Galilei, Galileo
,
The systems of the world
,
1661
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T I F, which is alſo rectangular, there is known the angle F,
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ken by the parallax. </
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>Then note in ſome place apart the two
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gles I O T and I F T, and of them take the ſines, which are
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here ſet down to them, as you ſeen. </
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>And becauſe in the triangle
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I O T, the ſine T I is 92276. of thoſe parts, whereof the whole
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ſine TO is 100000; and moreover in the triangle I F T, the ſine T I
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is 582. of thoſe parts, whereof the whole ſine T F is 100000, to
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find how many T F is of thoſe parts, whereof T O is 100000;
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we will ſay by the Rule of three: If T I be 582. T F is an
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100000. but if T I were 92276. how much would T F be.
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<
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>Let us multiply 92276. by 100000. and the product will be
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9227600000. and this muſt be divided by 582. and the quotient
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will be 15854982. and ſo many ſhall there be in T F of thoſe
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parts, of which there are in T O an 100000. So that if it were
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required to know how many lines T O, are in T F, we would
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divide 15854982 by 100000. and there will come forth 158. and
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very near an half; and ſo many diameters ſhall be the diſtance
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of the ſtar F, from the centre T, and to abreviate the
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tion, we ſeeing, that the product of the multiplication of 92276.
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by 100000, ought to be divided firſt by 582, and then the
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tient of that diviſion by 100000. we may without multiplying
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92276. by 100000. and with one onely diviſion of the ſine
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92276. by the ſine 582. ſoon obtain the ſame ſolution, as may
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be ſeen there below; where 92276. divided by 582. giveth us the
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ſaid 158 1/2, or thereabouts. </
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<
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>Let us bear in mind therefore, that
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the onely diviſion of the ſine T I, as the ſine of the angle T O I
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by the ſine T I, as the ſine of the angle I F T, giveth us the
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ſtance ſought T F, in ſo many diameters T
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