Galilei, Galileo
,
The systems of the world
,
1661
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on upon the Earths motion; for from the Earth in A it ſhall be
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ſeen according to the ray A E, with the elevation of the angle
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E A C; but from the Earth placed in B, it ſhall be ſeen
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cording to the ray B E, with the elevation of the angle E B C,
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bigger than the other E A C, that being extern, and this
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tern and oppoſite in the triangle E A B, the diſtance therefore
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of the ſtar E from the Ecliptick, ſhall appear changed; and
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likewiſe its altitude in the Meridian ſhall become greater in the
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poſition B, than in the place A, according as the angle E B C
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exceeds the angle E A C, which exceſſe is the quantity of the
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angle A E B: For in the triangle E A B, the ſide A B being
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continued to C, the exteriour angle E B C (as being equal to
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the two interiour and oppoſite E and A) exceedeth the ſaid
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gle A, by the quantity of the angle
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E.
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And if we ſhould take
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another ſtar in the ſame Meridian, more remote from the
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ptick, as for inſtance the ſtar H, the diverſity in it ſhall be
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greater by being obſerved from the two ſtations A and B,
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ding as the angle A H B is greater than the other
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E
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; which
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gle ſhall encreaſe continually according as the obſerved ſtar ſhall
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be farther and farther from the Ecliptick, till that at laſt the
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greateſt mutation will appear in that ſtar that ſhould be placed in
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the very Pole of the Ecliptick. </
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<
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>As for a full underſtanding
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of we thus demonſtrate. </
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<
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>Suppoſe the diameter of the Grand
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Orb to be A B, whoſe centre [
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in the ſame Figure
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] is G, and
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let it be ſuppoſed to be continued out as far as the Starry Sphere
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in the points D and C, and from the centre G let there be erected
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the Axis of the Ecliptick G F, prolonged till it arrive at the ſaid
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Sphere, in which a Meridian D F C is ſuppoſed to be deſcribed,
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that ſhall be perpendicular to the Plane of the Ecliptick; and
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in the arch F C any points H and
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E,
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are imagined to be taken,
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as places of fixed ſtars: Let the lines F A, F B, A H, H G,
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H B, A
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E,
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G
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E,
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B
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E,
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be conjoyned. </
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<
s
>And let the angle of
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ference, or, if you will, the Parallax of the ſtar placed in the
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Pole F, be A F B, and let that of the ſtar placed in H, be the
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angle A H
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B,
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and let that of the ſtar in
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E,
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be the angle
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A
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E
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B. </
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<
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>I ſay, that the angle of difference of the Polar ſtar F, is
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the greateſt, and that of the reſt, thoſe that are nearer to the
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greateſt are bigger than the more remote; that is to ſay, that the
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angle F is bigger than the angle H, and this bigger than the angle
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<
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E.
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Now about the triangle F A B, let us ſuppoſe a circle to be
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ſcribed. </
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<
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>And becauſe the angle F is acute, (by reaſon that its baſe
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AB is leſſe than the diameter DC, of the ſemicircle D F C) it ſhall
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be placed in the greater portion of the circumſcribed circle cut
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by the baſe A B. </
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>
<
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>And becauſe the ſaid A B is divided in the
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midſt, and at right angles by F G, the centre of the </
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