Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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which depart from two points marked upon another right line, are
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then wider above than below, when the angles included between
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them upon that right line are greater than two right angles; and
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if theſe angles ſhould be equal to two right angles, the lines would
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be parallels; but if they were leſs than two right angles, the lines
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would be concurrent, and being continued out would
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ly interſect the triangle.</
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<
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>SIMP. </
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>Without taking it upon truſt from you, I know the
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ſame; and am not ſo very naked of
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Geometry,
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as not to know a
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Propoſition, which I have had occaſion of reading very often in
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Ariſtotle,
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that is, that the three angles of all triangles are equall to
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two right angles: ſo that if I take in my Figure the triangle ABE,
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it being ſuppoſed that the line E A is right; I very well conceive,
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that its three angles A, E, B, are equal to two right angles; and
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that conſequently the two angles E and A are leſſe than two right
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angles, ſo much as is the angle B. </
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<
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>Whereupon widening the lines
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A B and E B (ſtill keeping them from moving out of the points A
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and E) untill that the angle conteined by them towards the parts
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B, diſappear, the two angles beneath ſhall be equal to two right
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angles, and thoſe lines ſhall be reduced to parallels: and if one
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ſhould proceed to enlarge them yet more, the angles at the points
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E and A would become greater than two right angles.</
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<
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>SALV. </
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<
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>You are an
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Archimedes,
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and have freed me from the
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expence of more words in declaring to you, that whenſoever the
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calculations make the two angles A and E to be greater than two
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right angles, the obſervations without more adoe will prove
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neous. </
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<
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>This is that which I had a deſire that you ſhould
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ly underſtand, and which I doubted that I was not able ſo to make
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out, as that a meer
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Peripatetick
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Philoſopher might attain to the
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certain knowledg thereof. </
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<
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>Now let us go on to what remains.
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>And re-aſſuming that which even now you granted me, namely,
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that the new ſtar could not poſſibly be in many places, but in one
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alone, when ever the ſupputations made upon the obſervations of
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theſe Aſtronomers do not aſſign it the ſame place, its neceſſary
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that it be an errour in the obſervations, that is, either in taking the
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altitudes of the pole, or in taking the elevations of the ſtar, or in
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the one or other working. </
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<
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>Now for that in the many workings
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made with the combinations two by two, there are very few of
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the obſervations that do agree to place the ſtar in the ſame
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tion; therefore theſe few onely may happily be the
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ous, but the others are all abſolutely falſe.</
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<
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>SAGR. </
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<
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>It will be neceſſary then to give more credit to theſe
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few alone, than to all the reſt together, and becauſe you ſay,
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that theſe which accord are very few, and I amongſt theſe 12,
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do find two that ſo accord, which both make the diſtance of the </
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