Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/307

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Let us now see the ninth. Here is the chord, the sines and the Parallax which is 15 m. From whence the Authour calculates the distance of the star from the superficies of the Earth to be lesse than a ** Here the Latine version is erroneous, making it a fortieth part of, &c. seven and fortieth part of a semidiameter, but this is an errour in the calculation, for it cometh forth truly, as we shall see here below, more than a fifth: See here the quotient is 20/436, which is more than one fifth.

Angles	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$	BD	Chord	232
		BDC	Sine	39046
		BCD	Sine	436

That which the Authour presently after subjoyns in way of amending the observations, that is, that it sufficeth not to reduce the difference of Parallax, neither to a minute, nor yet to the eighth part of a minute is true. But I say, that neither will the tenth part of a minute reduce the height of the star to 32. semidiameters; for the sine of the tenth part of a minute, that is of six seconds, is 3; by which if we according to our Rule should divide 90. or we may say, if we should divide 9058672. by 300000. the quotient will be 30 58672/100000, that is little more than 30. semidiameters and an half.

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The tenth giveth the altitude of the star one fifth of a semidiameter, with these angles, sines, and Parallax, that is, 4 gr.

30