Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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Second Book. </
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<
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>You muſt alſo know, that the point F which divi
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deth the Tangent E B in the middle, will many other times fall
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above the point A, and once alſo in the ſaid A: In which caſes it is
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evident of it ſelf, that the third proportional to the half of the Tan
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gent, and to B I (which giveth the Sublimity) is all above A. </
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<
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>But
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the Author hath taken a Caſe in which it was not manifeſt that the
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ſaid third Proportional is alwaies greater than F A: and which
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therefore being ſet off above the point F paſſeth beyond the Paral
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lel A G. </
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<
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>Now let us proceed.</
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It will not be unprofitable if by help of this Table we compoſe ano
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ther, ſhewing the Altitudes of the ſame Semiparabola's of Projects of
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the ſame
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Impetus.
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And the Conſtruction of it is in this manner.
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>PROBL. VI. PROP. XIII.</
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>From the given Amplitudes of Semiparabola's in
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the following Table ſet down, keeping the
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common
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Impeius
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with which every one of
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them is deſcribed, to compute the Altitudes of
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each ſeveral Semiparabola.</
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Let the Amplitude given be B C, and of the
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Impetus,
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which is
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ſuppoſed to be alwaies the ſame, let the Meaſure be O B, to wit,
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the Aggregate of the Altitude and Sublimity. </
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>The ſaid Altitude
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is required to be found and diſtinguiſhed. </
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>Which ſhall then be done when
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B O is ſo divided as that the Rectangle contained under its parts is
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equal to the Square of half the Amplitude B C. </
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<
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>Let that ſame divi
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ſion fall in F; and let both O B and B C be cut in the midſt at D and I.
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The Square I B, therefore, is equal to the
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Rectangle B F O: And the Square D O is
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equal to the ſame Rectangle together with the
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Square F D. </
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>If therefore from the Square
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D O we deduct the Square B I, which is equal
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to the Rectangle B F O, there ſhall remain
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the Square F D; to whoſe Side D F, B D be
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ing added it ſhall give the deſired Altitude
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Altitude B F. </
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>And it is thus compounded
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ex datis.
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From half of the Square B O known
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ſubſtract the Square B I alſo known, of the remainder take the Square
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Root, to which add D B known; and you ſhall have the Altitude ſought
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B F. </
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>For example. </
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>The Altitude of the Parabola deſcribed at the
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Elevation of 55 degrees is to be found. </
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>The Amplitude, by the follow
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ing Table is 9396, its half is 4698, the Square of that is 22071204,
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