1becauſe 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
midiameter A B is 100000. And to know how many
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
ber 347313294. divided by 58. giveth 5988160 1/4. as here you
may
gr.m.Its chord 8142 of thoſeAng. B A D440parts, whereof the ſemid.B D F9220A B is an 100000.B D C15445Sines42657B C D02585842657814281428531417062842657341256595834731329457155988160 1/4583473132945717941543equal 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
midiameter A B is 100000. And to know how many
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
ber 347313294. divided by 58. giveth 5988160 1/4. as here you
may
And this divided by 100000. the product is 59
1 |00000| 59 |88160.But we may much abbreviate the operation, dividing the firſt
quotient found, that is, 347313294. by the product of the
plication of the two numbers 58. and 100000. that
quotient found, that is, 347313294. by the product of the
plication of the two numbers 58. and 100000. that
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib