Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/314

 Page 287 TIF, which is also rectangular, there is known the angle F, taken by the parallax. Then note in some place apart the two angles IOT and IFT, and of them take the sines, which are here set down to them, as you seen. And because in the triangle IOT, the sine TI is 92276. of those parts, whereof the whole sine TO is 100000; and moreover in the triangle IFT, the sine TI is 582. of those parts, whereof the whole sine TF is 100000, to find how many TF is of those parts, whereof TO is 100000; we will say by the Rule of three: If TI be 582. TF is an 100000. but if T I were 92276. how much would T F be. Let us multiply 92276. by 100000. and the product will be 9227600000. and this must be divided by 582. and the quotient will be 15854982. and so many shall there be in TF of those parts, of which there are in TO an 100000. So that if it were required to know how many lines TO, are in TF, we would divide 15854982 by 100000. and there will come forth 158. and very near an half; and so many diameters shall be the distance of the star F, from the centre T, and to abreviate the operation, we seeing, that the product of the multiplication of 92276. by 100000, ought to be divided first by 582, and then the quotient of that division by 100000. we may without multiplying 92276. by 100000. and with one onely division of the sine 92276. by the sine 582. soon obtain the same solution, as may be seen there below; where 92276. divided by 582. giveth us the said 158 1/2, or thereabouts. Let us bear in mind therefore, that the onely division of the sine TI, as the sine of the angle TOI by the sine TI, as the sine of the angle IFT, giveth us the distance sought TF, in so many diameters TO.