :• M' O : M' □• For o ^ D = o = n = 0''U} ...•'. = n:'-40 = 4Qa2B.v.).
And as the same reasoning is generally applicable, we have O^D*.: M'0:M'Q .*. Magnitudes have the same ratio, &c.
Let A and B be two numbers, and C and D equimultiples of them, A : B :: C : D.
Let C ^z n A and D zz: « B ; then it is evident that A : B I ! n A : n B> r A n A '^^ B = 7b • Digitized by Google 42 DEFINITION XIII.
The technical term permutando, or altemando, by permutation or alternately, 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 is to the fourth : as is shown in the following proposi- tion : — Let • : A : : O : A, by *' permuntando " or "altemando '* it is inferred • : O : I A : A.
What to read after The Doctrine of Proportion Clearly Developed, On a Comprehensive, Original, And Very Easy System; Or, the Fifth book of Euclid Simplified?
You can find similar books in the "Read Also" column, or choose other free books by Byrne, Oliver to read onlineMoreLess
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