fe ft

66

Chapter

IRSTr

Apollodor.I. ,. c. y.ic£t. 25.

CHECNOLOGY.

bable that fhe had it from the Argonauts, who a in their returnhome failed to that iiland, and made forne ftay there' with herfather. So then in the time of the Argonautic expedition, thecardina! points of the equinoxes and folftices were in the middles.of the conftella-tions of Aries, Cancer, Chelas, andCapricorn.

XXXI. I11 the end of the year of our Lord 1689 the ftar calledPrima Arietis was in v. 1 8°. 5 iA. oo"* with north latitude 7 0 .8'. 5 8". And the ftar called ultima cauda. Arietis was in 8. 19 0 .-3/. 42 ,v . with north latitude 2 0 . 34'. And the Colurus ALqui-nociioruni paffing through the point in the middle between thofetw-o ftars did then cut the ecliptic in L 6°. 44' ('): and by this

reckoning.

§ XXXI.

( r ) By my calculations in g.6°. 50'. 2p".

The principies, uport which the calculation is four.ded, are thefe: 1

Let Tf.c be an arc of the ecliptic, T being the equino&ial point at the end of the year ofour Lord i68g,

Let the point p be the place of the. firft ftar in Aries(7 of Bayer), and c the place of the laft in the tail prof Bayer). Imagine a great circle of the fphere drawnthrough p and c ; and bifeft the arc pg in h. Then is H-the middle point between p and c, through which theequinodtialcolure of the primitive fphere paffed. There-fore through h draw a great circle, ha, which may 1xnake an angle of 66°. 30'. with the ecliptic, the acuteangle looking eaftward. Then ha will be the equinoc-tial colure of .the primitive fphere, and A the equinoc-tial point of that fphere.

To find the diftance of- a from V, the equino&ial'point of the fphere of 1690 ; find n the pole of theecliptic : and through p, c, and h, draw circles of lati-tude, rip, nc, na, meeting the ecliptic in the pointsp, c, and'Z>. And from p and h draw ares of greatcircles, pb and hd, perpendicular to nec. Now the ares T/, Tf, are given; being the givenlongitudes of the ftars p and c, at the end of the year 1689. Therefore pc, the ditference ofthefe ares is given, and the angle pXlc, which is meafured by that given arc pc. But the arc np isgiven, being the complement of the given latitude p p, Therefore in the right-angled fphericaltriangle, PBn, the hypotenufe pn is given, and the angle pllp. Therefore both the legs, pb,m, will be given by trigonometry. But Np being given; fince nc is alfo given, being the com-plement of the given latitude c c; their difference, bc, is given. Therefore in the right-angledfpherical triangle, pec, the two legs, pb and bc, are given. Therefore the hypotenufe pc, andthe angle pcb will be given by trigonometry. But pc being given, its half, hc, will be given.Therefore in the right-angled fpherical triangle, hdc, the hypotenufe ch being given with theangle hcd ; the legs, hd, dc, will be given by trigonometry. But dc being given, fince nc isalfo given, their difference, I 1 d, is given. And in the right-angled fpherical triangle, Odh, thetwo fides, no, dh, being given ; the angle dHh and the hypotenufe riH will be given by trigo-nometry. But n» being given, its complement, h b, which is the latitude of the point h isgiven. And in the right-angled fpherical triangle h^a, the fide nb being given with the angleha b ; the fide />a will be given by trigonometry. But the arc is given, being the meafure ofthe given angle dIIh. Therefore the arc ca, the fum of ch and /ja, is given. But Tr is given.Therefore t a is given. E. I.

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