SECTION XX. 801 I think there is no need to inform the reader that any part of the outward circle or meridian may be measured upon that scale of chords or quadrant, according to whose radius the whole analemma is drawn. As for the straight lines they are all tobe considered as sines ; those semidiameters which are drawn from the centre c to the circumference are so many whole lines of sines or 90 degrees to thecommon radius of the semicircle. But if you consider any whole diameter which passeth through the centre c, it is a line of versed sines, i. e. two lines of right sines joined at their begin- ning to the same common radius of the semicircle. If therefore you have a scale or line of sines at hand to the same radius of the circle, you may measure any part of those straight lines, setting one foot of the compasses in the centre e, and extending the other to the point proposed, then applying that extent to the beginning of the line of sines, and observing how far it reaches. But if you have no scale or line of sines at hand, you may find a quantity of any part of the semidiameter by the outward limb or semicircle, and by the scale of chords, accord- ing to whose radius the semicircle is drawn. The method of per- forming it see in figure xxv. where the quadrant y x b is drawn by the same radius as the semicircle in figure xxiv. But I choose to make it a distinct figure, lest the lines should interfere with one another and breed confusion ; and therefore in figure xxiv. I have used capital letters, in figure xxv. all the letters are small. Suppose I would find how many degrees are contained in v which is the sun's altitude at east or west. This is a part of the semidiameter e z : suppose therefore e z to be a whole line of sines, beginning to be numbered at c. Take the extent y c in your compasses, and carry oneleg up in the archy x till the other leg' will but just touch the diawetery b, and the leg of the coin- passes will rest at n ; wherefore it appears that c v in figure xxcv. is the sine of the archy n in figure xxv. or 21 degrees. Another way to perform it is this. Take the extent v c, set one leg of the compasses iny, and with that extent make a blind or obscure arch at e, and by the edge of that arch lay a rule from the centre b, and it will find the point n in the limb viz. 21 degrees. By the samepractice you may find the number of degrees contained in any part of those lines which are drawn from the centrec, viz. c n, c E, C M, e Z, c N, c o, all which are whole lines of sines to the common radius of the quadrant. But as for those lines in the analemma which are not drawn from the centre c, but are drawn across some other diameter and produced to the limb, such as the line 6 n, the line s w, the line r a, and the line s n, each of. these are, to be esteemed as a whole line of sines also, but to a less radius.
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