Salusbury, Thomas Mathematical collections and translations 1667

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270
because the angle B A D, conteined between the vertical lines, is
equal to the difference of the Polar altitudes, it shall be 4gr. 40m.
which I note here apart; and I finde the chord of it by the Table
of Arches and Chords, and set it down neer unto it, which is 8142
parts, of which the semidiameter A B is 100000. Next, I finde
the angle B D C with ease, for the half of the angle B A D, which
is 2 gr. 20 m. added to a right angle, giveth the angle B D F 92 gr.
20 m. to which adding the angle C D F, which is the distance from
the vertical point of the greatest altitude of the Star, which here is
62 gr. 15 m. it giveth us the quantity of the angle B D C,
154 grad. 45 min. the which I set down together with its Sine,
taken out of the Table, which is 42657, and under this I note
the angle of the Parallax B C D 0 gr. 2 m. with its Sine 58.
And because in the Triangle B C D, the side D B is to the side
B C; as the sine of the opposite angle B C D, to the sine of the
opposite angle B D C: therefore, if the line B D were 58. B C
would be 42657. And because the Chord D B is 8142. of those
parts whereof the semidiameter B A is 100000. and we seek to
know how many of those parts is B C; therefore we will say, by
the Golden Rule, if when B D is 58. B G is 42657. in case the
said D B were 8142. how much would B C be? I multiply the
second term by the third, and the product is 347313294. which
ought to be divided by the first, namely, by 58. and the quotient
shall be the number of the parts of the line B C, whereof the se­
midiameter A B is 100000. And to know how many semidiame­
ters B A, the said line B C doth contein, it will be necessary anew
to divide the said quotient so found by 100000. and we shall have
the number os semidiameters conteined in B G. Now the num­
ber 347313294. divided by 58. giveth 5988160 1/4. as here you
may see.

And this divided by 100000. the product is 59 88160/100000

But we may much abbreviate the operation, dividing the first
quotient found, that is, 347313294. by the product of the multi­
plication of the two numbers 58. and 100000. that is,